Time: 20:00, Tuesday, June 20, 2023
Venue: ZOOM
ZOOM ID：998 1247 7399
PASSCODE：538841
Speaker: Thierry De Pauw
Biography: De Pauw graduated with a PhD in mathematics from UCLouvain, Belgium, in 1998. He is currently a professor at the Université Paris Cité, Institut de Mathématiques de Jussieu, France. He contributed to the development of Geometric Measure Theory, including in general ambient metric spaces, a subfield of Calculus of Variations of which the paradigm is the Plateau problem, that is the study of the shape and singularities of soap bubbles.
Title：Radon-Nikodym from different angles: quantitative, geometric, undecidable, and Radon-Nikodymification
Abstract: In this talk I will review various forms of the Radon-Nikodym Theorem as they apply to Analysis. After recalling the Lebesgue Density Theorem, I will mention its quantitative version in the form of Morrey-Campanato spaces and an excursion to a differentiation problem of Zygmund. Next, I will move to geometric versions of these: the Mattila and Preiss Rectifiability Theorems correspond to the Lebesgue Density Theorem, and their quantitative versions as they apply to, for instance, partial regularity of minimal surfaces including in infinite dimensional Hilbert spaces. Finally, I will explore possible worlds when the Radon-Nikodym Theorem does not trivially apply, namely with respect to (non sigma-finite) Hausdorff or Integral Geometric Measures.
