Department of

# Mathematics

Seminar Calendar
for Probability Seminar events the year of Tuesday, February 20, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2018          February 2018            March 2018
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6                1  2  3                1  2  3
7  8  9 10 11 12 13    4  5  6  7  8  9 10    4  5  6  7  8  9 10
14 15 16 17 18 19 20   11 12 13 14 15 16 17   11 12 13 14 15 16 17
21 22 23 24 25 26 27   18 19 20 21 22 23 24   18 19 20 21 22 23 24
28 29 30 31            25 26 27 28            25 26 27 28 29 30 31



Tuesday, January 23, 2018

2:00 pm in 347 Altgeld Hall,Tuesday, January 23, 2018

#### Effective Analytic Combinatorics in Several Variables

###### Steve Melczer (U. Penn.)

Abstract: The field of analytic combinatorics studies the asymptotic behaviour of sequences through analytic properties of their generating functions. In addition to the now classical univariate theory, recent work in the study of analytic combinatorics in several variables (ACSV) has shown how to derive asymptotics for the coefficients of certain D-finite functions by representing them as diagonals of multivariate rational functions. We detail the rich theory of ACSV from a computer algebra viewpoint, with an eye towards automatic implementations that can be used by those with no specialized knowledge in the field. Applications from several areas of combinatorics, number theory, and physics will be discussed.

Tuesday, January 30, 2018

2:00 pm in 347 Altgeld Hall,Tuesday, January 30, 2018

#### ​Stochastic (partial) differential equations with singular coefficients

###### ​Longjie Xie (Jiangsu Normal University & UIUC)

Abstract: It is a classical result that the ordinary differential equation is well-posed for Lipschitz coefficient but usually ill-posed if the coefficient is only Holder continuous. However, this dramatically changes if the system is perturbed by a noise. The purpose of this talk is to give a brief introduction and overview of the topic of regularization and well-posedness by noise for ordinary and partial differential equations.

Tuesday, February 6, 2018

2:00 pm in 347 Altgeld Hall,Tuesday, February 6, 2018

#### Effective modelling for some SPDEs

###### Wei Wang (Nanjing University & IIT)

Abstract: This talk introduce some effective modelling for some SPDEs with separated time scales. First we consider SPDEs with slow-fast part and averaging method is applied to derive the averaged approximation model. Normal deviation is also considered and large deviations further confirms the effectivity of the averaged equation plus the normal deviation. Second, we consider diffusion approximation for a Burgers type equation wit stochastic advection. By constructing a martingale, the approximation on both finite tie interval and infinite time interval is derived. Last the diffusion approximation is also applied to study the Smoluchowski-Kramers approximation for a nonlinear wave equation with state-dependent damping and random fluctuation.

Tuesday, March 6, 2018

2:00 pm in 255 Armory,Tuesday, March 6, 2018

#### Local density estimate for a hypoelliptic SDE

###### Cheng Ouyang (UIC Math)

Abstract: In a series of three papers in the 80’s, Kusuoka and Stroock developed a probabilistic program in order to obtain sharp bounds for the density function of a hypoelliptic SDE driven by a Brownian motion. We aim to investigate how their method can be used to study rough SDEs driven by fractional Brownian motions. In this talk, I will outline Kusuoka and Stroock’s approach and point out where the difficulties are in our current setting. The talk is based on an ongoing project with Xi Geng and Samy Tindel.

Tuesday, March 13, 2018

2:00 pm in 347 Altgeld Hall,Tuesday, March 13, 2018

#### The size of the boundary in first-passage percolation

###### Wai-Kit Lam (Indiana University Bloomington)

Abstract: First-passage percolation is a random growth model defined using i.i.d. edge-weights $(t_e)$ on the nearest-neighbor edges of $\mathbb{Z}^d$. An initial infection occupies the origin and spreads along the edges, taking time $t_e$ to cross the edge $e$. In this talk, we study the size of the boundary of the infected region at time $t$, $B(t)$. Under a weak moment condition on the weights, we show that for most times, $\partial B(t)$ has size of order $t^{d-1}$ (smooth). On the other hand, for heavy-tailed distributions, $B(t)$ contains many small holes, and consequently we show that $\partial B(t)$ has size of order $t^{d-1+\alpha}$ for some $\alpha > 0$ depending on the distribution. In all cases, we show that the exterior boundary of $B(t)$ (edges touching the unbounded component of the complement of $B(t)$) is smooth for most times. Under the unproven assumption of uniformly positive curvature on the limit shape for $B(t)$, we show the inequality $\partial B(t) \leq (log t)^C t^{d-1}$ for all large t. This is a joint work with Michael Damron and Jack Hanson.