Research
Colloquium – Gieri Simonett (Vanderbilt University)
Title: Moving surfaces in geometry and physics Abstract: Moving surfaces are ubiquitous in many areas of mathematics and the applied sciences. In this talk I will first introduce some well-known geometric evolution equations, and then proceed to more complicated models that describe the motion of fluids and of materials that can undergo phase transitions.
Colloquium – Chi-Wang Shu (Brown University)
ZoomTitle: High order numerical methods for hyperbolic equations Abstract: Hyperbolic equations are used extensively in applications including fluid dynamics, astrophysics, electro-magnetism, semi-conductor devices, and biological sciences. High order accurate numerical methods are efficient for solving such partial differential equations, however they are difficult to design because solutions may contain discontinuities. In this talk we will
Analysis Seminar – Simon Bortz (University of Alabama)
ZoomTitle: A free boundary problem for the heat equation. Abstract: In his breakthrough result, it was shown by Dahlberg that the L^2 Dirichlet problem for the Laplacian (harmonic functions) is solvable in the region above a Lipschitz graph. Dahlberg did this by showing a local reverse Hölder inequality for the Poisson kernel in such domains.
Analysis Seminar – Armin Schikorra (University of Pittsburgh)
ZoomTitle: A Harmonic Analysis perspective on $W^{s,p}$ as $s \to 1^-$. Abstract: We revisit the Bourgain-Brezis-Mironescu result that the Gagliardo-Norm of the fractional Sobolev space W^{s,p}, up to rescaling, converges to W^{1,p} as s\to 1. We do so from the perspective of Triebel-Lizorkin spaces, by finding sharp $s$-dependencies for several embeddings between $W^{s,p}$ and $F^{s,p}_q$
Analysis Seminar – Ryan Alvarado (Amherst College)
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Optimal embeddings and extensions for Triebel-Lizorkin and Besov spaces in spaces in quasi-metric measure spaces. Abstract: Embedding and extension theorems for certain classes of function spaces in $\mathbb{R}^n$ (such as Sobolev spaces) have played a fundamental role in the area of partial differential equations. In this talk, we will discuss some recent work which
Analysis Seminar – Kabe Moen
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Best constants for maximal operators Abstract: In this talk I will survey some known results concerning best constants for the Hardy-Littlewood maximal operator and it’s variants. We will go over the sharp one dimensional theory for the uncentered maximal function. We will also talk about best constants for the dyadic maximal function and some
Algebra Topology Seminar – Tucker Ervin (UA)
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Mutations of reflections and existence of pseudo-acyclic orderings for type An Abstract: In a recent paper by K.-H. Lee, K. Lee and M. Mills, a mutation of reflections in the universal Coxeter group is defined in association with a mutation of a quiver. A matrix representation of these reflections is determined by a linear ordering
Colloquium – Professor David Gay (University of Georgia)
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United States**Refreshments will be served at 10:30 a.m. in 301 GP** The presentation will begin at 11:00 a.m. in 346 Gordon Palmer Hall Title: Smooth automorphisms of the 4‐dimensional sphere Abstract: This is a talk about smooth 4‐dimensional topology, in which the objects are smooth 4‐manifolds (spaces locally like R^4 equipped with the ability to do
Applied Math Seminar – Qiliang Wu (Ohio University)
ZoomTitle: Pearling and Localized Undulation of Bilayers in Amphiphilic Morphology Abstract: Amphiphiles, such as lipids and functionalized polymers, plays a central role in the self-assembly of solvent accessible, intricately structured nano-scaled network structures, which are vital in cell functionality and offer wide applications to drug delivery, detergent production, emulsion stabilization and energy conversion devices. We