# Graduate Student Probability Seminar

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### FALL 2021

This semester, we will meet Fridays at 10am and read the book Stochastic Analysis *Itô and Malliavin Calculus in Tandem*
by Hiroyuki Matsumoto and Setsuo Taniguchi. We decided to run the seminar online and if you are interested you can join us. Please send an e-mail to sefika.kuzgun@ku.edu.

Following you can find the schedule which will be updated each week.

Oct 15

**Speaker:** Josué Knorst

**Title:** Brownian motion and the Laplacian (1)

Oct 8

**Speaker:** Chen Ma

**Title:** Stochastic Integrals and Ito's Formula (3)

Oct 1

**Speaker:** Chen Ma

**Title:** Stochastic Integrals and Ito's Formula (2)

Sept 24

**Speaker:** Chen Ma

**Title:** Stochastic Integrals and Ito's Formula

Sept 17

**Speaker:** Ray Zhang

**Title: ** Adapted Brownian Motion and analogy to Path Integrals

Sept 10

**Speaker:** Ray Zhang

**Title: **Continuous Time Martingales

Sept 3

**Speaker:** Ray Zhang

**Title: **Fundamentals of Continuous Stochastic Processes

Aug 27

**Title: **Organizational Meeting

### SPRING 2021

This semester, we will meet Mondays at 3pm and read the book Conformally Invariant Process in the Plane
by Gregory Lawler together with the book Schramm-Loewner Evolution by Antti Kemppainen. Zoom link will be provided upon request. Please send an e-mail to sefika.kuzgun@ku.edu.

Following you can find the schedule which will be updated each week.

Apr 26

**Speaker:** Ray Zhang

**Title: **Advanced Properties of SLE

Apr 19

**Speaker:** Sefika Kuzgun

**Title: **Bessel Processes

Apr 5

**Speaker:** Ray Zhang

**Title: **Loewner Differential Equation Review and Examples-2

Mar 29

**Speaker:** Ray Zhang

**Title: **Loewner Differential Equation Review and Examples-1

Mar 22

**Speaker:** Chen Ma

**Title: **Loewner Differential Equation-2

Mar 8

**Speaker:** Bhargob Saikia

**Title: **Loewner Differential Equation-1

Mar 1

**Speaker:** Ray Zhang

**Title: **Conformal Mappings-2

Feb 22

**Speaker:** Raul Bolanos

**Title: **Conformal Mappings-1

Feb 15

**Speaker:** Sefika Kuzgun

**Title: **Complex Brownian Motion

### FALL 2020

This semester, we will meet Wednesdays at 5pm and read the book Large Deviations
by S.R.S Varadhan.

Following you can find the tentative schedule of the presentations:

Sept 23

**Speaker:** Sefika Kuzgun

**Title:** Chapters 1&2 Introduction&Basic Formulation

Sept 30

**Speaker:** Ray Zhang

**Title:** Sections 3.1&3.2 Exit Problem

Oct 7

**Speaker:** Mehmet Yenisey

**Title:** Sections 3.4-3.7 Superexponential Estimates

Oct 14

**Speaker:** Ray Zhang

**Title:** Sections 3.1&3.2 Exit Problem continued

Oct 21

**Speaker:** Chen Ma

**Title:** Sections 4.1-4.3 Large Time

Nov 11

**Speaker:** Guangqu Zheng

**Title:** Sections 4.4-4.8 Upper&Lower Bounds

Nov 18

**Speaker:** Ray Zhang

**Title:** Chapter 8 Some Comments about TASEP

**Abstract:** Interacting particle systems and their variants, such as TASEP, ASEP, DLPP, are interesting models in integrable probability and statistical physics. Plenty of large and moderate deviation results for these models have been derived via different approaches these decades and I will present some of these work. Proof will be discussed if time permits.

