Kelly Bickel

Educational Background

• Washington University in St. Louis, Ph.D. in Mathematics
• Washington University in St. Louis, M.A. in Mathematics
• Centre College, B.S. in Mathematics and Economics

Research interests

My research mostly lies in complex analysis and operator theory, with a focus on the structure and boundary behavior of multivariate functions and related operators. I am currently interested in singular rational inner functions, Agler decompositions, and generalizations of the unilateral shift on the bidisk and polydisk. Recently, I have become interested in Crouzeix’s Conjecture and its connections to one-variable compressions of the shift. I also study problems in harmonic analysis, mostly regarding the boundedness of operators between matrix weighted spaces. Many of these research questions involve polynomial and rational functions and have aspects well-suited to undergraduate research.

Selected Publications

1. Derivatives of Rational Inner Functions: Geometry of Singularities and Integrability at the Boundary (with J.E. Pascoe and A. Sola). Proc. Lond. Math. Soc. (3). 116 (2018), no. 2, 281-329.

2. Compressions of the Shift on the Bidisk and their Numerical Ranges (with P. Gorkin). J. Operator Theory. 79 (2018), no. 1, 225-265.

3. Two Weight Estimates with Matrix Measures for Well Localized Operators (with A. Culiuc, S. Treil, and B. Wick). Trans. Amer. Math. Soc. 371 (2019), no. 9, 6213-6240.