### Analysis Seminar – Edward Timko, Indiana University

227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, ALTitle : On polynomial n-tuples of commuting isometries Abstract : We extend some of the results of Agler, Knese, and McCarthy to n-tuples of commuting isometries for n>2. Let V=(V_1,...,V_n) be an n-tuple of a commuting isometries on a Hilbert space and let Ann(V) denote the set of all n-variable polynomials p such that p(V)=0.

### Analysis Seminar – Geoff Diestel, Texas A&M of Central Texas

227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, ALTitle: Determining Convex Bodies from Central Sections Abstract: Barker and Larman posed a problem which asks if a convex body in real n-space is uniquely determined by the volumes of its hyperplane sections supported by an internal compact convex set. A survey of some partial results along with the Minkowski uniqueness theorem are presented along

### Seminar – Hristo Sendov, University of Western Ontario

228 Gordon Palmer Hall Tuscaloosa, ALEvery Calculus student is familiar with the classical Rolle’s theorem stating that if a real polynomial p satisfies p(−1) = p(1), then it has a critical point in (−1, 1). In 1934, L. Tschakaloff strengthened this result by finding a minimal interval, contained in (−1, 1), that holds a critical point of every real polynomial

### Analysis Seminar – Yuanzhen Shao, Georgia Southern University

227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, ALTitle: Some Applications of Singular Manifold Theory to Applied Mathematics Abstract: Many applications of applied sciences lead to differential equations with various types of singularities, including singularities of the geometry of the underlying space and singularities of the coefficients of the differential equations. The aim of this talk is to introduce the concept of singular manifolds, which can describe various kinds of singularities in a unified way, and then my recent work on the partial differential equation theory over singular manifolds will be presented. I will illustrate by several examples from applied mathematics how to use this theory to treat different types of singularities via a unified approach.

### Analysis Seminar – Vjekoslav Kovac (University of Zagreb, Croatia and Georgia Tech)

346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, ALTitle: A Szemeredi-type theorem for subsets of the unit cube. Abstract: We are interested in arithmetic progressions in positive measure subsets of ^d. After a counterexample by Bourgain, it seemed as if nothing could be said about the longest interval formed by sizes of their gaps. However, Cook, Magyar, and Pramanik gave a positive result

### Analysis Seminar – John Hoffman (University of Missouri)

ZoomTitle: Regular Lip(1,1/2) Approximation of Parabolic Hypersurfaces Abstract: A classical result of David and Jerison states that a regular, n-dimensional set in R^{n+1} satisfying a two sided corkscrew condition is quantitatively approximated by Lipschitz graphs. After reviewing this result, we will discuss some recent advances in extending this result to the parabolic setting. The proofs

### Analysis Seminar – Timothy Robertson (University of Tennessee)

ZoomTitle: Masuda's Uniqueness Theorem for Leray-Hopf Weak Solutions of Navier-Stokes Equations: Revisited Abstract: In this talk, we revisit the classical Masuda's theorem on the uniqueness of Leray-Hopf weak solutions for the system of Naiver-Stokes equations. We extend this uniqueness result to a class of Leray-Hopf weak solutions in mixed-norm Lebesgue spaces. The talk is based on my

### Analysis Seminar – Naga Manasa Vempati (Washington University, Saint Louis)

Title: The two-weight inequality for Calder\'on-Zygmund operators with applications and results on two weight commutators of maximal functions on spaces of homogeneous type. Abstract: For (X,d,w) be a space of homogeneous type in the sense of Coifman and Weiss, i.e. d is a quasi metric on X and w is a positive measure satisfying the doubling

### Analysis Seminar – Kabe Moen

346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, ALTitle: 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

### Analysis Seminar – David Cruz-Uribe (UA)

346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, ALTitle: Everything I knew (and maybe that you know) about the Stieltjes integral is wrong. Abstract: I will discuss three definitions of the Riemann integral (the Riemann integral, the Darboux integral, and a variant of the Darboux integral) and why they are equivalent. I will then introduce the generalizations of these results to define the