### TCS+ talk: Wednesday, October 13 — Nutan Limaye, IT University of Copenhagen

#### by plustcs

The next TCS+ talk will take place next Wednesday, October 13th at 1:00 PM Eastern Time (10:00 AM Pacific Time, 19:00 Central European Time, 17:00 UTC: check your time zone!). **Nutan Limaye** from IT University of Copenhagen will speak about “*Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits*” (abstract below).

You can reserve a spot as an individual or a group to join us live by signing up on the online form. Registration is *not* required to attend the interactive talk, and the link will be posted on the website the day prior to the talk; however, by registering in the form, you will receive a reminder, along with the link. (The recorded talk will also be posted on our website afterwards) As usual, for more information about the TCS+ online seminar series and the upcoming talks, or to suggest a possible topic or speaker, please see the website.

Abstract: Every multivariate polynomial P(X) can be written as a sum of monomials, i.e. a sum of products of variables and field constants. In general, the size of such an expression is the number of monomials that have a non-zero coefficient in P.

What happens if we add another layer of complexity, and consider sums of products of sums (of variables and field constants) expressions? Now, it becomes unclear how to prove that a given polynomial P(X) does not have small expressions. In this result, we solve exactly this problem.

More precisely, we prove that certain explicit polynomials have no polynomial-sized “Sigma-Pi-Sigma” (sums of products of sums) representations. We can also show similar results for Sigma-Pi-Sigma-Pi, Sigma-Pi-Sigma-Pi-Sigma and so on for all “constant-depth” expressions.

The talk is based on a joint work of Nutan Limaye, Srikanth Srinivasan, and Sébastien Tavenas.