Luca Spolaor

Luca Spolaor is an Assistant Professor at the University of California, San Diego. His research focuses on geometric measure theory, free boundary problems, and the regularity theory of minimal surfaces and varifolds. He works on topics including modulo p minimization, epiperimetric inequalities, and the structure of singular sets in geometric variational problems.

Spolaor's work integrates advanced techniques from geometric analysis, partial differential equations, and calculus of variations. He has contributed to understanding the fine properties of solutions to free boundary problems, particularly in two-dimensional settings, and has developed novel methods for analyzing singularities in minimal surfaces and semicalibrated currents.

His recent research includes studies on the regularity of area-minimizing hypersurfaces modulo p, logarithmic epiperimetric inequalities for obstacle problems, and the uniqueness of tangent cones in geometric free-boundary problems. He collaborates with leading mathematicians such as Camillo De Lellis, Max Engelstein, and Bozhidar Velichkov.

Spolaor actively participates in academic events, organizing conferences on geometric measure theory and calculus of variations. His work is published in top journals like Inventiones mathematicae, Communications on Pure and Applied Mathematics, and Calculus of Variations and PDEs.