Fri, 20 May 2022

16:00 - 18:30
L1

Guest Speakers Seminar

Prof. Luis Caffarelli and Prof. Irene Gamba
(University of Texas at Austin)
Further Information

Event Timings:

16:00 – 16:10 Refreshments (Served in the North Mezzanine)

16:10 – 17:10  Talk by Prof. Luis Caffarelli

17:10 – 17:30 Refreshments Break (20mins - Served in the North Mezzanine)

17:30 – 18:30 Talk by Prof Irene Martínez Gamba

Each talk will have a Q&A afterwards.

Register your interest HERE

Abstract

 

 

Title: Topics on regularity theory for fully non-linear integro-differential equations

Abstract: We will focus on local and non-local Monge Ampere type equations, equations with deforming kernels and convex envelopes of functions with optimal special conditions. We discuss global solutions and their regularity properties.

 

Title: Quasilinear Conservative Collisional Transport in Kinetic Mean Field models

AbstractWe shall focus the on the interplay of nonlinear analysis  and numerical approximations to mean field models in particle physics where kinetic transport flows in momentum are strongly nonlinearly  modified by macroscopic quantities in classical or spectral density spaces. Two noteworthy models arise: the classical Fokker-Plank Landau dynamics as a low magnetized plasma regimes in the modeling of perturbative non-local high order terms. The other one corresponds to perturbation under strongly magnetized dynamics for fast electrons  in momentum space  give raise to a coupled system of classical kinetic diffusion processes described by the balance equations for electron probability density functions (electron pdf) coupled to the time dynamics on spectral energy waves  (quasi-particles) in a quantum process of their resonant interaction. Both models are rather different, yet there are derived form the Liouville-Maxwell system under different scaling. Analytical tools and some numerical  simulations show a presence of  strong hot tail anisotropy  formation taking the stationary states away from Classical equilibrium solutions stabilization for the iteration in a three dimensional cylindrical model. The semi-discrete schemes preserves the total system mass, momentum and energy, which are enforced by the numerical scheme. Error estimates can be obtained as well.

Work in collaboration with Clark Pennie and Kun Huang

Mon, 21 Jun 2021
14:15
Virtual

Floer homotopy theory and Morava K-theory

Andrew Blumberg
(University of Texas at Austin)
Abstract

I will describe joint work with Abouzaid which constructs a stable homotopy theory refinement of Floer homology that has coefficients in the Morava K-theory spectra. The classifying spaces of finite groups satisfy Poincare duality for the Morava K-theories, which allows us to use this version of Floer homology to produce virtual fundamental chains for moduli spaces of Floer trajectories. As an application, we prove the Arnold conjecture for ordinary cohomology with coefficients in finite fields.

Mon, 18 May 2020
15:45
Virtual

Boundaries and 3-dimensional topological field theories

Dan Freed
(University of Texas at Austin)
Abstract

Just as differential equations often boundary conditions of various types, so too do quantum field theories often admit boundary theories. I will explain these notions and then discuss a theorem proved with Constantin Teleman, essentially characterizing certain 3-dimensional topological field theories which admit nonzero boundary theories. One application is to gapped systems in condensed matter physics.

Thu, 27 Feb 2020

14:00 - 15:00
L4

Randomised algorithms for solving systems of linear equations

Gunnar Martinsson
(University of Texas at Austin)
Abstract

The task of solving large scale linear algebraic problems such as factorising matrices or solving linear systems is of central importance in many areas of scientific computing, as well as in data analysis and computational statistics. The talk will describe how randomisation can be used to design algorithms that in many environments have both better asymptotic complexities and better practical speed than standard deterministic methods.

The talk will in particular focus on randomised algorithms for solving large systems of linear equations. Both direct solution techniques based on fast factorisations of the coefficient matrix, and techniques based on randomised preconditioners, will be covered.

Note: There is a related talk in the Random Matrix Seminar on Tuesday Feb 25, at 15:30 in L4. That talk describes randomised methods for computing low rank approximations to matrices. The two talks are independent, but the Tuesday one introduces some of the analytical framework that supports the methods described here.

Mon, 11 Jun 2018
15:45
L2

Moduli stacks of vacua in geometric representation theory

David Ben-Zvi
(University of Texas at Austin)
Abstract

Topological field theories give rise to a wealth of algebraic structures, extending
the E_n algebra expressing the "topological OPE of local operators". We may interpret these algebraic structures as defining (slightly noncommutative) algebraic varieties and stacks, called moduli stacks of vacua, and relations among them. I will discuss some examples of these structures coming from the geometric Langlands program and their applications. Based on joint work with Andy Neitzke and Sam Gunningham. 

Thu, 08 Mar 2018

14:30 - 15:30
L5

tba

Thaleia Zariphopoulou
(University of Texas at Austin)
Fri, 26 Feb 2016

13:00 - 14:00
L3

Tunneling in Theories with Many Fields

Sonia Paban
(University of Texas at Austin)
Abstract

The possibility of a landscape of metastable vacua raises the question of what fraction of vacua are truly long lived. Naively any would-be vacuum state has many nearby decay paths, and all possible decays must be suppressed. An interesting model of this phenomena consists of N scalars with a random potential of fourth order. We show that the scaling of the typical minimal bounce action with N is readily understood. We discuss the extension to more realistic landscape models as well as the effects of gravity. 

Thu, 12 Mar 2015

16:00 - 17:00
C2

Multiplicative quiver varieties and their quantizations

Iordan Ganev
(University of Texas at Austin)
Abstract

Quiver varieties and their quantizations feature prominently in
geometric representation theory. Multiplicative quiver varieties are
group-like versions of ordinary quiver varieties whose quantizations
involve quantum groups and $q$-difference operators. In this talk, we will
define and give examples of representations of quivers, ordinary quiver
varieties, and multiplicative quiver varieties. No previous knowledge of
quivers will be assumed. If time permits, we will describe some phenomena
that occur when quantizing multiplicative quiver varieties at a root of
unity, and work-in-progress with Nicholas Cooney.

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