Events
Sudan Xing, University of Alberta, On Lp-Brunn-Minkowski type and Lp-isoperimetric type inequalities for measures
ZoomIn 2011, Lutwak, Yang and Zhang extended the definition of the Lp-Minkowski convex combination (p ≥ 1) from convex bodies containing the origin in their interiors to all measurable subsets in R n , and as a consequence, extended the Lp-Brunn-Minkowski inequality to the setting of all measurable sets. In this talk, I will present…
Ohad Klein, Bar-Ilan University, Israel, On the distribution of Randomly Signed Sums and Tomaszewski’s Conjecture
ZoomA Rademacher sum X is a random variable characterized by real numbers a_1, ..., a_n, and is equal to X = a_1 x_1 + ... + a_n x_n, where x_1, ..., x_n are independent signs (uniformly selected from {-1, 1}). A conjecture by Bogusław Tomaszewski, 1986: all Rademacher sums X satisfy Pr >= 1/2. We…
Christine Breiner, Fordham University, Harmonic branched coverings and uniformization of CAT(k) spheres
ZoomConsider a metric space (S,d) with an upper curvature bound in the sense of Alexandrov (i.e.~via triangle comparison). We show that if (S,d) is homeomorphically equivalent to the 2-sphere, then it is conformally equivalent to the 2-sphere. The method of proof is through harmonic maps, and we show that the conformal equivalence is achieved by…
Galyna Livshyts, Georgia Institute of Technology, On an inequality somewhat related to the Log-Brunn-Minkowski conjecture
ZoomI shall prove a neat inequality concerning convex bodies and semi-norms, and show that cylinders (i.e. direct products of intervals with convex bodies of lower dimension) give equality cases for it. I shall explain its connections to the Log-Brunn-Minkowski conjecture. If time permits, I will discuss related results and surrounding questions. Based on a joint…
Rupert Frank, Caltech, Lieb-Thirring bounds and other inequalities for orthonormal functions
ZoomWe discuss extensions of several inequalities in harmonic analysis to the setting of families of orthonormal functions. While the case of Sobolev-type inequalities is classical, newer results concern the Strichartz inequality, the Stein-Tomas inequality and Sogge’s spectral cluster estimates, among others. Of particular interest is the dependence of the constants in the resulting bounds on…
Andrew Papanicolaou, NC State, Consistent Inter-Model Specification for Time-Homogeneous SPX Stochastic Volatility and VIX Market Models
ZoomThis work explores the recovery stochastic volatility models (SVMs) from market models for the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore they are better-suited for pricing VIX futures and derivatives. But the VIX itself is a derivative of the S&P500 (SPX) and it is…
Mario Schulz, Queen Mary University, Families of free boundary minimal surfaces in the unit ball
ZoomThe study of extremals for Steklov eigenvalues has revitalised the theory of free boundary minimal surfaces. One of the most basic open questions can be phrased as follows: Can a surface of any given topology be realised as an embedded free boundary minimal surface in the 3-dimensional Euclidean unit ball? We will answer this question…
Erik Mainellis, Factor Systems and the Second Cohomology Group of Leibniz Algebras
ZoomFactor systems are a tool for working on the extension problem for algebraic structures such as groups, Lie algebras, and associative algebras. We construct the Leibniz algebra analogue to a series of group-theoretic results from W. R. Scott’s Group Theory. Fixing a pair of Leibniz algebras A and B, we develop a correspondence between factor systems…
Nicholas Cook, Duke University, Universality for the minimum modulus of random trigonometric polynomials
ZoomWe consider the restriction to the unit circle of random degree-n polynomials with iid coefficients (Kac polynomials). Recent work of Yakir and Zeitouni shows that for Gaussian coefficients, the minimum modulus (suitably rescaled) follows a limiting exponential distribution. We show this is a universal phenomenon, extending their result to arbitrary sub-Gaussian coefficients, such as Rademacher…
Corey Jones, NC State, Symmetries of affine buildings and tilting modules for SL_n
ZoomIn this talk, we will explain a (mysterious?) connection between the combinatorics of affine buildings and representation theory in type A. If a group acts simply and transitively on the vertices of an affine building in type A_n, it gives rise to a certain combinatorial structure called a triangle presentation. We will describe how triangle presentations…
Marta Lewicka, University of Pittsburgh, Expansions of averaging operators and applications
ZoomIn my talk, I will explain the approach of finding solutions to nonlinear PDEs via tug-of-war games. I will focus on the context of p-Laplacian and the non-local geometric p-Laplacian. Zoom meeting: Link
Ryan Hynd, University of Pennsylvania, A Conjecture of Meissner
ZoomA curve of constant width has the property that any two parallel supporting lines are the same distance apart in all directions. A fundamental problem involving these curves is to find one which encloses the smallest amount of area for a given width. This problem was resolved long ago and has a few relatively simple solutions.…
Bekah White, NC State, Inferring the microstructural properties of cortical bone from ultrasound attenuation
ZoomChair: Alen Alexanderian (alexanderian@ncsu.edu, contact for Zoom access)