Title: Gaussian Singular Integrals: Singular Integrals through the looking glass.

Abstract: In this talk we will first discuss the development process of the classical singular integrals up to the Calderón-Zygmund class of singular integrals. Then we will discuss the development process of the Gaussian singular integrals up to the general and the general alternative Gaussian singular integrals. Finally, we discuss their boundedness properties in Gaussian LebesgueLp spaces p >1, its weak (1,1) boundedness with respect to the Gaussian measure and also in Gaussian variable Lebesgue spaces.

About the speaker: Wilfredo Urbina is a Venezuelan mathematician transplanted to the US for a second career. He got his  Licenciatura from Universidad Central de Venezuela (UCV) under the direction of Misha Cotlar and his PhD in 1988 from the University of Minnesota under the direction of Eugene Fabes. He then returned to Venezuela and rose through the ranks until he became a Full Professor at UCV. In 2004 he left Venezuela for good, and was  a Visiting Professor for one year at University of Kansas,  for two years at UNM, for three years at De Paul University in Chicago and in 2010 joined the faculty at Roosevelt University in Chicago where he is now an Associate Professor. His research interests  include harmonic analysis, singular integrals, special functions, orthogonal polynomials, operator semigroups, functional inequalities, hypercontractivity, wavelets, stochastic process, martingales, stochastic integration, and  stochastic differential equations. He has authored more than 50 articles and many monographs the latest "Gaussian Harmonic Analysis" published by Springer in 2019. Wilfredo has trained more than 15 MS and PhD students. He has delivered talks all over the world and minicourses in Argentina, Mexico, Spain and Venezuela. He  has co-organized many conferences and co-edited several volumes. 

Wilfredo spent two years at UNM and has come back many times to various editions of the NM Analysis Seminar.  Wilfredo was co-organizer of  "An afternoon in honor of Misha Cotlar" and "An afternoon in honor of Cora Sadosky" held at UNM in 2007 and 2014 respectively. We were co-editors of two volumes honoring Cora Sadosky with contributions from Elias Stein, Loredana Lanzani, Aline Bonami,  Lukas Grafakos, Svitlana Mayboroda, Carlos Kenig, Gustavo Ponce, Sergei Treil, Sasha Volberg, Carlos Perez and a long list of very distinguished mathematicians.