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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