Department of Mathematics

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…

Alena Erchenko, Dartmouth An Anosov manifold with boundary is a compact smooth Riemannian manifold M with strictly convex boundary, hyperbolic trapped set (possibly empty), and no conjugate points. We will discuss when M admits a codimension zero isometric embedding into a closed Riemannian manifold with Anosov geodesic flow and…

Thomas Bury, McGill University Critical transitions --- abrupt, qualitative changes in a system's dynamics --- occur in a wide range of natural systems, from the human heart to the earth's climate. In recent years, substantial research has focused on identifying early warning signals for these transitions using insights from…

Mingtao xia, New York university In this talk, I will introduce two novel wasserstein-distance-based uncertainty quantification methods | developed for aiming at quantifying intrinsic fluctuations and extrinsic noise with applications in reconstructing noisy single-cell molecular dynamics. The methods i shall discuss…