Department of Mathematics

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 non-…

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…

Dr. Kinnari Atit, School of Education, University of California at Riverside  In the U.S., there is a disparity between the number of students pursuing STEM and the number of professionals needed to meet global and economic demands. Of those that do pursue STEM, few are women or individuals from underrepresented minority…

Dr. Rafe Mazzeo, Stanford Gravitational instantons are some of the simplest Riemannian manifolds with special holonomy: they are noncompact, Ricci flat, hyperkähler four-manifolds. There is now a scheme for classifying all of them which is well underway. Many of these spaces arise as moduli spaces of solutions to certain gauge-…

Challenges and Advantages of a Principle-Based Calculus Course Speaker: Dr. David Weisbart, Department of Mathematics, University of California at Riverside Abstract: We will discuss what it means for a course to be principle-based and describe an underlying philosophy of teaching and learning that supports principle-based…

Fanghua Lin, Courant Institute, NYU Energy minimizing harmonic maps from a three-ball into the two-sphere are well understood. A natural existence question for a continuous harmonic map with a suitably given Dirichlet boundary value or in a given homotopic class [a problem that I learned from R.Schoen in mid-80s] remains open.  …

Nicola Garofalo, University of Padova, Italy & Arizona State University A basic problem in analysis is the Dirichlet problem for the Laplacian in the upper half-space. It is a classical fact that the trace of the Neumann derivative of the solution equals the half-Laplacian of the boundary datum. In a seminal 2007 paper…