Title: An Operator Theory approach to Noncommutative Harmonic Analysis

Abstract: In the second talk, we will focus on how we may use the ideas and theory of noncommutative integration to study harmonic analysis on noncommutative groups. In particular, we will discuss the use of an operator-theoretic extension of Calderon-Zygmund theory to the noncommutative setting, and how it may be applied to study extensions of the Fourier transform to profinite groups. To conclude, we will discuss analogies of the Carleson-Hunt theorem for such groups, and how we may understand and study almost everywhere convergence in the noncommutative setting.

About the Speaker: Thomas Scheckter received his PhD  from the University of New South Wales, Sydney, Australia. He completed his thesis, Martingale convergence techniques in noncommutative integration, under the supervision of Fedor Sukochev in 2020, and for his efforts he won a UNSW Dean's Award for outstanding PhD Theses.   After graduation Dr. Schecter worked in the School of Mathematics and Statistics as a Research Associate alongside Professor Sukochev, Dr Dmitriy Zanin, and Dr Ed McDonald, studying Functional Analysis and Operator Theory. He has just finished a new position as a Research Fellow at the University of New Mexico. His work  with Professor Anna Skripka  focuses on Multilinear Operator Integration. In June 2021, Dr. Schechter was the keynote speaker for the Online Workshop in Sthocastic Analysis organized by Professor Skripka and supported by her NSF CAREER grant.