JANUARY SPEAKERS

January 30th, 12pm
Speaker: Herbert Spohn, IAS Princeton and Technical University Munich
Title/Abstract: "Equilibrium time correlations of anharmonic chain"
Location: Hill Center Building (Busch Campus), Room 705


BROWN BAG LUNCH FROM 1-2PM

January 30th, 2pm
Speaker: Abhishek Dhar, Indian Institute of Science
Title/Abstract: "Heat conduction in the asymmetric Fermi-Pasta-Ulam chain"
Location: Hill Center Building (Busch Campus), Room 705





FEBRUARY SPEAKERS
February 6th, 12pm & 2pm (Two-part seminar)
Speaker: David Huse, Princeton University
Title/Abstract: "Eigenstate statistical mechanics: thermalization and localization"(Part I & II)
Location: Hill Center Building (Busch Campus), Room 705


BROWN BAG LUNCH FROM 1-2PM

February 13th, 12pm
Speaker: Herbert Spohn, IAS Princeton and TUM Munich
Title/Abstract: "The KPZ equation and its universality class: replica solutions"
Location: Hill Center Building (Busch Campus), Room 705


BROWN BAG LUNCH FROM 1-2PM

February 13th, 2pm
Speaker: Jeremey Quastel, IAS Princeton and University of Toronto
Title/Abstract: "The KPZ equation and its universality class: exact solutions"
Location: Hill Center Building (Busch Campus), Room 705


BROWN BAG LUNCH FROM 1-2PM

February 20th, 12pm
Speaker: Haim Brezis, Rutgers University
Title/Abstract: "New approximations of the total variation and filters in Image Processing"
Location: Hill Center Building (Busch Campus), Room 705


February 20th, 2pm
Speaker: TBA
Title/Abstract: TBA
Location: Hill Center Building (Busch Campus), Room 705


February 27th, 12pm
Speaker: TBA
Title/Abstract: TBA
Location: Hill Center Building (Busch Campus), Room 705


February 27th, 2pm
Speaker: TBA
Title/Abstract: TBA
Location: Hill Center Building (Busch Campus), Room 705





MARCH SPEAKERS
March 6th, 12PM
Speaker: Jozsef Beck, Rutgers University
Title: "Uniform distribution and the Second Law"
Abstract: We study the typical time evolution of deterministic many-particle systems in motion in a closed environment, e.g., point billiards in a box or on a torus or on a sphere, also oscillating systems where the particles move on closed curves or on infinite curves wrapped up on a bounded surface (quasi-periodic motions). We focus on the following 4 questions: (1) what is (spatial) equilibrium; (2) how long does it take to reach (spatial) equilibrium; (3) how to define an intrinsic (spatial) entropy; (4) how to prove a Second Law.
Location: Hill Center Building (Busch Campus), Room 705


BROWN BAG LUNCH FROM 1-2PM

March 6th, 2PM
Speaker: Pierre Germain, Courant Institute
Title: "An extension of the Derrida-Lebowitz-Speer-Spohn equation"
Abstract: The Derrida-Lebowitz-Speer-Spohn (DLSS) equation is a PDE which was introduced as the continuum limit for the invariant measure in a spin model related to random interfaces. It recently drew a lot of attention as a nonlinear diffusion model. By revisiting the original derivation, we were able to find a higher order correction to the DLSS equation, in the so-called biased case. The resulting PDE could exhibit a trend to equilibrium, which makes it relevant from a probabilistic point of view. This is joint work with Charles Bordenave.
Location: Hill Center Building (Busch Campus), Room 705


