Piotr Hajlasz

Piotr Hajłasz is a Professor in the Department of Mathematics at the University of Pittsburgh, affiliated with The Dietrich School of Arts and Sciences. His research focuses on Geometric Function Theory, Sobolev spaces, analysis on metric spaces, and quantitative topology. He holds a PhD from Warsaw University and has contributed extensively to areas such as nonlinear elliptic PDEs, calculus of variations, and the structure of Lipschitz mappings. His work bridges classical analysis, geometric analysis, and algebraic topology.

Key research areas include the theory of Sobolev spaces on metric spaces, analysis on Heisenberg groups, and Lipschitz homotopy groups. He explores applications in convex analysis, differential forms, and topological obstructions to continuity. Hajłasz’s recent studies address Lusin approximation of convex functions, smooth approximations of mappings, and geometric approaches to second-order differentiability.

His publications examine topics like bi-Lipschitz mappings, Hölder continuity, and Sard-type theorems. He has developed techniques for constructing diffeomorphisms and homeomorphisms with prescribed derivatives. His work often reveals connections between geometric properties of spaces and functional-analytic structures.

While no explicit awards are listed, his extensive contributions to analysis and geometry are evident through his prolific publication record and international collaborations. Hajłasz mentors graduate students in advanced mathematical analysis and maintains an active research program in geometric and topological analysis.