Events for 05/07/2021 from all calendars

Seminar in Random Tensors

Time: 04:00AM - 05:00AM

Location: zoom

Speaker: G. Moshkovitz, City University of New York (Baruch College)

Title: An Optimal Inverse Theorem

Abstract: The partition rank and analytic rank of a tensor measure algebraic structure and bias, respectively. We prove that they are equivalent up to a constant, over any large enough finite field (independently of the number of variables). The proof constructs rational maps computing a rank decomposition for successive derivatives, on a carefully chosen subset of the kernel variety associated with the tensor. Proving the equivalence between these two quantities is the main question in the "bias implies low rank" line of work in higher-order Fourier analysis, and was reiterated by multiple authors. Joint work with Alex Cohen.

Noncommutative Geometry Seminar

Time: 1:00PM - 2:00PM

Location: Zoom 951 5490 42

Speaker: Zhizhang Xie, Texas A&M University

Title: A relative index theorem for incomplete manifolds and Gromov’s conjectures on positive scalar curvature

Abstract: In this talk, I will speak about my recent work on a relative index theorem for incomplete manifolds. As applications, this new relative index theorem gives positive solutions to some conjectures and open questions of Gromov on positive scalar curvature.

URL: Event link

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: zoom

Speaker: G. Moshkovitz, City University of New York (Baruch College)

Title: An Optimal Inverse Theorem

Abstract: The partition rank and analytic rank of a tensor measure algebraic structure and bias, respectively. We prove that they are equivalent up to a constant, over any large enough finite field (independently of the number of variables). The proof constructs rational maps computing a rank decomposition for successive derivatives, on a carefully chosen subset of the kernel variety associated with the tensor. Proving the equivalence between these two quantities is the main question in the "bias implies low rank" line of work in higher-order Fourier analysis, and was reiterated by multiple authors. Joint work with Alex Cohen.