Current Seminars

Hamiltonian Colloquium: Hydrodynamics from Hamilton
Location: MSRI: Simons Auditorium Speakers: Stamatis Dostoglou (University of Missouri)The talk will be on how to get hydrodynamic equations from the classical mechanics of molecules, something that goes back to JC Maxwell. We shall first recall some of the main ideas and aims of this approach to hydrodynamics. We shall then look at examples where things work as well as one might hope, mainly thanks to uniform estimates on certain solutions of Hamiltonian systems as the number of equations increases to infinity. For these cases the role of hydrodynamic Reynolds stresses becomes clear. If time allows, we might also mention how this approach might be useful for nonuniqueness results for macroscopic PDEs and the role of Gibbs ensembles.
Updated on Nov 06, 2018 08:48 AM PST 
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
Upcoming Seminars

Hamiltonian Postdoc Workshop: On the existence of exponentially decreasing solutions to time dependent hyperbolic systems
Location: MSRI: Simons Auditorium Speakers: Hongyu Cheng (Chern Institute of Mathematics)For any hyperbolic systems (the hyperbolic systems we mean here are systems
that the sepctra of the linear operator of these systems are not the pure imaginary), if
the inhomogeneous terms decrease exponentially about time t in and small, the linear
perturbations are small and the higher order perturbations are bounded, our main result
(Theorem 2.1) shows that there is a small solution that decreases exponentially in .
We take the timedependent complex Ginaburgandau equations, Boussinesq equations
and the duffing equations, which are infinitedimensional and finitedimensional systems
respectively, as examples.Updated on Nov 07, 2018 08:52 AM PST 
Hamiltonian Postdoc Workshop: Optimal time estimate of the Arnold diffusion for analytic quasiconvex nearly integrable systems
Location: MSRI: Simons Auditorium Speakers: Jianlu Zhang (University of Maryland)By improving the global Nekhoroshev stability for analytic quasiconvex nearly
integrable Hamiltonian systems, we get the optimal time estimate of Arnold diffusion.Updated on Nov 07, 2018 08:53 AM PST 
Hamiltonian Postdoc Workshop: Equilibrium quasiperiodic configurations in quasiperiodic media
Location: MSRI: Simons Auditorium Speakers: Lei Zhang (University of Toronto, Mississauga)We consider a quasiperiodic version of the wellknown FrenkelKontorova
model and looking for quasiperiodic equilibria with a frequency that resonates with the
frequencies of the medium. We show that there are always perturbative expansions and
prove a KAM theorem in aposteriori form. We show that if there is an approximate
solution of the equilibrium equation satisfying nondegeneracy conditions, we can adjust
one parameter and obtain a true solution which is close to the approximate solution. The
proof is based on an iterative method of the KAM type.Updated on Nov 07, 2018 08:54 AM PST 
Hamiltonian Postdoc Workshop: A proof of Jonesâ€™ conjecture: counting and discounting periodic orbits in a delay differential equation
Location: MSRI: Simons Auditorium Speakers: Jonathan Jaquette (MSRI  Mathematical Sciences Research Institute)In 1962 G.S. Jones conjectured that the nonlinear delay differential equation
known as Wright’s equation has a unique slowly oscillating periodic solution for all pa
rameters above a particular value. This talk presents a computerassisted proof of theconjecture. Furthermore, we show there are no isolas of periodic solutions to Wright's
equation; all periodic orbits arise from Hopf bifurcations.Updated on Nov 07, 2018 09:09 AM PST 
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: Singularity Theory for Nontwist Tori: from symplectic geometry to applications through analysis.
