Talk 1
Organizers：
吴昊，杨帆，姜建平，顾陈琳
Speaker：
Wei Wu 吴炜 (NYU Shanghai)
Time：
Wed., 4:00 - 5:00 pm, Nov. 27, 2024
Venue：
B626, Shuangqing Complex Building A
Title：
Maximum of the Ginsburg-Landau field
Abstract:
We consider the Ginzburg-Landau field with potential satisfying a uniform convexity condition, in two dimensions, and prove that its maximum upon centering is tight. Joint work with Florian Schweiger and Ofer Zeitouni.
About the speaker:
吴炜教授现任上海纽约大学数学副教授。加入上海纽约大学前曾在纽约大学柯朗数学研究所及华威大学任教。他的研究兴趣包括概率、数学物理和偏微分方程，专注于吉布斯随机场、自旋模型、相变和均质化等方面的课题。
Talk 2
Organizers：
吴昊，杨帆，姜建平，顾陈琳
Speaker：
Elena Kosygina (NYU Shanghai and CUNY)
Time：
Thur., 3:40 - 4:40 pm, Nov. 28, 2024
Venue：
C548, Shuangqing Complex Building A
Title：
Generalized Ray-Knight theorems: their applications and limitations
Abstract:
For several classes of self-interacting random walks on the integers, the generalized Ray-Knight theorems serve as the main tool for finding a candidate for a scaling limit and proving the convergence to that limiting process. A natural question to ask is whether theorems are not just a tool but whether, in fact, they uniquely identify the limiting process and, under some mild conditions, imply convergence. Recently, in a joint work with T. Mountford and J. Peterson, we showed that this need not be the case in general, and more information is needed to imply convergence. This negative answer prompted the follow-up question: would the joint generalized Ray-Knight theorems suffice for the task? In our ongoing project, we explore this idea for two classes of self-interacting random walks that were introduced and studied by B. Tóth in 1995-96.
About the speaker:
Elena Kosygina is a Visiting Professor of Mathematics at NYU Shanghai and a Professor of Mathematics at Baruch College and the CUNY Graduate Center. After completing her PhD at the Courant Institute of Mathematical Sciences, NYU, she was a (non-tenure-track) R. Boas Assistant Professor at Northwestern University, and then moved to CUNY to a tenure-track position and received tenure. She was a member of the Institute of Advanced Studies (Spring 2009) and a Simons Fellow in Mathematics (2014-2015).
Prof. Kosygina’s research is in probability, stochastic processes, and partial differential equations. In particular, she is interested in scaling limits of self-interacting random walks and in homogenization of Hamilton-Jacobi equations in random media.
