Overview
My research lies in convex geometry and geometric analysis, with connections to several complex variables. I study extremal problems involving volume and duality of convex bodies and functions. My work combines techniques from convex and functional analysis, geometric flows, and several complex variables to establish geometric and functional inequalities. I am particularly motivated by long standing conjectures, such as those of Mahler and Bourgain’s, which often reveal surprising connections such as Bergman kernels to polarity, or Ricci curvature bounds to the volume of hyperplane sections.
Research Focus
Convex Geometry, Geometric Analysis, Several Complex Variables.
Publications
- A Santaló inequality for the Lp-polar body, Contemp. Math. (2025), 31–52.
- Two dimensional Błocki, Lp-Mahler, and Bourgain Conjectures (with Y.A. Rubinstein), to appear in Indiana Univ. Math. J.
- Lp-polarity, Mahler volumes, and the isotropic constant (with B. Berndtsson and Y.A. Rubinstein), Analysis & PDE 17-6 (2024), 2179–2245.