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Colloquia & Seminars


Current Seminars

  1. 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
  2. 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
  3. Celestial Mechanics: Shape space figure 8 solution of the three body problem with two equal masses

    Location: MSRI: Baker Board Room
    Speakers: Guowei Yu

    For the planar three body problem with a-homogeneous potential (1/r^a), when two of the masses are equal, using action minimization method, we show that for 1<a<2, there is a collision-free periodic solution, whose projection in the shape space looks like a figure 8; for a=1(the Newtonian potential), the minimizer is either a collision-free periodic solution as above, or it is a Schubart solution (a collinear periodic solution containing binary collisions). 

    Updated on Oct 11, 2018 08:56 AM PDT

Upcoming Seminars

  1. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  2. Hamiltonian Seminar: Analytic invariant curves for analytic twist map

    Location: MSRI: Simons Auditorium
    Speakers: Abed Bounemoura (Université de Paris IX (Paris-Dauphine))

    Yoccoz proved that Bruno's arithmetic condition is optimal for the analytic linearization of a circle diffeomorphism close to a rotation. We will explain how to use this result to prove that the same condition is optimal for the analytic preservation of quasi-periodic invariant curves of twists maps, as well as new questions in this context. We will also discuss partial results in higher dimension.

    Updated on Oct 11, 2018 10:00 AM PDT
  3. Arnold Diffusion First Cycle 2

    Location: MSRI: Simons Auditorium
    Created on Oct 17, 2018 12:10 PM PDT
  4. Arnold Diffusion First Cycle 2

    Location: MSRI: Simons Auditorium
    Created on Oct 17, 2018 12:11 PM PDT
  5. Combinatorics Seminar: TBA

    Location: UC Berkeley Math (Evans Hall 939)
    Speakers: Mariel Supina (University of California, Berkeley)
    Created on Oct 17, 2018 04:00 PM PDT
  6. Arnold Diffusion First Cycle 2

    Location: MSRI: Simons Auditorium
    Created on Oct 17, 2018 12:14 PM PDT
  7. Hamiltonian Colloquium: Symplectic reduction of the 3-body problem in 4-dimensional space

    Location: MSRI: Simons Auditorium
    Speakers: Holger Dullin (University of Sydney)

    The N-body problem in d-dimension space has symmetry group SE(d).
    Centre of mass reduction leads to a system with SO(d) symmetry acting
    diagonally on positions and momenta. For N=3, d=4 reduction of the SO(4)
    symmetry is complicated because the tensor of inertia is non-invertible.
    The fully reduced system has 4 degrees of freedom and a Hamiltonian that 
    is not polynomial in the momenta. The most surprising property of the 
    reduced Hamiltonian is that it has equilibria that are minima.

    Updated on Oct 03, 2018 09:54 AM PDT
  8. 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
  9. 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
  10. Lunch with Hamilton: Using Greene's residue criterion to study torus breakup in area-preserving maps

    Location: MSRI: Baker Board Room
    Speakers: Alexander Wurm (Western New England University)

    I will discuss the use of Greene’s residue criterion in the study of the breakup of invariant tori in area-preserving maps. The main focus will be on the breakup of shearless invariant tori in various nontwist maps, but results from twist maps and open problems will also be mentioned.

    Updated on Oct 17, 2018 04:35 PM PDT
  11. 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
  12. 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
  13. Celestial Mechanics:

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

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

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 03:29 PM PDT
  16. 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
  17. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 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 03:30 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. Lunch with Hamilton:

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

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

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

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

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

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  28. 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
  29. 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
  30. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  31. 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
  32. 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
  33. Celestial Mechanics:

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

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

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

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 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 03:31 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. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  40. 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
  41. 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
  42. Celestial Mechanics:

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

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

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  45. 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
  46. 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
  47. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  48. 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
  49. 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
  50. 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
  51. 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
  52. Hamiltonian Colloquium:

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  53. 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
  54. 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
  55. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  56. 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
  57. 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
  58. Celestial Mechanics:

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

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

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

    Location: MSRI: Simons Auditorium
    Created on Aug 24, 2018 01:40 PM PDT
  62. 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
  63. 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
  64. Lunch with Hamilton:

    Location: MSRI: Baker Board Room
    Created on Aug 24, 2018 02:30 PM PDT
  65. 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
  66. 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
  67. Celestial Mechanics:

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

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

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

Past Seminars

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