Intriguing questions in mathematics often lie at the intersection of different areas. One of my main research projects is funded by an ERC Starting Grant and delves into an intersection between the calculus of variations, geometric measure theory, harmonic analysis, and partial differential equations. This project explores the properties of functions and measures that satisfy a linear partial differential equation, aiming to unlock answers to longstanding conjectures in various fields of analysis through the lens of compensated compactness theory.
Currently, I am Junior Research Group Leader at the University of Bonn. I also hold a (paused) research position (FNRS Charge de Recherches) at the Université catholique de Louvain.
I was awarded a Ph.D. degree in October 2017 at the University of Bonn, under the supervision of Stefan Müller, for the work ‘‘Lower semicontinuity, optimization and regularity of variational problems under general PDE constraints’’.
Pisa, Italy
Selected Publications
Representation of the total variation as a Γ-limit of BMO-type seminorms
with Paolo Bonicatto and Giacomo Del Nin
Indiana Univ. Math. J. (2024, 21 pages)Characterization of generalized Young measures generated by A-free measures
Arch. Ration. Mech. Anal. (2021, 91 pages)Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints
with Guido De Philippis and Filip Rindler
Adv. Calc. Var. (2020, 36 pages).Dimensional estimates and rectifiability for measures satisfying linear PDE constraints
with Guido De Philippis, Jonas Hirsch and Filip Rindler
Geom. Funct. Anal. (2019, 19 pages).
Selected talks/invites
BIRS Workshop: 6th Meeting of Mexican Mathematicians in the World
Casa Matemática Oaxaca, México (2024)BIRS Workshop: Compensated Compactness and Applications to Materials
Banff, Canada (2023)2022 SIAM Annual Meeting: Advances in variational methods and applications to materials and machine learning 2022 as part of the Hybrid
Pittsburgh, U.S. (2022)8th European Congress of Mathematics
Portorož, Slovenia (2021)Université Paris Saclay - Orsay, France (2022)
University of Oxford - Oxford, UK (2019)
Collaborators
Paolo Bonicatto (Warwick)
Johannes Diermeier
Giacomo Del Nin (Warwick)
Jonas Hirsch (Leipzig)
Heiner Olbermann (UCLoiuvain)
Guido de Philippis (Courant NYU)
Filip Rindler (Warwick)
Anna Skorobogatova (Princeton)
José Simental (UNAM)
Jean Van Schaftingen (UCLouvain)
Raphael Winter (Vienna)