Abstract:
This presentation explores the role of renewal mechanisms in mathematical models of interacting particle systems, with a specific focus on integrate-and-fire neurons and pulse coupled oscillators. Renewal processes, where particles interact when renewal events take place, introduce singular interactions into the macroscopic descriptions of these systems, and the mean renewal rate may become the source of nonlinearity. We investigate the long-term behavior of these models, emphasizing the need for novel mathematical tools to handle their unique structure. Probability reformulations and a dynamical time rescaling emerge as crucial techniques in this analysis.
Biography:
Zhennan Zhou is an Assistant Professor at Beijing International Center for Mathematical Research (BICMR) of Peking University. He received his Ph.D. from the University of Wisconsin-Madison in 2014. Following his doctoral studies, he worked as an Assistant Research Professor at Duke University from 2014 to 2017. Later, he joined BICMR, Peking University in 2017. Dr. Zhou's research interests mainly include applied analysis of differential equations, numerical methods of differential equations, applied stochastic analysis, stochastic simulations, with a focus on applied mathematical problems arising from natural sciences.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.