Current Seminars
Upcoming Seminars

Hamiltonian Postdoc Workshop: Emphasizing nonlinear behaviors for cubic coupled systems
Location: MSRI: Simons Auditorium Speakers: Victor Vilaça Da Rocha (Basque Center for Applied Mathematics)The purpose of this talk is to propose a study of various nonlinear behav
iors for a system of two coupled cubic Schr ̈odinger equations with small initial data.Depending on the choice of the spatial domain, we highlight different examples of non
linear behaviors. On the one hand, we observe on the torus a truly nonlinear behavior(exchanges on energy) in finite time. On the other hand, on the real line, we highlight
through scattering methods an almost linear behavior in infinite time. The goal is to
mix these two approaches to obtain on the product space a truly nonlinear behavior in
infinite time, via the construction of a modified scattering theorem.Updated on Nov 16, 2018 09:39 AM PST 
Hamiltonian Postdoc Workshop: The effect of threshold energy obstructions on the L 1 → L∞ dispersive esti mates for some Schr ̈odinger type equations
Location: MSRI: Simons Auditorium Speakers: Ebru Toprak (University of Illinois at 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 16, 2018 09:40 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 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 16, 2018 09:41 AM PST 
Hamiltonian Seminar: Construction of unstable KAM tori for a system of coupled NLS equations.
Location: MSRI: Simons Auditorium Speakers: Victor Vilaça Da Rocha (Basque Center for Applied Mathematics)The systems of coupled NLS equations occur in some physical problems, in particular in nonlinear optics (coupling between two optical waveguides, pulses or polarized components...). From the mathematical point of view, the coupling effects can lead to truly nonlinear behaviors, such as the beating effect (solutions with Fourier modes exchanging energy) of Grébert, Paturel and Thomann (2013).
In this talk, I will use the coupling between two NLS equations on the 1D torus to construct a family of linearly unstable tori, and therefore unstable quasiperiodic solutions. The idea is to take profit of the Hamiltonian structure of the system via the construction of a Birkhoff normal form and the application of a KAM theorem. In particular, we will see of this surprising behavior (this is the first example of unstable tori for a 1D PDE) is strongly related to the existence of beating solutions.
This is a work in collaboration with Benoît Grébert (Université de Nantes).
Updated on Nov 16, 2018 08:43 AM PST 
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 16, 2018 09:43 AM PST 
Hamiltonian Colloquium: C⁰ symplectic topology and dynamics
Location: MSRI: Simons Auditorium Speakers: Claude Viterbo (École Normale Supérieure)Created on Nov 16, 2018 10:48 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 03:32 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: 3D Billiards: visualization of the 4D phase space and powerlaw trapping of chaotic trajectories
Location: MSRI: Baker Board Room Speakers: Arnd BaeckerUnderstanding the transport properties of higherdimensional
systems is of great importance in a wide variety of applications,
e.g., for celestial mechanics, particle accelerators, or the
dynamics of atoms and molecules. A prototypical class of model
systems are billiards for which a Poincaré section leads to
discretetime map. For the dynamics in threedimensional
billiards a fourdimensional symplectic map is obtained which is
challenging to visualize. By means of the recently introduced 3D
phasespace slices an intuitive representation of the
organization of the mixed phase space with regular and chaotic
dynamics is obtained. Of particular interest for applications are
constraints to classical transport between different regions of
phase space which manifest in the statistics of Poincaré
recurrence times. For a 3D paraboloid billiard we observe a slow
powerlaw decay caused by longtrapped trajectories which we
analyze in phase space and in frequency space. Consistent with
previous results for 4D maps we find that: (i) Trapping takes
place close to regular structures outside the Arnold web. (ii)
Trapping is not due to a generalized islandaroundisland
hierarchy. (iii) The dynamics of sticky orbits is governed by
resonance channels which extend far into the chaotic sea. We find
clear signatures of partial transport barriers. Moreover, we
visualize the geometry of stochastic layers in resonance channels
explored by sticky orbits.
Reference:
3D Billiards: Visualization of Regular Structures and
Trapping of Chaotic Trajectories
M. Firmbach, S. Lange, R. Ketzmerick, and A. Bäcker,
Phys. Rev. E 98, 022214 (2018)
https://doi.org/10.1103/PhysRevE.98.022214 Created on Nov 15, 2018 09:09 AM PST 
Combinatorics Seminar: Cyclotomic factors of necklace polynomials.
Location: UC Berkeley Math (Evans Hall 939) Speakers: Trevor Hyde (University of Michigan)Updated on Nov 15, 2018 11:30 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 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: Singularity Theory for Nontwist Tori: from symplectic geometry to applications through analysis.
Updated on Nov 09, 2018 08:36 AM PST 
Seminar Chancellor Course: Topics in Analysis
Updated on Aug 17, 2018 03:31 PM PDT 
Seminar Hamiltonian Postdoc Workshop: A proof of Jones’ conjecture: counting and discounting periodic orbits in a delay differential equation
Updated on Nov 07, 2018 09:09 AM PST 
Seminar Hamiltonian Postdoc Workshop: Equilibrium quasiperiodic configurations in quasiperiodic media
Updated on Nov 07, 2018 08:54 AM PST 
Seminar Hamiltonian Postdoc Workshop: Optimal time estimate of the Arnold diffusion for analytic quasiconvex nearly integrable systems
Updated on Nov 07, 2018 08:53 AM PST 
Seminar Hamiltonian Postdoc Workshop: On the existence of exponentially decreasing solutions to time dependent hyperbolic systems
Updated on Nov 07, 2018 08:52 AM PST 
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 03:31 PM PDT 
Seminar Hamiltonian Colloquium: Hydrodynamics from Hamilton
Updated on Nov 06, 2018 08:48 AM PST 
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 Schrödinger equation near 1D quasiperiodic solutions
Updated on Oct 26, 2018 10:08 AM PDT