Mathematics Colloquium

Mode: TBA Title: General-relativistic viscous fluids Abstract: In this talk, we will review some recent developments at the intersection of mathematics and physics regarding theories of relativistic fluids with viscosity. The discovery of the quark-gluon plasma that forms in heavy-ion … Read more

Mode: In- Person Title: Hodge theoretic generalizations of Satake-Baily-Borel Abstract: There are many ways to compactify a locally hermitian symmetric space.  Distinguished amongst this is a minimal compactification due to Satake.  I will give a general audience introduction to a … Read more

Mode: In-Person Title: Quantitative Diffeerentiation Abstract: Abstract: Quantitative differentiation deals with the behavior of function or geometric object at all locations and on all scales. We will give a relatively short elementary proof of the main theorem in the simplest … Read more

The mathematics and mechanics of bodies described by implicit constitutive equations Abstract. After first discussing the need for implicit constitutive relations to describe the response of both solids and fluids, I will then discuss applications wherein such implicit constitutive relations … Read more

Eigenfunction concentration and Weyl Laws via geodesic beams Abstract. A broad spectrum of physical phenomena, including the localization of quantum particles, is governed by the behavior of Laplace eigenvalues and eigenfunctions. This behavior is intrinsically connected to that of the … Read more

Shape-morphing modes for solving PDEs with conserved quantities Abstract. I introduce shape-morphing modes for efficient and scalable approximation of solutions to time-dependent PDEs. Numerical methods typically assume the solution of a PDE as the linear combination of static modes, such as … Read more

Stochastic and continuum modeling of protein polymer dynamics in neurons Abstract. Microtubules are protein polymers present in most cells; in neurons, microtubules are believed to be stable and to have specific orientations. This is crucial, since other key proteins get transported … Read more

Positive geometry Abstract. Positive geometries are topological spaces sitting inside algebraic varieties that generalize convex polytopes embedded in projective space. Examples of positive geometries appear in the study of total positivity, toric varieties, and configuration spaces. I will give a … Read more

Galois actions on cohomology of algebraic varieties Abstract. This talk will be an overview of a few big open problems which are of great importance in arithmetic algebraic geometry, number theory, and representation theory. The focus will be on the … Read more