The CUNY Probability Seminar will be held by videoconference for the rest of the semester. Its usual time will be Tuesdays from 3:30 to 4:30. Exact dates, times and locations are mentioned below. If you want to talk at the seminar, or want to be added to/removed from the seminar mailing list, then please contact the Seminar Coordinator.
Shirshendu Chatterjee (http://shirshendu.ccny.cuny.edu/)
Tuesday, , 4:30-5:30 pm EST
Videoconference Link: Zoom
Time: October 6, 3:30 – 4:30 pm EST
Speaker: Winston Heap; Max Planck Institute
Title: Random multiplicative functions and a model for the Riemann zeta function
Abstract: We look at a weighted sum of random multiplicative functions and view this as a model for the Riemann zeta function. We investigate various aspects including its high moments, distribution and maxima.
Time: September 01, 3:30 – 4:30 pm EST
Speaker: Matthew Junge; Baruch College; Department of Mathematics, CUNY
Title: Modeling COVID-19 Spread in Small Colleges
Abstract: Many colleges are reopening amid Fall 2020 of the COVID-19 pandemic with extreme measures in place: testing, dedensification, building closures, among others. We develop an agent-based network model to test intervention effectiveness. Our focus is on small colleges, which in aggregate serve over one million U.S. students, and have not been considered in-depth by existing models. We will survey how COVID-19 predictions are made for large areas like countries and cities, then go into detail about the models that came out this summer for disease spread on college campuses. From there, we will describe our model and findings. One of the more striking findings suggests that building closures may have unintended negative consequences. This is part of a broader observation that how students conduct themselves will determine if they get to enjoy, albeit a bit differently, the benefits of college life, or pass another year learning from a screen in their bedroom. Preprint available at https://arxiv.org/abs/2008.09597.
Time: September 08, 4:30 – 5:30 pm EST
Speaker: Emma Bailey; Graduate Center, CUNY
Title: Branching random walks and moments of moments
Abstract: Recently there has been a great deal of interest in understanding the moments of partition functions of logarithmically correlated processes. In this talk, I will present results for the moments of the partition function for a branching random walk on a binary tree of depth n with Gaussian weightings. We obtain explicit formulae for the first few moments, and in the large n limit, our expression coincides with recent conjectures and results for the moments of moments of characteristic polynomials of random unitary matrices. This is joint work with Jon Keating.
Time: September 15, 4:45 – 5:45 pm EST
Speaker: Yanghui Liu; Baruch College, CUNY
Title: Discrete rough paths and numerical approximations.
Abstract: In this talk, I will focus on a series of results concerning the numerical approximation of rough integration and rough differential equations, as well as the Malliavin differentiability and weak convergence problems of numerical schemes. I will explain the links between numerical approximations and weighted random sums, and show how to transfer limits taken on a Gaussian signature to limits involving controlled processes, by means of the typical expansions of the rough-paths theory. I will try to introduce most of my notations carefully, and keep the needed stochastic analysis to a minimum level. The talk does not require the rough-path background.
Time: September 22, 4:30-5:30 pm EST
Speaker: Wai Tong (Louis) Fan, Indiana University, Bloomington.
Title: Stochastic PDE as scaling limits of interacting particle systems
Abstract: Interacting particle models are often employed to gain an understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as the efficiency and robustness of macroscopic models.
In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics.
Time: October 06, 4:30-5:30 pm EST
Speaker: Winston Heap, Max Planck Institute for Mathematics.
Time: October 13, 4:30-5:30 pm EST
Speaker: Sayan Banerjee, University of North Carolina, Chapel Hill.