Department of

# Mathematics

Seminar Calendar
for Graduate Probability Seminar events the year of Thursday, November 21, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     October 2019          November 2019          December 2019
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Thursday, January 24, 2019

2:00 pm in 347 Altgeld Hall,Thursday, January 24, 2019

#### Introduction to Percolation Theory

###### Grigory Terlov (UIUC Math)

Abstract: This is the first part of two talks designed to introduce students to Percolation Theory. We will describe the model, talk about infinite clusters, prove the existence of the phase transition, introduce the universality principle and more.

Thursday, January 31, 2019

2:00 pm in 347 Altgeld Hall,Thursday, January 31, 2019

#### Introduction to Percolation Theory (Part 2)

###### Grigory Terlov (UIUC Math)

Abstract: This is the second part of two talks designed to introduce students to Percolation Theory. We will discuss an upper bound for critical probability for $\mathbb{Z}^d$ via cut-sets and duality. This talk should be accessible for people who missed the first part.

Thursday, February 7, 2019

2:00 pm in 347 Altgeld Hall,Thursday, February 7, 2019

#### An Introduction to Dyson Brownian Motion and Universality

###### Kesav Krishnan (UIUC Math)

Abstract: We define Brownian motion on the space of N×N Hermitian Matrices, and derive an SDE for the corresponding process of the eigenvalues. We then establish that the eigenvalue process is identical to Brownian motion in R^n confined to the Weyl Chamber.

Thursday, February 14, 2019

2:00 pm in 347 Altgeld Hall,Thursday, February 14, 2019

#### An Introduction to Dyson Brownian Motion and Universality (Part 2)

###### Kesav Krishnan (UIUC Math)

Abstract: We will discuss the connections of Dyson Brownian Motion and the Totally Asymmetric Simple Exclusion Process (TASEP). This will be the first glimpse of the Kardar Parisi Zhang Universality class.

Thursday, April 11, 2019

2:00 pm in 347 Altgeld Hall,Thursday, April 11, 2019

#### Local Limit Theorem

###### Qiang Wu (UIUC Math)

Abstract: This talk is an introduction to some classical CLT variants, specifically on local limit theorem (LLT). The proof of classical LLT for lattice and non-lattice distribution will be discussed using the characteristic approach. Other various generalizations of LLT will be pointed out. Finally, a concise combinatorial approach for LLT of simple random walk will be sketched. Time permits, I will talk about the generalized Berry-Esseen Inequality.

Thursday, April 18, 2019

2:00 pm in 347 Altgeld Hall,Thursday, April 18, 2019

#### Local Limit Theorem (Part 2)

###### Qiang Wu (UIUC Math)

Abstract: This talk the second part of an introduction to some classical CLT variants, specifically on local limit theorem (LLT). The proof of classical LLT for lattice and non-lattice distribution will be discussed using the characteristic approach. Other various generalizations of LLT will be pointed out. Finally, a concise combinatorial approach for LLT of simple random walk will be sketched. Time permits, I will talk about the generalized Berry-Esseen Inequality.

Thursday, April 25, 2019

2:00 pm in 347 Altgeld Hall,Thursday, April 25, 2019

#### Coupling and its applications

###### Peixue Wu (UIUC Math)

Abstract: I will define what is coupling. The beginning example is the transport problem, which leads to the concepts of optimal coupling and probability distance. We will also talk about applications of coupling to study ergodicity, gradient estimate and Harnack's inequality for Markov processes.

