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Upcoming Colloquia & 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 03:29 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. Arnold Diffusion First Cycle 2

    Location: MSRI: Baker Board Room
    Speakers: Ke Zhang (University of Toronto)
    Updated on Oct 18, 2018 11:33 AM PDT
  4. Arnold Diffusion First Cycle 2

    Location: MSRI: Baker Board Room
    Speakers: Ke Zhang (University of Toronto)
    Updated on Oct 17, 2018 12:26 PM PDT
  5. Arnold Diffusion First Cycle 2: On Arnold diffusion, the higher dimensional case

    Location: MSRI: Baker Board Room
    Speakers: Jinxin Xue (Tsinghua University)

    We continue the lectures of the last week. In this week, we will finish the construction of global diffusing orbit in the higher dimensional case. 

     

    We first finish describing the normal form at the complete resonance, and explain how to cross the complete resonance by combining the mechanism of cohomology equivalence and a new mechanism. Next, we will also show how to switch from one frequency segment from the next. 

    Updated on Oct 18, 2018 12:18 PM PDT
  6. 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
  7. Arnold Diffusion First Cycle 2

    Location: MSRI: Baker Board Room
    Speakers: Ke Zhang (University of Toronto)
    Created on Oct 17, 2018 01:11 PM PDT
  8. Arnold Diffusion First Cycle 2

    Location: MSRI: Baker Board Room
    Speakers: Ke Zhang (University of Toronto)
    Created on Oct 17, 2018 01:42 PM PDT
  9. 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
  10. 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
  11. Arnold Diffusion First Cycle 2

    Location: MSRI: Baker Board Room
    Speakers: Ke Zhang (University of Toronto)
    Created on Oct 18, 2018 11:14 AM PDT
  12. Arnold Diffusion First Cycle 2: On Arnold diffusion, the higher dimensional case

    Location: MSRI: Baker Board Room
    Speakers: Jinxin Xue (Tsinghua University)

    We continue the lectures of the last week. In this week, we will finish the construction of global diffusing orbit in the higher dimensional case. 

     

    We first finish describing the normal form at the complete resonance, and explain how to cross the complete resonance by combining the mechanism of cohomology equivalence and a new mechanism. Next, we will also show how to switch from one frequency segment from the next. 

    Updated on Oct 18, 2018 12:19 PM PDT
  13. Graduate Student Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 07, 2018 01:47 PM PDT
  14. Hamiltonian Seminar: Quasi periodic coorbital motions (joint work with Philippe Robutel and Alexandre Pousse)

    Location: MSRI: Simons Auditorium
    Speakers: Laurent Niederman (Université de Paris XI)

    Quasi periodic coorbital motions (joint work with Philippe Robutel and Alexandre Pousse)

    Abstract: The motions of the satellites Janus and Epimetheus around 

    Saturn are among the most intriguing in the solar system since they 

    exchange their orbits every four years.

    We give a rigorous proof of the existence of quasi-periodic orbits of this 

    kind in the three body planetary problem thanks to KAM theory.

    Updated on Oct 18, 2018 04:44 PM PDT
  15. Arnold Diffusion First Cycle 2

    Location: MSRI: Baker Board Room
    Speakers: Ke Zhang (University of Toronto)
    Created on Oct 17, 2018 01:44 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: Simons Auditorium
    Updated on Oct 18, 2018 09:35 AM 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