We will talk about the recent developments of the sign uncertainty principle and its relation with sphere packing and quadrature formulas. The talk will mainly be a report of the paper New Sign Uncertainty Principles, joint work with J. P. Ramos and D. Oliveira e Silva. Website: https://sites.google.com/view/paw-seminar Host: Paata Ivanisvili pivanis@ncsu.edu
We show that among nonnegative quadratic forms in n independent standard normal random variables, a diagonal form with equal coefficients maximizes differential entropy when variance is fixed. We also discuss some related open problems. Website: https://sites.google.com/view/paw-seminar Host: Paata Ivanisvili pivanis@ncsu.edu
The r-parallel set of a measurable set A is the set of all points whose distance from A is at most r. In this talk, we discuss some recent results that establish upper bounds on the Euclidean and Gaussian surface areas of r-parallel sets. We also discuss a reverse form of the Brunn-Minkowski inequality for…
The Poisson hyperplane process describes, roughly speaking, infinitely many hyperplanes thrown uniformly at random into the d-dimensional Euclidean space. The hyperplanes dissect the space into countably many cells. The a.s. unique cell containing the origin is called the Poisson zero polytope. We prove an explicit combinatorial formula for the expected number of k-dimensional faces of…
Website: https://sites.google.com/view/paw-seminar Host: Paata Ivanisvili pivanis@ncsu.edu
Website: https://sites.google.com/view/paw-seminar Host: Paata Ivanisvili pivanis@ncsu.edu
Website: https://sites.google.com/view/paw-seminar Host: Paata Ivanisvili pivanis@ncsu.edu
SIO (Singular Integral Operator) theory and, Calderón-Zygmund theory specifically, developed starting from the '60s, provides a vast array of tools for dealing with operators that resemble the Hilbert transform, an ubiquitous operator in Complex Analysis, semi-linear PDEs, and many other branches of mathematics. Results valid for complex-valued functions were extended to Banach spaces-valued functions thanks…
The talk aims at providing an introduction into some basic problems occurring in the ergodic theory of uncountable group actions and a setup and a few tools on how to resolve these issues. This part of the talk shall be accessible to anyone with a graduate-level background in probability and analysis. Towards the end of…