Department of Mathematics

Integral equations with nonlocal operators: applications and recent development Qiang Du, Columbia University  Recent applications and theoretical developments of models of integral equations using nonlocal operators have shown promise as effective alternatives to local models, especially in the presence of singularities and…

Computing high dimensional Wasserstein geometric flows in neural network parameter space Haomin Zhou, Georgia Tech Machine learning based strategies have impacted computational mathematics significantly in recent years. Many used-to-be intractable tasks such as solving high dimensional PDEs or computing solution operators for…

Jeff Danciger, University of Texas at Austin The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry.  It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have…

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.…