The Analysts' Traveling Salesman Problem in Banach spaces

Abstract: This talk discusses recent work (joint with Matthew Badger, UCONN) on generalizations of the Analysts' Traveling Salesman Theorem to uniformly smooth and uniformly convex Banach spaces (e.g., l_p spaces). In 1990, motivated by problems in Singular Integral Operators, Peter Jones posed and solved his celebrated Analysts' Traveling Salesman Problem: namely, to characterize all subsets of rectifiable curves in the plane. Since then, many authors have contributed, proving similar results in Euclidean spaces, Hilbert Spaces, Carnot groups, for 1-rectifiable measures, etc. This talk will give a broad overview of some of these results and their core ideas. In the end, we will discuss the challenges in Banach spaces and what generalizations hold there. This talk will include lots of pictures and examples.

analysis of PDEsclassical analysis and ODEsfunctional analysismetric geometry

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.