Department of Mathematics

Jiaping Wang, U. Minnesota Abstract: The classical de Rham-Hodge theory implies that each cohomology class of a compact manifold is uniquely represented by a harmonic form, signifying the important role of Laplacian in geometry. The talk aims to explain some results concerning the size and structure of its spectrum. After a brief…

Jiaping Wang, U. Minnesota Abstract: The entropy rate of a stationary sequence of random symbols was introduced by Shannon in his foundational work on information theory in 1948.  In the early 1950s, Kolmogorov and Sinai realized that they could turn this quantity into an isomorphism invariant for measure-preserving…

Dr. Guofang Wei, UCSB Abstract: It is of general interest to study the difference between Ricci and sectional curvature lower bound. A well known difference is their control on Betti numbers. Recently, joint with J. Pan, we constructed manifolds/singular spaces with nonnegative Ricci curvature which give negative answers to two…

Dr. Zhiqin Lu, UC Irvine Abstract: In this talk, we present the proof of the following theorem: let M be a complete non-compact Riemannian manifold whose curvature goes to zero at infinity, then its essential spectrum of the Laplacian on differential forms is a connected set. In particular, we study the case of form spectrum when…

Spatial Ecology & Singularly Perturbed Reaction-Diffusion Equations Prof. Arjen Doelman, Mathematisch Instituut, Lorentz Center; Leiden University, The Netherlands Abstract: Pattern formation in ecological systems is driven by counteracting feedback mechanisms on widely different spatial scales. Moreover, ecosystem models…

M. Susan Montgomery, USC Orthogonal representations: from groups to Hopd algebras to tensor categories Let G be a finite group and V a finite dimensional representation of G over the complex numbers. According to a wonderful theorem of Frobenius and Schur from 1906, there are only three possibilities for V: V has a…

Catherine Searle, Wichita State University Positively curved manifolds are notoriously hard to classify. In the early 90's, based on the observation that the few known examples are all highly symmetric, Karsten Grove proposed his "Symmetry Program" which suggests trying to classify such manifolds with the additional hypothesis of…

Burton Jones Lecture Information: Bill Goldman, University of Maryland May 11th - Skye Hall 284 Classification of Geometric Structures on Manifolds In 1872 F. Klein, based on ideas of S. Lie, proposed that the classical geometries be understood via the theory of transformation groups and homogeneous spaces. Later in the…