Carlos Pérez in NOVA Distinguished Lecture Series in Mathematics

The next edition of the NOVA Distinguished Lecture Series in Mathematics will welcome Professor Carlos Pérez, Professor at the University of the Basque Country and BCAM (Basque Centre for Applied Mathematics), with the title: "A MODERN GEOMETRIC PERSPECTIVE ON POINCARÉ-SOBOLEV INEQUALITIES THROUGH HARMONIC ANALYSIS AND WITHOUT DERIVATIVES".  

Abstract: In this lecture, we present a modern perspective on function smoothness and regularity by employing sharp tools from Harmonic Analysis. The first part of the talk moves beyond classical pointwise analysis to explore functional smoothness through the lens of local averages. This approach provides a more flexible and robust framework for understanding analytical behavior, particularly in settings where traditional derivatives are not or cannot be considered.

     In the second part, we apply these harmonic analysis techniques to derive local Poincaré-Sobolev estimates and the celebrated John-Nirenberg theorem about BMO functions. A central theme of the discussion will be the ’self-improving’ property—a remarkable phenomenon where modest local control on oscillations leads to significantly stronger global integrability. We will demonstrate that this behavior is fundamentally a consequence of the underlying geometry and measure-theoretic structure, offering a natural path to understand weighted estimates involving Muckenhoupt weights.

Short bio: Professor Carlos Pérez research interests include Harmonic Analysis and Analysis on Metric Spaces. He received his PhD in 1989 from Washington University in St. Louis and currently is Professor in the Department of Mathematics of Basque University and Researcher of the Basque Center of Applied Mathematics.

We recall that the NOVA Distinguished Lecture Series in Mathematics is a joint initiative of NOVA Math and the Department of Mathematics of NOVA School of Science and Technology (NOVA FCT), that brings together outstanding researchers and the NOVA FCT community, aiming to broaden students' mathematical education, present new challenges and spark their scientific curiosity regarding research in Mathematics.

On March 11 (Wednesday) at 14:30 in Library Auditorium.