Abstract: In this talk, we consider a competition between d+1 players, and aim to identify the “most exciting game” of this kind. This is translated, mathematically, into a stochastic optimization problem over martingales that live on the d-dimensional subprobability simplex and terminate on the vertices of the simplex, with a cost function related to a scaling limit of Shannon entropies. We uncover a surprising connection between this problem and the seemingly unrelated field of Monge-Ampère equations, and identify the optimal martingale via a detailed analysis of boundary asymptotics of a Monge-Ampère equation.

Speaker’s bio: Dr. Xin Zhang is an assistant professor in the Financial and Risk Engineering (FRE) department at New York University (NYU). Before joining NYU, he was a University Assistant at the University of Vienna from 2021 to 2024. He earned his Ph.D. in Mathematics from the University of Michigan in 2021, after completing a B.S. in Mathematics at Fudan University in 2016. Xin’s research focuses on optimal transport, stochastic analysis and control, particularly their applications in Finance and Machine Learning. His specific interests include viscosity solutions of nonlinear partial differential equations and optimal transport in robust finance. Please visit his website https://sites.google.com/umich.edu/xzhang/home for more information.

In the 19th century, Cantor discovered that infinities come in various sizes. In particular, he showed that the size (or cardinality) of the set of real numbers is strictly greater than the size of the set of natural numbers, even though both sets are infinite.

This discovery raised the question of whether there could be a size of infinity that is strictly between the size of the natural numbers and the size of the real numbers. The continuum hypothesis, written as CH, is the statement that there is no such infinite size. In this talk, we will explore these ideas in more detail and consider how mathematicians have tried to figure out whether CH is true or not.

Note: Free refreshments. The talk starts at 5:40.

Join us in the Logic Colloquium for a talk by Tyler Knowlton (Linguistics & Cognitive Science, U Delaware).

Details t.b.a.

https://logic.uconn.edu/calendar/

TBA

Note: Free refreshments. The talk starts at 5:40.

TBA

Note: Free refreshments. The talk starts at 5:40.

TBA

Join us in the Logic Colloquium for a talk by Matthew Chrisman (Edinburgh)!

Details t.b.a.

https://logic.uconn.edu/calendar/

TBA

https://mat.ufpb.br/jmbo/