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Colloquia & Seminars


Current Seminars

  1. Graduate Student Seminar:

    Location: MSRI: Baker Board Room
    Speakers: Melvin Leok (University of California, San Diego)
    Updated on Sep 18, 2018 12:26 PM PDT
  2. Hamiltonian Seminar: Stability for PDEs, the Maslov Index, and Spatial Dynamics

    Location: MSRI: Simons Auditorium
    Speakers: Margaret Beck (Boston University)

    Understanding the stability of solutions to PDEs is important, because it is typically only stable solutions which are observable. For many PDEs in one spatial dimension, stability is well-understood, largely due to a formulation of the problem in terms of so-called spatial dynamics, where one views the single spatial variable as a time-like evolution variable. This allows for many powerful techniques from the theory of dynamical systems to be applied. In higher spatial dimensions, this perspective is not clearly applicable. In this talk, I will discuss recent work that suggests both that the Maslov index could be a important tool for understanding stability when the system has a symplectic structure, particularly in the multi-dimensional setting, and also suggests a possible analogue of spatial dynamics in the multi-dimensional setting.

    Updated on Sep 14, 2018 08:46 AM PDT

Upcoming Seminars

  1. Combinatorics Seminar: Near-Equality of Ribbon Schur Functions

    Location: UC Berkeley Math (Evans Hall 939)
    Speakers: Tom Foster (University of California, Berkeley)

    We consider the problem of when the difference of two ribbon Schur functions is a single Schur function. We prove that this near-equality phenomenon occurs in fourteen infinite families and we conjecture that these are the only possible cases. Towards this converse, we prove that under certain additional assumptions the only instances of near-equality are among our fourteen families. In particular, we prove that our first ten families are a complete classification of all cases where the difference of two ribbon Schur functions is a single Schur function whose corresponding partition has at most two parts at least 2. We also provide a framework for interpreting the remaining four families and we explore some ideas towards resolving our conjecture in general. We also determine some necessary conditions for the difference of two ribbon Schur functions to be Schur-positive.

    Updated on Sep 13, 2018 01:18 PM PDT
  2. Hamiltonian Colloquium: From Hamiltonian systems with infinitely many periodic orbits to pseudo-rotations via symplectic topology

    Location: MSRI: Simons Auditorium
    Speakers: Basak Gurel (University of Central Florida)

    Ever since the Conley-Zehnder proof of the Arnold conjecture for tori, the study of periodic orbits has arguably been the most important interface between Hamiltonian dynamical systems and symplectic topology. A general feature of Hamiltonian systems is that they tend to have numerous periodic orbits. In fact, for a broad class of closed symplectic manifolds, every Hamiltonian diffeomorphism has infinitely many simple periodic orbits.

    There are, however, notable exceptions. Namely, an important class of symplectic manifolds including the two-sphere admits Hamiltonian diffeomorphisms with finitely many periodic orbits — the so-called pseudo-rotations — which are of particular interest in dynamical systems. Furthermore, recent works by Bramham (in dimension two) and by Ginzburg and myself (in dimensions greater than two) show that one can obtain a lot of information about the dynamics of pseudo-rotations, going far beyond periodic orbits, via symplectic techniques.

    In this talk I will discuss various aspects of the existence question for periodic orbits of Hamiltonian systems, focusing on recent higher dimensional results about pseudo-rotations.

    Updated on Sep 20, 2018 02:36 PM PDT
  3. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:26 PM PDT
  4. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  5. Lunch with Hamilton: Topological dynamics in three-dimensional volume-preserving maps

    Location: MSRI: Baker Board Room
    Speakers: Kevin Mitchell (University of California, Merced)

    Symbolic dynamics, and the associated topological entropy, are well
    developed tools for analyzing two-dimensional area-preserving
    dynamics, such as arise in 2D symplectic maps and the chaotic mixing
    of 2D fluids.  For example, topological entropy has been useful in
    quantifying the mixing of fluids stirred by periodically braiding
    rods.  However, at present no analogous symbolic techniques exist for
    extracting topological dynamics from symplectic maps in higher
    dimensions.  Here, we address chaotic, volume-preserving maps in
    three-dimensions, which is a stepping stone to 4D symplectic maps and
    a system of intrinsic interest for mixing of 3D fluids.  We address
    this challenge using the topology of intersecting codimension-one
    stable and unstable manifolds.  This leads to a symbolic dynamics of
    2D surfaces based on homotopy theory.  This symbolic dynamics can be
    understood as resulting from stirring by loops that undergo a kind of
    3D braiding.  The resulting theory provides a rigorous lower bound on
    the growth rates of both two-dimensional surfaces and one-dimensional
    curves.  We illustrate our theory with a mathematical model of a
    chaotic ring vortex.  Finally, we will present results that hint at
    the presence of a subtle duality in the topological dynamics.

