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Colloquia & Seminars


Current Seminars

  1. Hamiltonian Colloquium: Hydrodynamics from Hamilton

    Location: MSRI: Simons Auditorium
    Speakers: Stamatis Dostoglou (University of Missouri)

    The talk will be on how to get hydrodynamic equations from the classical mechanics of molecules, something that goes back to JC Maxwell. We shall first recall some of the main ideas and aims of this approach to hydrodynamics. We shall then look at examples where things work as well as one might hope, mainly thanks to uniform estimates on certain solutions of Hamiltonian systems as the number of equations increases to infinity. For these cases the role of hydrodynamic Reynolds stresses becomes clear. If time allows, we might also mention how this approach might be useful for non-uniqueness results for macroscopic PDEs and the role of Gibbs ensembles.

    Updated on Nov 06, 2018 08:48 AM PST
  2. 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
  3. 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

Upcoming Seminars

  1. Hamiltonian Postdoc Workshop: On the existence of exponentially decreasing solutions to time dependent hyperbolic systems

    Location: MSRI: Simons Auditorium
    Speakers: Hongyu Cheng (Chern Institute of Mathematics)

    For any hyperbolic systems (the hyperbolic systems we mean here are systems
    that the sepctra of the linear operator of these systems are not the pure imaginary), if
    the inhomogeneous terms decrease exponentially about time t in and small, the linear
    perturbations are small and the higher order perturbations are bounded, our main result
    (Theorem 2.1) shows that there is a small solution that decreases exponentially in .
    We take the time-dependent complex Ginaburg-andau equations, Boussinesq equations
    and the duffing equations, which are infinite-dimensional and finite-dimensional systems
    respectively, as examples.

    Updated on Nov 07, 2018 08:52 AM PST
  2. Hamiltonian Postdoc Workshop: Equilibrium quasi-periodic configurations in quasi-periodic media

    Location: MSRI: Simons Auditorium
    Speakers: Lei Zhang (University of Toronto, Mississauga)

    We consider a quasi-periodic version of the well-known Frenkel-Kontorova
    model and looking for quasi-periodic equilibria with a frequency that resonates with the
    frequencies of the medium. We show that there are always perturbative expansions and
    prove a KAM theorem in a-posteriori form. We show that if there is an approximate
    solution of the equilibrium equation satisfying non-degeneracy conditions, we can adjust
    one parameter and obtain a true solution which is close to the approximate solution. The
    proof is based on an iterative method of the KAM type.

    Updated on Nov 07, 2018 08:54 AM PST
  3. Hamiltonian Postdoc Workshop: A proof of Jones’ conjecture: counting and discounting periodic orbits in a delay differential equation

    Location: MSRI: Simons Auditorium
    Speakers: Jonathan Jaquette (MSRI - Mathematical Sciences Research Institute)

    In 1962 G.S. Jones conjectured that the nonlinear delay differential equation

    known as Wright’s equation has a unique slowly oscillating periodic solution for all pa-
    rameters above a particular value. This talk presents a computer-assisted proof of the

    conjecture. Furthermore, we show there are no isolas of periodic solutions to Wright's
    equation; all periodic orbits arise from Hopf bifurcations.

    Updated on Nov 07, 2018 09:09 AM PST
  4. 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
  5. 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
  6. Hamiltonian Postdoc Workshop: Emphasizing nonlinear behaviors for cubic coupled systems

    Location: MSRI: Simons Auditorium
    Speakers: Victor Vilaça Da Rocha (Basque Center for Applied Mathematics)

    The purpose of this talk is to propose a study of various nonlinear behav-
    iors for a system of two coupled cubic Schr ̈odinger equations with small initial data.

    Depending on the choice of the spatial domain, we highlight different examples of non-
    linear behaviors. On the one hand, we observe on the torus a truly nonlinear behavior

    (exchanges on energy) in finite time. On the other hand, on the real line, we highlight
    through scattering methods an almost linear behavior in infinite time. The goal is to
    mix these two approaches to obtain on the product space a truly nonlinear behavior in
    infinite time, via the construction of a modified scattering theorem.

