
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
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 
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 
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 
Lunch with Hamilton: Using Greene's residue criterion to study torus breakup in areapreserving 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 areapreserving 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 
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 
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 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
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 
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 
Graduate Student Seminar
Location: MSRI: Baker Board RoomCreated on Sep 07, 2018 01:47 PM PDT 
Hamiltonian Seminar: Quasi periodic coorbital motions (joint work with Philippe Robutel and Alexandre Pousse)
Location: MSRI: Simons Auditorium Speakers: Laurent Niederman (UniversitÃ© 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 quasiperiodic orbits of this
kind in the three body planetary problem thanks to KAM theory.
Updated on Oct 18, 2018 04:44 PM PDT 
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 
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 
Hamiltonian Colloquium:
Location: MSRI: Simons AuditoriumCreated on Aug 24, 2018 01:40 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Lunch with Hamilton:
Location: MSRI: Simons AuditoriumUpdated on Oct 18, 2018 09:35 AM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Celestial Mechanics:
Location: MSRI: Baker Board RoomCreated on Sep 21, 2018 10:51 AM PDT 
Graduate Student Seminar
Location: MSRI: Baker Board RoomCreated on Sep 07, 2018 01:47 PM PDT 
Hamiltonian Seminar:
Location: MSRI: Simons AuditoriumCreated on Aug 24, 2018 03:29 PM PDT 
Combinatorics Seminar
Location: UC Berkeley Math (Evans Hall 939)Created on Sep 13, 2018 11:21 AM PDT 
Hamiltonian Colloquium:
Location: MSRI: Simons AuditoriumCreated on Aug 24, 2018 01:40 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Lunch with Hamilton:
Location: MSRI: Baker Board RoomCreated on Aug 24, 2018 02:30 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Celestial Mechanics:
Location: MSRI: Baker Board RoomCreated on Sep 21, 2018 10:51 AM PDT 
Graduate Student Seminar
Location: MSRI: Baker Board RoomCreated on Sep 07, 2018 01:47 PM PDT 
Hamiltonian Seminar:
Location: MSRI: Simons AuditoriumCreated on Aug 24, 2018 03:29 PM PDT 
Hamiltonian Colloquium:
Location: MSRI: Simons AuditoriumCreated on Aug 24, 2018 01:40 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Lunch with Hamilton:
Location: MSRI: Baker Board RoomCreated on Aug 24, 2018 02:30 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Celestial Mechanics:
Location: MSRI: Baker Board RoomCreated on Sep 21, 2018 10:51 AM PDT 
Graduate Student Seminar
Location: MSRI: Baker Board RoomCreated on Sep 07, 2018 01:47 PM PDT 
Hamiltonian Colloquium:
Location: MSRI: Simons AuditoriumCreated on Aug 24, 2018 01:40 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Lunch with Hamilton:
Location: MSRI: Baker Board RoomCreated on Aug 24, 2018 02:30 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Hamiltonian Colloquium:
Location: MSRI: Simons AuditoriumCreated on Aug 24, 2018 01:40 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Lunch with Hamilton:
Location: MSRI: Baker Board RoomCreated on Aug 24, 2018 02:30 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Celestial Mechanics:
Location: MSRI: Baker Board RoomCreated on Sep 21, 2018 10:54 AM PDT 
Graduate Student Seminar
Location: MSRI: Baker Board RoomCreated on Sep 07, 2018 01:47 PM PDT 
Hamiltonian Seminar:
Location: MSRI: Simons AuditoriumCreated on Aug 24, 2018 03:29 PM PDT 
Hamiltonian Colloquium:
Location: MSRI: Simons AuditoriumCreated on Aug 24, 2018 01:40 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Lunch with Hamilton:
Location: MSRI: Baker Board RoomCreated on Aug 24, 2018 02:30 PM PDT 
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 
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 HamiltonJacobi 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 KolmogorovArnoldMoser (KAM) Theory, many of the invariant tori survive when a completely integrable system is slightly perturbed. AubryMather 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 HamiltonJacobi PDE to construct AubryMather invariant measures. Recently there have been several interesting works to understand the connection between AubryMather Theory and Symplectic Topology. The hope is to use tools from Symplectic Topology to construct interesting invariant sets/measures for Hamiltonian systems associated with nonconvex Hamiltonian functions. In this course, we also explore the connection between AubryMather Theory and the homogenization phenomena for HamiltonJacobi PDEs when the Hamiltonian function is selected randomly according to a translation invariant probability measure.
Created on Aug 24, 2018 03:42 PM PDT 
Celestial Mechanics:
Location: MSRI: Baker Board RoomCreated on Sep 21, 2018 10:51 AM PDT 
Graduate Student Seminar
Location: MSRI: Baker Board RoomCreated on Sep 07, 2018 01:47 PM PDT 
Hamiltonian Seminar:
Location: MSRI: Simons AuditoriumCreated on Aug 24, 2018 03:29 PM PDT

Upcoming Colloquia & Seminars 