Department of Mathematics

Dr. Renato Bettiol, Lehman College Minimal surfaces in elongated ellipsoids Imagine stretching an n-dimensional ellipsoid inside Euclidean space so that one of its semiaxes becomes very large. This causes a corresponding stretching of geometric objects that locally minimize length (geodesics) or area (minimal surfaces) inside…

Dick Canary, University of Michigan Abstract: Fuchsian groups arise naturally as groups of covering transformations of hyperbolic surfaces. One may view them as images of discrete faithful representation of free groups and surface groups into PSL(2,R). The study of hyperbolic surfaces and deformation spaces of Fuchsian groups is…

Damir Kinzebulatov, Université Laval, Canada I will discuss various realizations of Nash's method that allows us to study heat kernels of local and non-local Kolmogorov equations with singular drifts. The latter includes some drifts arising in particle systems with strong attracting interactions of Keller-Segel type.…

Tom Gannon, UCLA A time tested strategy used to answer questions about the representation theory of a Lie group is to translate them to questions on the geometry of its quotients. After giving a survey of representation theory aimed at a broad audience, I will describe the theorems I have obtained using this strategy, including…

Nicolle Gonzalez, UC Berkeley Catalan numbers are among the most ubiquitous objects in mathematics, arising naturally in combinatorics, representation theory, geometry, and many other areas. Although there are various polynomial generalizations of these numbers, particularly fruitful are the so-called (q,t)-Catalan polynomials.…

Xiaolong Li, Wichita State University In 1986, Nishikawa conjectured that a closed Riemannian manifold with positive (or nonnegative) curvature operator of the second kind is diffeomorphic to a spherical space form (or a Riemannian locally symmetric space, respectively). In this talk, I will begin with an overview of sphere…

Changhan He, UC Irvine Cell Pattern formation and cell-cell communication are critical processes that drive the organization and functionality of biological systems. This talk will introduce the investigations of these phenomena and their underlying mechanisms through the lens of multi-scale modeling and computational inference.…

Tingwei Meng, UCLA The convergence of artificial intelligence (AI) and applied mathematics offers transformative potential for addressing challenges in scientific computing and control. In this talk, I will highlight my research at the intersection of optimal control and modern AI methods, focusing on the development of scalable…