Math Department
Analysis Seminar – Christos Grigoriadis (Michigan State University)
ZoomTitle: Necessary and sufficient conditions in weighted theory Abstract: Starting with the L^p boundedness of the Hilbert transform by Riesz in 1928 we go through the development of weighted theory. First Muckenhoupt and the necessary and sufficient A_p condition for one weight inequalities, then Sawyer with the testing conditions on two weight inequalities leading up
Applied Math Seminar – Libin Rong (University of Florida)
ZoomTITLE: Recent developments in modeling HIV infection and treatment ABSTRACT: HIV infection is still a serious public health problem in the world. Highly active antiretroviral therapy can suppress viral replication to a very low level but cannot eradicate the virus. Mathematical models, combined with experimental data, have provided important insights into HIV dynamics, immune responses, and drug
Applied Math Seminar – Yuan Chen (Michigan State University)
ZoomTITLE: Geometry of curve lengthening membranes. ABSTRACT: In this talk, I’ll present rigorous results of the transient evolution of bilayer interfaces evolving of the mass preserving L^2-gradient flow of the functionalized Cahn-Hilliard equation. The proof is based on energy modulated method, which requires a construction of slow manifold – bilayer manifold, composed of approximated solutions dressed around
Analysis Seminar – Simon Bortz (University of Alabama)
ZoomSimon Bortz is going to talk about the ideas in a recent paper which can be found at https://arxiv.org/abs/2008.11544. Roughly speaking, the talk will be about how a quantitative approximation scheme, in fact, gives a form of quantitative coincidence. The main theorem has some nice applications (e.g. transference of boundedness of singular integrals and `geometric
Applied Math Seminar – Ben Jones (University of Alabama)
ZoomTITLE: Adaptive pseudo-time methods for the Poisson-Boltzmann equation with Eulerian solvent excluded surface ABSTRACT: This work further improves the pseudo-transient approach for the Poisson Boltzmann equation (PBE) in the electrostatic analysis of solvated biomolecules. The numerical solution of the nonlinear PBE is known to involve many difficulties, such as exponential nonlinear term, strong singularity by the source
Analysis Seminar – Alyssa Genschaw (University of Connecticut)
ZoomTitle: Solvability of the Dirichlet Problem with L^p Data for Caloric Measure Abstract: This talk concerns two probability measures. First, we consider harmonic measure, which gives solutions to the Dirichlet problem associated to Laplace's equation. Additionally, we may view harmonic measure as the “hitting probability" for Brownian motion. This probabilistic interpretation shows the connection between
Algebra/Topology Seminar – Ina Petkova (Dartmouth College)
ZoomTitle: A contact invariant from bordered Heegaard Floer homology Abstract: Given a contact structure on a bordered 3-manifold, we describe an invariant which takes values in the bordered sutured Floer homology of the manifold. This invariant satisfies a nice gluing formula, and recovers the Oszvath-Szabo contact class in Heegaard Floer homology. This is joint work
Analysis Seminar – Trang Nguyen (University of South Australia)
ZoomTitle: Non-homogeneous T(1) theorem for singular integrals on product quasimetric spaces Abstract: In the Calderón-Zygmund Theory of Singular Integrals, the T(1) theorem of David and Journé is one of the most celebrated theorems. It gives easily-checked criteria for a singular integral operator T to be bounded from L^2(R^n) to L^2(R^n), meaning T(f) is bounded for
Analysis Seminar – Brandon Sweeting (University of Cincinnati)
ZoomTitle: Novel Bellman Estimates for Ap Weights Abstract: The Bellman function method is an assortment of tools for obtaining sharp inequalities in harmonic analysis. To handle an inequality, one fixes a set of parameters, called Bellman variables, and maximizes (or minimizes) the left-hand side subject to these constraints. The solution of the corresponding extremal problem
Applied Math Seminar – Yuanzhen Shao (University of Alabama)
ZoomTITLE: Variations of the sharp interfaces in multiphase problems ABSTRACT: During recent decades, there has been a tremendous growth of activity on multi-phase problems, e.g. multiphase fluids. In most such models, different phases are separated by a sharp interface. This talk aims at introducing some basic geometric tools for taking first and second variations of the