    Updated on Sep 20, 2018 11:46 AM PDT
  6. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:26 PM PDT
  7. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  8. Celestial Mechanics: Scattering Ct'd

    Location: MSRI: Baker Board Room
    Speakers: Richard Montgomery (University of California, Santa Cruz)

    I will describe the classical Rutherford

    scattering, following Knauf's treatment

    in which the scattering cross section is the 

    push-forward of the Lebesque measure

    to the sphere of outgoing directions.  

    Created on Sep 21, 2018 08:36 AM PDT
  9. UC Berkeley Colloquium: You can hear the shape of a billiard table

    Location: UC Berkeley Math (Evans Hall 60)
    Speakers: Moon Duchin (Tufts University)

    A great deal of fundamental mathematics has been directed at the  question of "hearing the shape of a drum," or reading geometric features of a plane domain or manifold off from its Laplace spectrum. I'll address a parallel question in symbolic dynamics:  if you have a Euclidean polygon and only know the sequences of sides struck in succession by billiard trajectories—that is, the bounce spectrum—does it determine the polygon?  Spoiler: The answer is basically yes.  This is joint work with Erlandsson, Leininger, and Sadanand.

    Updated on Sep 06, 2018 11:14 AM PDT
  10. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  11. Hamiltonian Seminar: Lagrangian spectral invariants, graph selector and Aubry-Mather theory

    Location: MSRI: Simons Auditorium
    Speakers: Yong-Geun Oh (Institute for basic science)

    In this talk, I will first introduce Bernad-Oliviera dos Santos's symplectic description of Mane critical value, Aubry set and Mane set, and Arnaud's graphicality theorem of  invariant Lagrangian submanifold under the flow of Tonelli Hamiltonians. Then I will explain construction of the graph selector of exact Lagrangian submanifold  and its extension to the class of Lipschitz-exact Lagrangian submanifolds. Finally I will explain generalization of above mentioned results in Aubry-Mather theory to this class of Lipschitz-exact Lagrangian submanifolds. The main ingredient of the constructions is the Floer homology theory in symplectic topology. This talk is based on the joint work with Amorim and Oliviera dos Santos.

    Updated on Sep 19, 2018 10:18 AM PDT
  12. Combinatorics Seminar

    Location: UC Berkeley Math (Evans Hall 939)
    Speakers: Thomas McConville (Massachusetts Institute of Technology)
    Created on Sep 13, 2018 11:21 AM PDT
  13. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:27 PM PDT
  14. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  15. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:27 PM PDT
  16. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  17. An introduction to Delay Differential Equations and the Infinite Limit Cycle Bifurcation

    Location: UC Berkeley Engineering (Etcheverry Hall 3110)
    Speakers: Richard Rand (University of California Berkeley)

    The differential equation x(t)'' + x(t) + x(t)^3 = 0 is conservative and admits no limit cycles. If the linear term x(t)
    is replaced by a delayed term x(t-T), where T is the delay, the resulting delay differential equation exhibits an
    infinite number of limit cycles. The amplitudes of the limit cycles go to infinity in the limit as T approaches zero.
    This newly discovered bifurcation will be illustrated after a general introduction to delay differential equations.
    This work is based on a 2017 paper with graduate students M. Davidow and B. Shayak.

    Created on Sep 13, 2018 04:03 PM PDT
  18. Combinatorics Seminar: The Taylor coefficients of the Jacobi theta constant θ3

    Location: UC Berkeley Math (Evans Hall 939)
    Speakers: Dan Romik (University of California, Davis)

    We study the Taylor expansion around the point x=1 of a classical modular form, the Jacobi theta constant θ3. This leads naturally to a new sequence (d(n))∞n=0=1,1,−1,51,849,−26199,… of integers, which arise as the Taylor coefficients in the expansion of a related "centered" version of θ3. We prove several results about the numbers d(n) and conjecture that they satisfy the congruence d(n)≡(−1)n−1 (mod 5) and other similar congruence relations.

    Updated on Sep 13, 2018 01:25 PM PDT
  19. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:28 PM PDT
  20. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  21. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:29 PM PDT
  22. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  23. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  24. Combinatorics Seminar: Walks, groups and Difference Equations

    Location: UC Berkeley Math (Evans Hall 939)
    Speakers: Michael Singer (University College)

    Many questions in combinatorics, probability and statistical mechanics can be reduced to counting lattice paths (walks) in regions of the plane. A standard approach to counting problems is to consider properties of the associated generating function. These functions have long been well understood for walks in the full plane and in a half plane. Recently much attention has focused on walks in the first quadrant of the plane and has now resulted in a complete characterization of those walks whose generating functions are algebraic, holonomic (solutions of linear differential equations) or at least differentially algebraic (solutions of algebraic differential equations).
    I will give an introduction to this topic, discuss previous work of Bousquet-Melou, Kauers, Mishna, and others and then present recent work by Dreyfus, Hardouin, Roques and myself applying the theory of QRT maps and Galois theory of difference equations to determine which generating functions satisfy differential equations and which do not.