Thursday, August 29, 2019

2:00 pm in 347 Altgeld Hall,Thursday, August 29, 2019

#### Organizational Meeting

Thursday, September 5, 2019

2:00 pm in 347 Altgeld Hall,Thursday, September 5, 2019

#### Introduction to Random Planar Maps

###### Grigory Terlov (UIUC Math)

Abstract: A "typical" continuous curve on a plane looks like a path of Brownian motion. A natural next question we might ask is "what does a "typical" continuous 2d-surface looks like?" One of the ways to construct such a model is to find a discrete object and consider a scaling limit of it (analogous to considering a scaling limit of a random walk to construct Brownian motion). Such objects are called random planar maps - planar multi-graphs embedded in a sphere or a plane. Of course, similarly to random walks, there are many other reasons why these discrete objects are interesting. In these two talks we will consider several ways of defining random planar maps and a measure on them, connections with random walks and random trees. Finally, in the remaining time I will try to mention several highlights of the field in connection with combinatorics, percolation theory, scaling limits, and Ergodic theory.

Thursday, September 12, 2019

2:00 pm in 347 Altgeld Hall,Thursday, September 12, 2019

#### Introduction to Random Planar Maps part 2

###### Grigory Terlov (UIUC Math)

Abstract: The main focus of the second part of this talk is to discuss bisections between random bipartite planar maps and decorated Galton Watson trees. Then if time permits we will continue connecting this model with other areas of probability that audience might be familiar with and/or interested in exploring.

Thursday, September 19, 2019

2:00 pm in 347 Altgeld Hall,Thursday, September 19, 2019

#### The Yang Mills Problem for Probabilists

###### Kesav Krishnan (UIUC math)

Abstract: We aim to introduce the problem of rigorously defining the Yang-Mills field from the probability perspective. In this first talk, we will introduce lattice guage theory, and some geometric preliminaries

Thursday, October 3, 2019

2:00 pm in 347 Altgeld Hall,Thursday, October 3, 2019

#### Introduction to Spin Glasses Part I

###### Qiang Wu (UIUC Math)

Abstract: I will introduce some spin glass models in the first talk, such as Curie-Weiss(CW) model, Sherrington-Kirkpatrick(SK) model etc, then particularly discuss the high temperature analysis of SK model by Guerra’s interpolation.

Tuesday, October 8, 2019

2:00 pm in 347 Altgeld Hall,Tuesday, October 8, 2019

#### Introduction to Spin Glasses Part II

###### Qiang Wu (UIUC Math)

Abstract: This time we will discuss the parisi formula of free energy, I will describe how to derive the formula along with the parisi PDE. If time permits, ultrametricity of asymptotic Gibbs measure will be briefly introduced from probabilistic and geometric view.

Thursday, October 17, 2019

2:00 pm in 347 Altgeld Hall,Thursday, October 17, 2019

#### Branching Processes Part 1

###### Peixue Wu (UIUC Math)

Abstract: The first part of this talk is very introductory, I will talk about the basic ideas of branching mechanism (originated from random walk) and some generalizations of the simple branching process, e.g., age-dependent processes, multi-type branching process. ​I will focus on the limit theorem of branching processes.​ ​In the second part, I will talk about the superprocess (which is measure-valued branching processes) and some recent works about it.

Thursday, October 24, 2019

2:00 pm in 347 Altgeld Hall,Thursday, October 24, 2019

#### Branching Processes Part 2

###### Peixue Wu (UIUC Math)

Abstract: The first part of this talk is very introductory, I will talk about the basic ideas of branching mechanism (originated from random walk) and some generalizations of the simple branching process, e.g., age-dependent processes, multi-type branching process. ​I will focus on the limit theorem of branching processes.​ ​In the second part, I will talk about the superprocess (which is measure-valued branching processes) and some recent works about it.

Thursday, November 14, 2019

2:00 pm in 347 Altgeld Hall,Thursday, November 14, 2019

#### Probabilistic solutions for fluid systems and stochastic Noether-Kelvin theorem

###### Jianyu Hu (UIUC Math)

Abstract: In this talk, we will study a probabilistic representations for the fluid systems based on stochastic Lagrangian paths. Unlike the Feynman-Kac formula, this theorem is a representation for nonlinear equations. When the systems have some noise, we will study the stochastic Noether-Kelvin theorem for a class of stochastic fluid equations. In general, the solutions of these systems do not preserve energy conservation, but rather than circulation conservation.