IPS on Geometric Measure Theory, Harmonic Analysis, Partial Diff. Equations - MAA MathFest 2023

Saturday, August 5, 2023
MAA MathFest 2023

AWM-MAA Invited Paper Session
Geometric Measure Theory, Harmonic Analysis, and Partial Differential Equations

Geometric measure theory provides a useful framework for studying the geometry and regularity of sets and measures in Euclidean and non-Euclidean settings, and has many useful applications to interesting problems in various fields of mathematics. This invited paper session aims to showcase the vibrant interactions between geometric measure theory, partial differential equations, and harmonic analysis. In this session, we will see exciting new developments at the interface of these areas, highlighting the ways in which they intertwine to produce deep insights.

Organizers:
Max Goering, Max Planck Institute Leipzig
Anna Skorobogatova, Princeton University
Mariana Smit Vega Garcia, Western Washington University

Schedule

Dorronsoro's Theorem and Vertical Versus Horizontal Inequalities on Carnot Groups
2:00 p.m. - 2:20 p.m.
Seung-Yeon Ryoo, Princeton University

Carnot Groups and Bi-Lipschitz Embeddings into L^1
3:00 p.m. - 3:20 p.m.
Lisa Naples, Macalester College

Low Dimensional Cantor Sets with Absolutely Continuous Harmonic Measure
3:30 p.m. - 3:50 p.m.
Cole Jeznach, University of Minnesota

Decoupling and Restriction for Ruled Hypersurfaces Generated by a Curve
4:00 p.m. - 4:20 p.m.
Dóminique Kemp, Institute for Advanced Study

A Definition of Fractional k-Dimensional Measure
4:30 p.m. - 4:50 p.m.
Cornelia Mihaila, Saint Michael’s College

A Singular Integral Identity for Surface Measure
5:00 p.m. - 5:20 p.m.
Ryan Bushling, University of Washington

A Local Bernstein Inequality for Laplace Eigenfunctions
5:30 p.m. - 5:50 p.m.
Stefano Decio, University of Minnesota