Location: MSRI: Baker Board Room Speakers: Alex Haro (Universitat de Barcelona)Updated on Nov 09, 2018 08:36 AM PST 
Hamiltonian Postdoc Workshop: Emphasizing nonlinear behaviors for cubic coupled systems
Location: MSRI: Simons Auditorium Speakers: Victor VilaÃ§a Da Rocha (Basque Center for Applied Mathematics)The purpose of this talk is to propose a study of various nonlinear behav
iors for a system of two coupled cubic Schr Ìˆodinger equations with small initial data.Depending on the choice of the spatial domain, we highlight different examples of non
linear behaviors. On the one hand, we observe on the torus a truly nonlinear behavior(exchanges on energy) in finite time. On the other hand, on the real line, we highlight
through scattering methods an almost linear behavior in infinite time. The goal is to
mix these two approaches to obtain on the product space a truly nonlinear behavior in
infinite time, via the construction of a modified scattering theorem.Updated on Nov 07, 2018 09:00 AM PST 
Graduate Student Seminar
Location: MSRI: Baker Board RoomCreated on Sep 07, 2018 01:47 PM PDT 
Hamiltonian Postdoc Workshop: The effect of threshold energy obstructions on the L 1 â†’ Lâˆž dispersive esti mates for some Schr Ìˆodinger type equations
Location: MSRI: Simons Auditorium Speakers: Ebru Toprak (University of Illinois at UrbanaChampaign)In this talk, I will discuss the differential equation iut = Hu, H := H0 + V ,
where V is a decaying potential and H0 is a Laplacian related operator. In particular,
I will focus on when H0 is Laplacian, Bilaplacian and Dirac operators. I will discuss
how the threshold energy obstructions, eigenvalues and resonances, effect the L
1 → L∞behavior of e
itHPac(H). The threshold obstructions are known as the distributional so
lutions of Hψ = 0 in certain dimension dependent spaces. Due to its unwanted effectson the dispersive estimates, its absence have been assumed in many work. I will mention
our previous results on Dirac operator and recent results on Bilaplacian operator under
different assumptions on threshold energy obstructions.Updated on Nov 07, 2018 09:05 AM PST 
Hamiltonian Postdoc Workshop: Linear WhithamBoussinesq modes in channels of constant crosssection and trapped modes associated with continental shelves.
Location: MSRI: Simons Auditorium Speakers: Rosa Vargas (MSRI  Mathematical Sciences Research Institute)In this talk, we will study two classical problems of linear water waves with
varying depth. One problem is related to normal modes for the linear water wave problem
on infinite straight channels of constant crosssection. The second problem is about
trapped waves, that is, the phenomenon whereby waves can remain confined in some
region of the fluid domain. Here we will discuss the wave trapping problem associated
with continental shelves by way of a simple model such as a rectangular shelf. It is
important to point out that for problem one only a few special solutions are known. For
problem two, no exact solutions are known but there is a simplified approach in which is
possible to find that eigenfrequencies exist which correspond to modes trapped over the
shelf. These modes are analogous to the socalled bound states in a squarewell potential
in quantum mechanics. The main motivation of choosing these problems that involve
depth geometries and models with known exact results was to test simplifications of the
lowest order variable depth DirichletNeumann operator for variable depth.Updated on Nov 07, 2018 09:06 AM PST 
Hamiltonian Postdoc Workshop: Critical transition to the inverse cascade
Location: MSRI: Simons Auditorium Speakers: George Miloshevich (The University of Texas at Austin)Astrophysical plasmas exist in a large
range of lengthscales throughout the universe. At sufficiently small scales, one must
account for many twofluid effects, such as the ion or electron skindepths, as well as
Larmor radii. These effects occur when ignoring electron mass, for example, is no longerpossible. We are interested in studying idealized turbulence in the context of such Hamil
tonian plasma models which include twofluid effects. In particular, we look at a extended2D MHD model which includes the electron skindepth.This model has been applied to
understanding collisionless reconnection in past. Twodimensional simulations are less
computationally intensive and thus allow us to perform a parameter study of many runs,
in which we look at the cascade of conserved quadratic quantities (that happen to be
Casimir invariants of the Poisson bracket) as we vary the effective electron skindepth.
We find that the cascade directions depend strongly on whether these length scales are
relevant in the system, and, furthermore, that these transitions in cascade directions
happen in a critical way, as was previously observed in other studies of the kind but in
different systems. Finally, we compare these results to predictions made by the authors
in a previous theoretical study using Absolute Equilibrium States.Updated on Nov 07, 2018 09:07 AM PST 
Combinatorics Seminar: Electrical networks and hyperplane arrangements
Location: UC Berkeley Math (Evans Hall 939) Speakers: Bob Lutz (University of Michigan)This talk defines Dirichlet arrangements, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. After establishing some basic properties we characterize Dirichlet arrangements whose OrlikSolomon algebras are Koszul and show that the underlying matroids satisfy the halfplane property. We also discuss the role of Dirichlet arrangements and harmonic functions on electrical networks in problems coming from mathematical physics.
