[Colloquium] 7/29 Talks at TTIC: Siddharth Bhandari, UC Berkeley

[Mary Marre]

 *When:*        Friday, July 29th at* 12:30 pm CT*


*Where:       *Talk will be given *live, in-person* at

                   TTIC, 6045 S. Kenwood Avenue

                   5th Floor, Room 530

*Virtually:*  via Panopto (*livestream*
<https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=9ecd58c6-a39c-4d7c-a7bf-aede0161590b>
)


*Who: *         Siddharth Bhandari, UC Berkeley


------------------------------

*Title:*   Vanishing Spaces of Random Sets and Applications
*Abstract: *In this talk we will study the following natural question:
given a random set of k points in $F_2^m$ (m-dim vector space over GF(2)),
what is the dimension of the space of degree at most r multilinear
polynomials that vanish on all points in the set? This question comes up in
a variety of areas such as combinatorics (Kakeya set), coding theory
(weight distribution), etc.
We will analyze the above question and also see how it connects with:
1>BEC-capacity of high-degree Reed-Muller codes
2> Learning a hidden subspace from a mixture.

Based on joint work with Prahladh Harsha, Ramprasad Saptharishi and
Srikanth Srinivasan.
[2205.10749] Vanishing Spaces of Random Sets and Applications to
Reed-Muller Codes (arxiv.org <https://arxiv.org/abs/2205.10749>


*Host:* *Madhur Tulsiani* <madhurt at ttic.edu>




Mary C. Marre
Faculty Administrative Support
*Toyota Technological Institute*
*6045 S. Kenwood Avenue*
*Chicago, IL  60637*
*mmarre at ttic.edu <mmarre at ttic.edu>*
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