Title: Oscillatory integrals with strongly singular kernels

Abstract: In this talk we discuss results on oscillatory integrals with strongly singular kernels, where the singularity is much worse than 1/x or 1/x^n. In particular, we discuss how to adapt the classical Calderón-Zygmund theory to obtain weak 1-1 estimates with high oscillations.

About the Speaker: Ricardo Saenz received his BS from University of Texas at El Paso and his PhD  from Princeton University under the supervision of the late Elias Stein. He has been a professor at Universidad de Colima in México since 2003,  and the Director of the School of Sciences (2013-2017). Dr. Saenz area of research is in harmonic analysis, in particular harmonic analysis on fractals and oscillatory integrals. He has mentored countless MS and Honors (Tesis de Licenciatura) students at Colima and received many teaching awards. In 2017 Dr. Saenz visited UNM and gave a minicourse on Analysis on Fractals, a colloquium, and analysis seminar, and a talk for middle school kids in Taos, one of our undergraduate students spent the Summer at Colima doing an REU with him as a result of this visit. He gave a series of lectures at the 2018 Park City Mathematics Institute (IAS/PCMI) and as a byproduct a book, "An introduction to Harmonic Analysis", was published in 2023 by the AMS.