# Analysis Seminar

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

346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: 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, 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

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

346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: 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

### Analysis Seminar – Simon Bortz

Title: Heat extensions of doubling weights and A_infty A_infty weights play a fundamental role in weighted inequalities for operators used in harmonic analysis. It is known that if w is an A_infty weight then log w in the space of bounded mean oscillation (BMO) and the converse is `almost’ true (up to taking a

### Analysis Seminar 9/14 – Abba Ramadan

302 Gordon Palmer HallTitle: Standing Waves of the Schrodinger Equation with Concentrated Nonlinearity With Atanas Stefanov, we study the concentrated Nonlinear Schrodinger Equations in n-dimensions, with power non-linearities, driven by the fractional Laplacian. We construct the solitary waves explicitly, in an optimal range of the parameters, so that they belong to the natural energy space $H^s$. We

### Analysis Seminar – Brandon Sweeting

302 Gordon Palmer HallTitle: Mixed Weak-Type Estimates for Classical Operators Abstract: We prove new mixed weak type estimates for various classical operators of Harmonic analysis. Mixed weak type inequalities were first studied by Muckenhoupt and Wheeden and later by Sawyer to prove the $L^p$ boundedness of the Hardy-Littlewood maximal operator as a consequence of the Jones factorization

### Analysis Seminar – Atanas Stefanov

231 Gordon Palmer HallTitle: On the long term dynamics of the Landau-DeGennes gradient flow Abstract: We study the gradient flow of the Landau-deGennes energy functionals, in the physically relevant spatial dimensions $d=2,3$. We establish global well-posedness and global exponential time decay bounds for large $H^1$ data in the 2D case, and uniform bounds for large data in 3D.