Bozhidar Velichkov

Bozhidar Velichkov is a Full Professor at the Department of Mathematics, University of Pisa, where he has been working since June 2020. Previously, he served as an Associate Professor at Università di Napoli Federico II (2019-2020) and at Université Grenoble Alpes (2014-2019). He is the Principal Investigator of the ERC VaReg project (2020-2025), a European Research Council Starting Grant focused on the regularity of free boundaries.

His educational background includes PhD studies at Scuola Normale Superiore (2010-2013) and undergraduate studies at both Scuola Normale Superiore and University of Pisa (2005-2010).

Professor Velichkov's research focuses on Calculus of Variations and Partial Differential Equations, with particular emphasis on Regularity Theory and Free Boundary Problems. His work investigates the fine structure of solutions to variational and PDE problems, especially concerning the regularity of free boundaries in various contexts including one-phase and two-phase Bernoulli problems, obstacle problems, and vectorial free boundary systems. His approach often involves developing new techniques such as epiperimetric inequalities and monotonicity formulas to analyze the structure of solutions near singularities.

His recent publications demonstrate a strong trend toward understanding the regularity of free boundaries in increasingly complex settings, including capillarity problems, thin obstacle problems, and vectorial systems. His work bridges geometric analysis, PDE theory, and calculus of variations, with applications to shape optimization and geometric variational problems.

• Principal Investigator of ERC VaReg project (2020-2025)
• Deputy Coordinator of PhD program in Mathematics at University of Pisa
• Organizer of multiple international workshops on Free Boundary Problems

Professor Velichkov has supervised numerous PhD students and post-doctoral researchers, leading an active research group focused on free boundary regularity. His ERC project supports a vibrant team of researchers working on cutting-edge problems in geometric analysis and partial differential equations.