Abstract: We discuss a recent result, obtained in collaboration with Guillermo Rey (University of Madrid) and Kristina Skreb (University of Zagreb), in which we find the exact Bellman function associated with level sets of sparse operators acting on characteristic functions. We will start with a lighter introduction to modern dyadic harmonic analysis and the role these operators play in the so-called “sparse revolution” in harmonic analysis. Then, we will try to explain the key ideas of our Bellman function proof.

About the Speaker: Irina  Holmes received her PhD in 2014 from Louisiana State University, under the direction of Ambar Niel Sengupta, an expert in probability theory. She then was a Hale Postdoctoral Fellow at Georgia Institute of Technology (2014-16), and an NSF Postdoctoral Research Fellow at Washington University in St. Louis (2016-17) and at Michigan State University (2017-2019). It was during her postdoctoral positions that she turned to harmonic analysis. She was mentored by Michael Lacey, Brett Wick and Alexander Volberg. It is in these postdoctoral positions where Dr. Holmes became very interested in dyadic harmonic analysis, weighted inequalities, Bellman functions, square functions, paraproducts, and commutators, and later sparse domination. Her upbringing as a probabilist provides her with a set of tools that sets her apart from other harmonic analysts. In 2019, she joined the faculty at Texas A&M as an Assistant Professor. She has publications in top journals and has received and currently has NSF and Simons Foundation funding. She has coorganized multiple conferences and  workshops (with NSF support) including last Fall at ICERM,  AMS Special Sessions (including one at the Fall 2021 meeting that was supposed to be held at UNM), During Covid she and co-organizers created PAW: Probability and Analysis Webinar, which has survived the pandemic and meets weekly online. She has co-organized the Summer Informal Regional Functional Analysis Seminar (SUMIRFAS) at her university every year since she joined. Dr. Holmes is also successfully mentoring PhD and undergraduate students.

Zoom Meeting:
https://unm.zoom.us/j/95873329721