Seminars and Colloquia Schedule

Matrix completion and tensor codes

Series
Algebra Seminar
Time
Monday, September 23, 2024 - 11:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matt Larson – Princeton University and the Institute for Advanced Study

There will be a pre-seminar at 10:50 am in Skiles 005.

The rank r matrix completion problem studies whether a matrix where some of the entries have been filled in with generic complex numbers can be completed to a matrix of rank at most r. This problem is governed by the bipartite rigidity matroid, which is a matroid studied in combinatorial rigidity theory. We show that the study of the bipartite rigidity matroid is related to the study of tensor codes, a topic in information theory, and use this relation to understand new cases of both problems. Joint work with Joshua Brakensiek, Manik Dhar, Jiyang Gao, and Sivakanth Gopi.

An ergodic theorem in the Gaussian integer setting

Series
Analysis Seminar
Time
Wednesday, September 25, 2024 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker

We discuss the Pointwise Ergodic Theorem for the Gaussian divisor function $d(n)$, that is, for a measure preserving $\mathbb Z [i]$ action $T$, the ergodic averages weighted by the divisor function converge pointwise for all functions in $L^p$, for $p>1$.  We obtain improving and sparse bounds for these averages.

Additive energies of subsets of discrete cubes

Series
Number Theory
Time
Wednesday, September 25, 2024 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Fernando Xuancheng Shao – University of Kentucky –

 For a positive integer , define  to be the smallest number such that the additive energy of any subset and any  is at most . In this talk, I will survey recent results on bounds for , explore the connections with (variants of) the Hausdorff-Young inequality in analysis and with the Balog-Szemeredi-Gowers theorem in additive combinatorics, and then discuss new results on the asymptotic behavior of  as .