Updated on Nov 13, 2018 12:29 PM PST 
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 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 11:15 AM PST 
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 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST 
Combinatorics Seminar:
Location: UC Berkeley Math (Evans Hall 939)Created on Nov 06, 2018 01:41 PM PST
Past Seminars

Seminar Hamiltonian Postdoc Workshop: Magnetic Confinement from a Dynamical Perspective
Updated on Nov 07, 2018 08:50 AM PST 
Seminar Hamiltonian Postdoc Workshop: Integrable magnetic flows on the twotorus whose trajectories are all closed
Updated on Nov 07, 2018 08:50 AM PST 
Seminar Hamiltonian Postdoc Workshop: Sectional curvatures in the strong force 4body problem
Updated on Nov 07, 2018 08:49 AM PST 
Seminar Hamiltonian Postdoc Workshop: Connecting planar linear chains in the spatial Nbody problem with equal masses
Updated on Nov 07, 2018 09:11 AM PST 
Seminar Hamiltonian Seminar: Barcodes and areapreserving homeomorphisms
Created on Nov 05, 2018 03:58 PM PST 
Seminar Graduate Student Seminar
Created on Sep 07, 2018 01:47 PM PDT 
Seminar Weak KAM Theory, Homogenization and Symplectic Topology
Created on Aug 24, 2018 03:42 PM PDT 
Seminar Celestial Mechanics: Whiskered parabolic tori in the planar (n+1)body problem
Updated on Nov 02, 2018 12:26 PM PDT 
Seminar Chancellor Course: Topics in Analysis
Updated on Aug 17, 2018 03:31 PM PDT 
Seminar Lunch with Hamilton: Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
Updated on Oct 31, 2018 09:29 AM PDT 
Seminar Weak KAM Theory, Homogenization and Symplectic Topology
Created on Aug 24, 2018 03:42 PM PDT 
Seminar Chancellor Course: Topics in Analysis
Updated on Aug 17, 2018 03:30 PM PDT 
Seminar Combinatorics Seminar: Inequalities for families of symmetric functions Abstract
Updated on Oct 29, 2018 10:00 AM PDT 
Seminar Hamiltonian Seminar: Fibrations of R^3 and contact structures
Updated on Oct 22, 2018 04:56 PM PDT 
Seminar Graduate Student Seminar
Created on Sep 07, 2018 01:47 PM PDT 
Seminar Weak KAM Theory, Homogenization and Symplectic Topology
Created on Aug 24, 2018 03:42 PM PDT 
Seminar Celestial Mechanics: Global instability in the elliptic restricted three body problem
Updated on Oct 26, 2018 08:39 AM PDT 
Seminar Chancellor Course: Topics in Analysis
Updated on Aug 17, 2018 03:30 PM PDT 
Seminar (Pre) Lunch with Hamilton: Growth of Sobolev norms for the cubic nonlinear SchrÃ¶dinger equation near 1D quasiperiodic solutions
Updated on Oct 26, 2018 10:08 AM PDT 
Seminar Weak KAM Theory, Homogenization and Symplectic Topology
Created on Aug 24, 2018 03:42 PM PDT 
Seminar Chancellor Course: Topics in Analysis
Updated on Aug 17, 2018 03:30 PM PDT 
Seminar Hamiltonian Colloquium: Reductions of the VlasovMaxwell System with Applications to PlasmaBased Accelerators
Updated on Oct 24, 2018 03:16 PM PDT 
Seminar Combinatorics Seminar: Nonsymmetric Macdonald polynomials and Demazure characters
Updated on Oct 24, 2018 10:36 AM PDT 
Seminar Arnold Diffusion First Cycle 2
Created on Oct 17, 2018 01:44 PM PDT 
Seminar Hamiltonian Seminar: Quasi periodic coorbital motions (joint work with Philippe Robutel and Alexandre Pousse)
Updated on Oct 18, 2018 04:44 PM PDT 
Seminar Arnold Diffusion First Cycle 2
Created on Oct 22, 2018 03:46 PM PDT 
Seminar Arnold Diffusion First Cycle 2
Created on Oct 22, 2018 03:45 PM PDT 
Seminar Graduate Student Seminar
Created on Sep 07, 2018 01:47 PM PDT 
Seminar Arnold Diffusion First Cycle 2: On Arnold diffusion, the higher dimensional case
Updated on Oct 18, 2018 12:19 PM PDT 
Seminar Arnold Diffusion First Cycle 2
Created on Oct 18, 2018 11:14 AM PDT