March 13th, 12PM
Speaker: Peter Pickl, LMU
Title: "Dynamics of Sound Waves in an Interacting Bose Gas"
Abstract: We consider a non-relativistic quantum gas of $N$ bosonic atoms confined to a box of volume $\Lambda$ in physical space. The atoms interact with each other through a pair potential whose strength is inversely proportional to the density, $\rho=\frac{N}{\Lambda}$, of the gas. We study the time evolution of coherent excitations above the ground state of the gas in a regime of large volume $\Lambda$ and small $\frac{\Lambda}{\rho}$. The initial state of the gas is assumed to be close to a \textit{product state} of one-particle wave functions that are approximately constant throughout the box. The initial one-particle wave function of an excitation is assumed to have a compact support independent of $\Lambda$. We derive an effective non-linear equation for the time evolution of the one-particle wave function of an excitation and establish an explicit error bound tracking the accuracy of the effective non-linear dynamics in terms of the fraction $\frac{\Lambda}{\rho}$. We conclude with a discussion of the dispersion law of low-energy excitations, recovering Bogolyubov's well-known formula for the speed of sound in the gas, and a dynamical instability for attractive two-body potentials.
Location: Hill Center Building (Busch Campus), Room 705



BROWN BAG LUNCH FROM 1-2PM

March 13th, 2PM
Speaker: Thierry Bodineau, École Normale Supérieure
Title: "Lyapunov functionals for boundary-driven nonlinear drift-diffusions"
Abstract: We will describe a large class of Lyapunov functionals for nonlinear drift-diffusion equations with non-homogeneous Dirichlet boundary conditions. These are generalizations of large deviation functionals for underlying stochastic many-particle systems, the zero range process and the Ginzburg-Landau dynamics. More generally, we will discuss the connection between Lyapunov functionals and large deviation functionals of particle systems.
Location: Hill Center Building (Busch Campus), Room 705


March 28th, 1:30PM
Speaker: Michael Loss, Georgia Tech
Title: "The Kac model coupled to a thermal bath"
Abstract: I present a model of randomly colliding particles interacting with a thermal bath. Collisions between particles are modeled via the Kac master equation while the thermostat is seen as an infinite gas at thermal equilibrium at inverse temperature $\beta$. The system admits the canonical distribution at inverse temperature $\beta$ as the unique equilibrium state. I talk about a number of issues but chief among them is the rate at which the system tends to equilibrium, both, in the sense of the spactral gap and in the sense of relative entropy. This is joint work with Federico Bonetto and Ranjini Vaidyanathan.
Location: Hill Center Building (Busch Campus), Room 705



APRIL SPEAKERS
March 31st - April 4th
Topic: Workshop on Random Matrices and Random Systems
Location: Institute for Advanced Study
Please visit this link for details: https://www.math.ias.edu/wrmrs/agenda

April 10th, 12PM
Speaker: Herbert Spohn, IAS Princeton and Technical University Munich
Title: "The KPZ equation and its universality class: replica solutions"
Abstract: In 1986 Kardar Parisi and Zhang proposed a stochastic PDE for interface motion. On the one-dimensional case (two-dimensional bulk and one-dimensional interface) there has been much activity recently. In my talk I provide some physical background and discuss replica solutions which are based on the Lieb Liniger delta-Bose gas with attractive interactions.
Location: Hill Center Building (Busch Campus), Room 705


BROWN BAG LUNCH FROM 1-2PM

April 10th, 2PM
Speaker: Jeremy Quastel, IAS and University of Toronto
Title: "The KPZ equation and its universality class: exact solutions"
Abstract: We will survey recent progress on exact formulas for fluctuations of the KPZ equation and models in the universality class.
Location: Hill Center Building (Busch Campus), Room 705




MAY SPEAKERS
May 1st, 12PM
Clement Mouhot, University of Cambridge Title: "Factorization of semigroups and applications to PDEs" Abstract: We will present a general factorization method for estimating growth of semigroups in Banach spaces for a class of operators, and discuss various applications for linear and nonlinear PDEs of Boltzmann and Fokker-Planck types.

THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM. PLEASE JOIN US

May 1st, 2PM
Subhro Ghosh, Princeton University Title: "Rigidity phenomena in random point sets and applications" Abstract: In several naturally occurring (infinite) point processes, we show that the number (and other statistical properties) of the points inside a finite domain are determined, almost surely, by the point configuration outside the domain. This curious phenomenon we refer to as "rigidity". We will discuss rigidity phenomena in point processes and their applications. Depending on time, we will talk about applications to stochastic geometry and to random instances of some classical questions in Fourier analysis.