    Updated on Nov 07, 2018 09:00 AM PST
  7. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  8. Hamiltonian Postdoc Workshop: The effect of threshold energy obstructions on the L 1 → L∞ dispersive esti- mates for some Schr ̈odinger type equations

    Location: MSRI: Simons Auditorium
    Speakers: Ebru Toprak (University of Illinois at Urbana-Champaign)

    In this talk, I will discuss the differential equation iut = Hu, H := H0 + V ,
    where V is a decaying potential and H0 is a Laplacian related operator. In particular,
    I will focus on when H0 is Laplacian, Bilaplacian and Dirac operators. I will discuss
    how the threshold energy obstructions, eigenvalues and resonances, effect the L
    1 → L∞

    behavior of e

    itHPac(H). The threshold obstructions are known as the distributional so-
    lutions of Hψ = 0 in certain dimension dependent spaces. Due to its unwanted effects

    on the dispersive estimates, its absence have been assumed in many work. I will mention
    our previous results on Dirac operator and recent results on Bilaplacian operator under
    different assumptions on threshold energy obstructions.

    Updated on Nov 07, 2018 09:05 AM PST
  9. Hamiltonian Postdoc Workshop: Linear Whitham-Boussinesq modes in channels of constant cross-section and trapped modes associated with continental shelves.

    Location: MSRI: Simons Auditorium
    Speakers: Rosa Vargas (MSRI - Mathematical Sciences Research Institute)

    In this talk, we will study two classical problems of linear water waves with
    varying depth. One problem is related to normal modes for the linear water wave problem
    on infinite straight channels of constant cross-section. The second problem is about
    trapped waves, that is, the phenomenon whereby waves can remain confined in some
    region of the fluid domain. Here we will discuss the wave trapping problem associated
    with continental shelves by way of a simple model such as a rectangular shelf. It is
    important to point out that for problem one only a few special solutions are known. For
    problem two, no exact solutions are known but there is a simplified approach in which is
    possible to find that eigenfrequencies exist which correspond to modes trapped over the
    shelf. These modes are analogous to the so-called bound states in a square-well potential
    in quantum mechanics. The main motivation of choosing these problems that involve
    depth geometries and models with known exact results was to test simplifications of the
    lowest order variable depth Dirichlet-Neumann operator for variable depth.

    Updated on Nov 07, 2018 09:06 AM PST
  10. Hamiltonian Postdoc Workshop: Critical transition to the inverse cascade

    Location: MSRI: Simons Auditorium
    Speakers: George Miloshevich (The University of Texas at Austin)

    Astrophysical plasmas exist in a large
    range of length-scales throughout the universe. At sufficiently small scales, one must
    account for many two-fluid effects, such as the ion or electron skin-depths, as well as
    Larmor radii. These effects occur when ignoring electron mass, for example, is no longer

    possible. We are interested in studying idealized turbulence in the context of such Hamil-
    tonian plasma models which include two-fluid effects. In particular, we look at a extended

    2D MHD model which includes the electron skin-depth.This model has been applied to

    understanding collisionless reconnection in past. Two-dimensional simulations are less
    computationally intensive and thus allow us to perform a parameter study of many runs,
    in which we look at the cascade of conserved quadratic quantities (that happen to be
    Casimir invariants of the Poisson bracket) as we vary the effective electron skin-depth.
    We find that the cascade directions depend strongly on whether these length scales are
    relevant in the system, and, furthermore, that these transitions in cascade directions
    happen in a critical way, as was previously observed in other studies of the kind but in
    different systems. Finally, we compare these results to predictions made by the authors
    in a previous theoretical study using Absolute Equilibrium States.

    Updated on Nov 07, 2018 09:07 AM PST
  11. Combinatorics Seminar: Electrical networks and hyperplane arrangements

    Location: UC Berkeley Math (Evans Hall 939)
    Speakers: Bob Lutz (University of Michigan)

    This talk defines Dirichlet arrangements, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. After establishing some basic properties we characterize Dirichlet arrangements whose Orlik-Solomon algebras are Koszul and show that the underlying matroids satisfy the half-plane property. We also discuss the role of Dirichlet arrangements and harmonic functions on electrical networks in problems coming from mathematical physics.

    Updated on Nov 13, 2018 12:29 PM PST
  12. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM 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 03:32 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. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 11:15 AM PST
  16. 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
  17. 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
  18. 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
  19. 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
  20. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 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 03:33 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. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  24. 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
  25. 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
  26. Celestial Mechanics:

    Location: MSRI: Baker Board Room
    Created on Sep 21, 2018 10:54 AM PDT
  27. Graduate Student Seminar

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

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

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  30. 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
  31. 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
  32. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  33. 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
  34. 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
  35. Celestial Mechanics:

    Location: MSRI: Baker Board Room
    Created on Sep 21, 2018 10:51 AM PDT
  36. Graduate Student Seminar

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

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

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  39. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  40. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  41. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  42. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  43. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  44. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  45. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  46. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  47. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  48. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  49. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  50. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  51. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST

Past Seminars

There are more then 30 past seminars. Please go to Past seminars to see all past seminars.