### SPRING 2020

This page is for information specifically to the Stochastic Analysis student seminar, which meets on **Wednesdays 2pm-3pm** in 456 Snow. This semester we decided to read the book Stochastic Analysis
by Ichiro Shigekawa. Following you can find the schedule:

** The ones marked as * are cancelled due to coronavirus.**

May 6

**Speaker:** Guangqu Zheng

**Title:** 6.3 Fundamental Estimate *

Apr 29

**Speaker:** Bhargob Saikia

**Title:** 6.2 Degenerate Stochastic differential equations*

Apr 22

**Speaker:** Bhargob Saikia

**Title:** 6.1 Stochastic differential equations*

Apr 15

**Speaker:** Raul Bolanos Guerrero

**Title:** 5.2 Smoothness of distributions defined by Wiener functionals*

Apr 8

**Speaker:** Raul Bolanos Guerrero

**Title:** 5.1 Absolute continuity of distributions*

Apr 1

**Speaker:** Sefika Kuzgun

**Title:** 4.2 Sobolev Spaces*

Mar 25

**Speaker:** Sefika Kuzgun

**Title:** 4.1 Equivalence of norms*

Mar 18

**Speaker:** Panqiu Xia

**Title:** 3.2 Littlewood-Paley-Stein inequality *

Mar 4

**Speaker:** Panqiu Xia

**Title:** 3.1 Fundamental inequalities

Feb 26

**Speaker:** Ray Zhang

**Title:** 2.2 Hypercontractivity and logarithmic Sobolev inequality

Feb 19

**Speaker:** Ray Zhang

**Title:** 2.1 Ornstein-Uhlenbeck semigroup

Feb 12

**Speaker:** Guangqu Zheng

**Title:**1.1&1.2 Wiener Space

### FALL 2019

This page is for information specifically to the Stochastic Analysis student seminar, which meets on **Tuesdays from 4-5:00 pm in 256 Snow** in the Fall 2019.

12 November

**Speaker:**Sefika Kuzgun

**Title:** Feynman-Kac formulas for the moments of the solution to stochastic heat equation

**Abstract:**I will introduce the Feymann-Kac formula for the moments of stochastic heat equation runned by space-time noise satisfying Dalang's condition.

5 November

**Speaker:**Ray Zhang

**Title:** An introduction to directed random polymers in random environment (3)

29 October

**Speaker:**Ray Zhang

**Title:**An introduction to directed random polymers in random environment (2)

22 October

**Speaker:**Ray Zhang

**Title:** An introduction to directed random polymers in random environment

**Abstract:** We will introduce the basic definitions and some simple examples for directed polymers in random environment, and derive the Markov property and the phase transition for the polymer model. If time permitting, we will see some results concerning the Log-Gamma polymer model and take a pedestrian view on the KPZ equation.

8 October

**Speaker:** Raul Bolanos Guerrero

**Title:** A central limit theorem for the stochastic heat equation

1 October

**Speaker:** Panqiu Xia

**Title:** Regularity and irregularity with (1+beta)-stable branching mechanism

**Abstract:** The aim of this talk is to present the paper "Regularity and irregularity with (1+beta)-stable branching mechanism" by Mytnik and Wechtel.

24 September

**Speaker:** Guangqu Zheng

**Title:** The renormalized self-intersection local time of planar Brownian motion

**Abstract:** We follow Le Gall's exposition for defining the self-intersection local time of planar Brownian motion, using Varadhan's renormalization method.

17 September

**Speaker:** Guangqu Zheng

**Title:** Exponential moments for the renornmalized self-intersection local time

**Abstract:** We will study Le Gall's idea (1994) on how to obtain the exponential moment for the renornmalized self-intersection local time of planar Brownian motion, we will also mention some recent work that applied his idea for SPDE.

10 September

**Speaker:** Raul Bolanos Guerrero

**Title:** Limit theorems for singular Skorohod integrals

### SPRING 2019

This semester, the Stochastic Analysis student seminar meets on **Fridays from 1:30-2:30 pm in 456 Snow**.

3 May

**Speaker:** Guangqu Zheng

**Title:** Central limit theorem for spatial averages of SPDEs

26 April

**Speaker:** Raul Bolanos Guerrero

**Title:** Malliavin calculus to study convergence in law of Skorohod integrals

19 April

**Speaker:**Guangqu Zheng

**Title:** Introduction to stochastic partial differential equations (3)

12 April

**Speaker:** Guangqu Zheng

**Title:** Introduction to stochastic partial differential equations (2)

5 April

**Speaker:** Guangqu Zheng

**Title:** Introduction to stochastic partial differential equations (1)

29 March

**Speaker:** Sefika Kuzgun

**Title:** Breuer-Major theorem

22 March

**Speaker:** Bhargob Saikia

**Title:** An introduction to anticipating stochastic calculus

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