FALL 2021 Nonlinear Analysis Seminar Series

Professor Itai Shafrir,  Technion-Israel Institute of Technology

Title: Minimizers of a variational problem for nematic liquid crystals with variable degree of orientation in two dimensions

FALL 2021 Nonlinear Analysis Seminar Series

Professor Oscar Domingues Bonilla, The University of Lyon

Title: John–Nirenberg spaces revisited

Abstract:

We study John—Nirenberg-type spaces where oscillations of functions are controlled via covering lemmas. Our methods give new surprising results and clarify classical inequalities. Joint work with Mario Milman (Florida and Buenos Aires).

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FALL 2021 Nonlinear Analysis Seminar Series

Dr. João Pedro Ramos, Eidgenössische Technische Hochschule Zürich

Title: STABILITY FOR GEOMETRIC AND FUNCTIONAL INEQUALITIES

Abstract

FALL 2021 Nonlinear Analysis Seminar Series

Professor Alex Iosevich, University of Rochester

Title: Finite point configurations and the Vapnik-Chervonenkis dimension

Abstract:

The Vapnik-Chervonenkis (VC) dimension was invented in 1970 to study learning models. This notion has since become one of the cornerstones of modern data science. This beautiful idea has also found applications in other areas of mathematics. In this talk we are going to describe how the study of the VC-dimension in the context of families of indicator functions of spheres centered at points in sets of a given Hausdorff dimension (or in sets of a given size inside vector spaces over finite fields) gives rise to interesting, and in some sense extremal, point configurations. 

FALL 2021 Nonlinear Analysis Seminar Series

FALL 2021 Nonlinear Analysis Online Seminar Seminar Series

Sagun Chanillo, Rutgers University

Title: Local Version of Courant's Nodal domain theorem.

Abstract:

Consider a smooth, compact Riemannian manifold with no boundary, endowed with a smooth metric. A famous theorem of Courant states that the k-th eigenfunction for the Laplace-Beltrami operator can have at most k nodal domains. Nodal domains are the open and connected sets where the eigenfunction does not vanish. H. Donnelly and Fefferman obtained some 30 years ago a local version of this theorem. Improvements were made by Chanillo-Muckenhoupt and others. In this talk we obtain the optimal local version of the local Courant theorem. We also relate this result to conjectures of S.-T. Yau on nodal sets, that is the zero set of eigenfunctions. The results of our talk have been obtained jointly with A. Logunov, E. Mallinikova and D. Mangoubi.

SPRING 2021 Nonlinear Analysis Seminar Series

Professor Jan Kristensen,  University of Oxford

Title: Regularity and uniqueness results in some variational problems

SPRING 2021 Nonlinear Analysis Seminar Series

Professor Giovanni Leoni , Carnegie Mellon University

Title: Some remarks on homogeneous fractional Sobolev spaces

SPRING 2021 Nonlinear Analysis Seminar Series

Associate Professor Jean Van Schaftingen, Université catholique de Louvain

Title: Vortex dynamics for the lake equations

SPRING 2021 Nonlinear Analysis Special Lecture Series

★SPECIAL LECTURE Part 2/3

Dr. Adolfo Arroyo-Rabasa, University of Warwick

Title: Slicing and fine properties for functions with Bounded \(\mathcal{A}\)-variation - Proof of the slicing characterization and statement of the structure theorem

SPRING 2021 Nonlinear Analysis Special Lecture Series

Professor Giuseppe Mingione, University of Parma

Title: Perturbations beyond Schauder