Wed, August 4, 2021
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4:00pm [4:00pm] Mathematics Colloquium: Sriknath Srinivasan (Department of Mathematics, IIT Bombay and Department of Computer Science, Aarhus University)
Description:
Speaker: Sriknath Srinivasan (Department of Mathematics, IIT Bombay and Department of Computer Science, Aarhus University) Title: A Recent Result in Algebraic Complexity Theory Time, Day and Date: 16:00, Wednesday, August 4. Abstract: Given a multivariate polynomial P from C[x_1,...,x_n], one can always write it as a sum of monomials, i.e. a sum of products of variables. However, for most polynomials, such an expression is very verbose, and one can ask if more complicated but succinct expressions can be found. Such expressions can take the form of a sum of products of sums of variables, or a sum of products of sums of products, and so on. The main result here is negative, showing that for some interesting families of polynomials (e.g. the Determinant), there are no such "small" expressions. The aim of the talk is to present the formal statement of the above result and the motivation behind it, which stems from an algebraic analogue of the P vs. NP question (due to Valiant). If there is time, I might even present (part of) the proof, which is short and elementary, needing only some combinatorial and linear-algebraic arguments. Joint work with Nutan Limaye (IITB CSE) and S├ębastien Tavenas (Univ. Grenoble Alpes, Univ. Savoie Mont Blanc). Join Zoom Meeting https://zoom.us/j/96441833399?pwd=OWlIcnFabHIzL1Y3ajhlbzhZalhYdz09 Meeting ID: 964 4183 3399 Passcode: 313170

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