The Brown analysis seminar typically meets on Mondays at 3pm in Kassar 105.
The Brown analysis seminar typically meets on Mondays at 3pm in Kassar 105.
Current schedule of talks, Fall 2025
Title: Vector-Valued Concentration on the Symmetric Group
Abstract: Existing concentration inequalities for functions that take values in a general Banach space, such as the classical results of Pisier, are known only in very special settings, such as the Gaussian measure on R^n and the uniform measure on the discrete hypercube {-1,1}^n. We present a novel vector-valued concentration inequality for the uniform measure on the symmetric group which goes beyond the product setting of the prior known results. Furthermore, we discuss the implications of this result for the non-embeddability of the symmetric group into Banach spaces of nontrivial Rademacher type, which is of interest in studying the metric geometry of Banach spaces. The proof uses a variety of tools related to concentration of Markov semigroups, including discrete analogs of Ricci curvature, and methods of proof for various functional inequalities of independent interest. This talk is based on joint work with Ramon van Handel.
Title: Quantitative rectifiability and singular integrals in Heisenberg groups
Abstract: Rectifiable sets extend the class of surfaces considered in classical differential geometry; while admitting a few edges and sharp corners, they are still smooth enough to support a rich theory of local analysis. However, for certain questions of global nature the notion of rectifiability is too qualitative. In a series of influential papers around the year 1990, David and Semmes developed an extensive theory of quantitative rectifiability in Euclidean spaces. A motivation for their efforts was the significance of a geometric framework for the study of certain singular integrals and their connections to removability.
We will discuss recent results which lay the foundations for a theory of quantitative rectifiability for $1$-dimensional and $1$-codimensional subsets of Heisenberg groups. As in the Euclidean case, partial motivation stems from questions involving singular integrals and removability. We will see that, in certain aspects, the situation is very different than in Euclidean spaces and new phenomena appear.
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Schedule of talks, Spring 2026
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If you have questions or comment, please contact the organizers:, Jill Pipher. Sergei Treil, or Martin Ulmer