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Colloquia & Seminars


Current Seminars

No current seminar

Upcoming Seminars

  1. 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 16, 2018 09:39 AM PST
  2. 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 16, 2018 09:40 AM PST
  3. 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
  4. 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 16, 2018 09:41 AM PST
  5. Hamiltonian Seminar: Construction of unstable KAM tori for a system of coupled NLS equations.

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

    The systems of coupled NLS equations occur in some physical problems, in particular in nonlinear optics (coupling between two optical waveguides, pulses or polarized components...). From the mathematical point of view, the coupling effects can lead to truly nonlinear behaviors, such as the beating effect (solutions with Fourier modes exchanging energy) of Grébert, Paturel and Thomann (2013).

    In this talk, I will use the coupling between two NLS equations on the 1D torus to construct a family of linearly unstable tori, and therefore unstable quasi-periodic solutions. The idea is to take profit of the Hamiltonian structure of the system via the construction of a Birkhoff normal form and the application of a KAM theorem. In particular, we will see of this surprising behavior (this is the first example of unstable tori for a 1D PDE) is strongly related to the existence of beating solutions. 

    This is a work in collaboration with Benoît Grébert (Université de Nantes).

    Updated on Nov 16, 2018 08:43 AM PST
  6. 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 16, 2018 09:43 AM PST
  7. 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
  8. 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
  9. Lunch with Hamilton: 3D Billiards: visualization of the 4D phase space and power-law trapping of chaotic trajectories

    Location: MSRI: Baker Board Room
    Speakers: Arnd Baecker

    Understanding the transport properties of higher-dimensional
    systems is of great importance in a wide variety of applications,
    e.g., for celestial mechanics, particle accelerators, or the
    dynamics of atoms and molecules.  A prototypical class of model
    systems are billiards for which a Poincaré section leads to
    discrete-time map.  For the dynamics in three-dimensional
    billiards a four-dimensional symplectic map is obtained which is
    challenging to visualize. By means of the recently introduced 3D
    phase-space slices an intuitive representation of the
    organization of the mixed phase space with regular and chaotic
    dynamics is obtained. Of particular interest for applications are
    constraints to classical transport between different regions of
    phase space which manifest in the statistics of Poincaré
    recurrence times. For a 3D paraboloid billiard we observe a slow
    power-law decay caused by long-trapped trajectories which we
    analyze in phase space and in frequency space. Consistent with
    previous results for 4D maps we find that: (i) Trapping takes
    place close to regular structures outside the Arnold web. (ii)
    Trapping is not due to a generalized island-around-island
    hierarchy. (iii) The dynamics of sticky orbits is governed by
    resonance channels which extend far into the chaotic sea. We find
    clear signatures of partial transport barriers. Moreover, we
    visualize the geometry of stochastic layers in resonance channels
    explored by sticky orbits.

    Reference:
     3D Billiards: Visualization of Regular Structures and
     Trapping of Chaotic Trajectories
     M. Firmbach, S. Lange, R. Ketzmerick, and A. Bäcker,
     Phys. Rev. E 98, 022214 (2018)
     https://doi.org/10.1103/PhysRevE.98.022214

    Created on Nov 15, 2018 09:09 AM PST
  10. 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
  11. 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
  12. 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
  13. 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
  14. Hamiltonian Colloquium:

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

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 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 03:34 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. Celestial Mechanics:

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

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

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

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

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  27. 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
  28. 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
  29. Celestial Mechanics:

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

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

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

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

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

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

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

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

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

Past Seminars

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