    Updated on Sep 13, 2018 01:36 PM PDT
  25. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  26. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:35 PM PDT
  27. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  28. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  29. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:27 PM PDT
  30. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  31. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  32. Hamiltonian Seminar:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 03:29 PM PDT
  33. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  34. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:29 PM PDT
  35. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  36. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  37. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:29 PM PDT
  38. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  39. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  40. Hamiltonian Seminar:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 03:29 PM PDT
  41. Combinatorics Seminar

    Location: UC Berkeley Math (Evans Hall 939)
    Speakers: Mariel Supina (University of California, Berkeley)
    Created on Sep 13, 2018 11:21 AM PDT
  42. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  43. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:30 PM PDT
  44. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  45. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  46. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:30 PM PDT
  47. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  48. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  49. Hamiltonian Seminar:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 03:29 PM PDT
  50. Combinatorics Seminar

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Sep 13, 2018 11:21 AM PDT
  51. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  52. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:30 PM PDT
  53. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  54. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  55. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:31 PM PDT
  56. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  57. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  58. Hamiltonian Seminar:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 03:29 PM PDT
  59. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  60. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:31 PM PDT
  61. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  62. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  63. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:31 PM PDT
  64. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  65. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  66. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  67. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:32 PM PDT
  68. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  69. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  70. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  71. Hamiltonian Seminar:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 03:29 PM PDT
  72. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:32 PM PDT
  73. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  74. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:33 PM PDT
  75. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  76. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  77. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:33 PM PDT
  78. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  79. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  80. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:34 PM PDT
  81. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  82. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  83. Hamiltonian Seminar:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 03:29 PM PDT
  84. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  85. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:34 PM PDT
  86. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  87. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  88. Chancellor Course: Topics in Analysis

    Location: UC Berkeley: Evans Hall, Room 748
    Speakers: Wilfrid Gangbo (University of California, Los Angeles)

    This is a graduate level course, to cover some of the analytical aspects of Mean Field Games. In the recent years, the number of areas of applications of the Mean Field Games theory have exploded, especially because the theory provides the simplest method to handle control problems with several agents. This includes communication networks, data networks, power systems, crowd motion, trade crowding and learning in Mean FieldGames. Despite the recent pioneer work by Cardialaguet–Delarue–Lasry–Lions, the theoryof Mean Field Games is not yet out of its infancy. We will briefly cover the needed stochastic analysis aspect at the undergraduate course level. Other useful geometric concepts will be briefly mentioned in order to quickly get to the heart of the matter.

    This course will be taught by visiting Chancellor's Professor Wilfrid Gangbo.

    Updated on Aug 17, 2018 03:34 PM PDT
  89. Weak KAM Theory, Homogenization and Symplectic Topology

    Location: UC Berkeley Math
    Speakers: Fraydoun Rezakhanlou (University of California, Berkeley)

    In this course we will explore the connection between Hamilton-Jacobi PDE, Hamiltonian ODE and Symplectic Topology. Hamiltonian systems of ordinary differential equations appear in celestial mechanics to describe the motion of planets. We regard a Hamiltonian system  completely integrable if there exists a change of coordinates such that our Hamiltonian system in new coordinates is still Hamiltonian but now associated with a Hamiltonian function that is independent of position. For completely integrable systems the new momentum coordinates are conserved and the set of points at which the new momentum takes a fixed vector is invariant for the flow of our system. These invariant sets are homeomorphic to tori in many classical examples of completely integrable systems. According to Kolmogorov-Arnold-Moser (KAM) Theory, many of the invariant tori survive when a completely integrable system  is slightly perturbed. Aubry-Mather Theory construct a family of invariant sets provided that the Hamiltonian function is convex in the momentum variable.  A. Fathi uses viscosity solutions of the associated Hamilton-Jacobi PDE to construct Aubry-Mather invariant measures. Recently there have been several interesting works to understand the connection between Aubry-Mather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with non-convex Hamiltonian functions. In this course, we also explore the connection between Aubry-Mather Theory and the homogenization phenomena for Hamilton-Jacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.

    Created on Aug 24, 2018 03:42 PM PDT
  90. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  91. Hamiltonian Seminar:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 03:29 PM PDT

Past Seminars

  1. Seminar Graduate Student Seminar

    Created on Sep 07, 2018 10:39 AM PDT
  2. Seminar Five Minute Talks

    Updated on Aug 24, 2018 09:08 AM PDT
There are more then 30 past seminars. Please go to Past seminars to see all past seminars.