Mon, 14 May 2018
17:00
L5

G-actions in quantum mechanics and Koszul duality

Tudor Dimofte
(University of California, Davis)
Abstract

 I will discuss the quantum-field-theory origins of a classic result of Goresky-Kottwitz-MacPherson concerning the Koszul duality between the homology of G and the G-equivariant cohomology of a point. The physical narrative starts from an analysis of supersymmetric quantum mechanics with G symmetry, and leads naturally to a definition of the category of boundary conditions in two-dimensional topological gauge theory, which might be called the "G-equivariant Fukaya category of a point." This simple example illustrates a more general phenomenon (also appearing in C. Teleman's work in recent years) that pure gauge theory in d dimensions seems to control the structure of G-actions in (d-1)-dimensional QFT. This is part of joint work with C. Beem, D. Ben Zvi, M. Bullimore, and A. Neitzke.

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. 

Mon, 11 Jun 2018

15:45 - 16:45
L3

An order/disorder perturbation of percolation model. A highroad to Cardy's formula.

MIKHAIL KHRISTOFOROV
(University of Geneve)
Abstract

We will discuss the percolation model on the hexagonal grid. In 2001 S. Smirnov proved conformal invariance of its scaling limit through the use of a tricky auxiliary combinatorial construction.

We present a more conceptual approach, implying that the construction in question can be thought of as geometrically natural one.

The main goal of the talk is to make it believable that not all nice and useful objects in the field have been already found.

No background is required.

Mon, 11 Jun 2018

14:15 - 15:15
L3

Gradient estimates and applications to nonlinear filtering

CHRISTIAN LITTERER
(University of York)
Abstract

We present sharp gradient estimates for the solution of the filtering equation and report on its applications in a high order cubature method for the nonlinear filtering problem.

Mon, 04 Jun 2018

15:45 - 16:45
L3

Genetic isolation by distance in a random environment

RAPHAEL FORIEN
(Ecole Polytechnique (ParisTech))
Abstract

I will present a mathematical model for the genetic evolution of a population which is divided in discrete colonies along a linear habitat, and for which the population size of each colony is random and constant in time. I will show that, under reasonable assumptions on the distribution of the population sizes, over large spatial and temporal scales, this population can be described by the solution to a stochastic partial differential equation with constant coefficients. These coefficients describe the effective diffusion rate of genes within the population and its effective population density, which are both different from the mean population density and the mean diffusion rate of genes at the microscopic scale. To do this, I will present a duality technique and a new convergence result for coalescing random walks in a random environment.

 

Mon, 04 Jun 2018

14:15 - 15:15
L3

Laws of large numbers for a set of probability measures

ZENGJING CHEN
(Shandong University)
Abstract

In this paper, we investigate the limit properties of frequency of empirical averages when random variables are described by a set of probability measures and obtain a law of large numbers for upper-lower probabilities. Our result is an extension of the classical Kinchin's law of large numbers, but the proof is totally different.

keywords: Law of large numbers,capacity, non-additive probability, sub-linear expectation, indepence

paper by: Zengjing Chen School of Mathematics, Shandong University and Qingyang Liu Center for Economic Research, Shandong University

Mon, 21 May 2018

15:45 - 16:45
L3

Invariants of the signature

JOSCHA DIEHL
(Max Planck Institute Leipzig)
Abstract

Based on classical invariant theory, I describe a complete set of elements of the signature that is invariant to the general linear group, rotations or permutations.

A geometric interpretation of some of these invariants will be given.

Joint work with Jeremy Reizenstein (Warwick).

Mon, 21 May 2018

14:15 - 15:15
L3

Algebraic flow

DANYU YANG
(Norwegian University of Science and Technology)
Abstract

We present an algebraic formulation for the flow of a differential equation driven by a path in a Lie group. The formulation is motivated by formal differential equations considered by Chen.

Mon, 14 May 2018

15:45 - 16:45
L3

Unbounded Rough Drivers, Sobolev Spaces and Moser Iteration

ANTOINE HOCQUET
(Technische Universitat Berlin)
Abstract

Recently, Deya, Gubinelli, Hofmanova and Tindel ('16) (also Bailleul-Gubinelli '15) have provided a general approach in order to obtain a priori estimates for rough partial differential equations of the form
(*)    du = Au dt + Bu dX
where X is a two-step rough path, A is a second order operator (elliptic), while B is first order. We will pursue the line of this work by presenting an L^p theory "à la Krylov" for generalized versions of (*). We will give an application of this theory by proving boundedness of solutions for a certain class

Mon, 14 May 2018

14:15 - 15:15
L3

Statistical Arbitrage in Black-Scholes Theory

WEIAN ZHENG
(UCI China)
Abstract

The celebrated Black-Scholes theory shows that one can get a risk-neutral option price through hedging. The Cameron-Martin-Girsanov theorem for diffusion processes plays a key role in this theory. We show that one can get some statistical arbitrage from a sequence of well-designed repeated trading at their prices according to the ergodic theorem for stationary process. Our result is based on both theoretical model and the real market data. 

 

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