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 Sébastien Tavenas (Univ.
Grenoble Alpes, Univ. Savoie Mont Blanc).
Speaker: Purna Bangere, University of Kansas, Lawrence, KS, USA.
Date/Time: 6 August 2021, 6:30pm IST/ 1:00pm GMT / 9:00am EDT (joining
time 6:15pm IST).
Google meet link: https://meet.google.com/ffu-vhwk-mjd
Title: Syzygies and Gonality
Abstract: In this talk we will deal with recent results on the so-called
property N_p and M_p. These concern the structure of free resolutions
associated with a very ample line bundle on a projective variety. There
are interesting conjectures and ideas related to the structure of free
resolutions and the intrinsic geometry connected with properties N_p and
M_p. A lot of attention has been paid of property N_p, not so much for
property M_p. In this talk we will describe some new results about
properties M_p for an algebraic surface, some higher dimensional
varieties, and even interesting everywhere non reduced schemes called
carpets.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar