Speaker: Atharva Korde
Title: Cartan's theory of the highest weight and Verma modules
Day and Date: Monday, August 13
Time: 15:30 - 17:00
Venue: Room 215, 2nd floor, Department of Mathematics
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Combinatorics Seminar
Speaker: Vaidy Sivaraman (University of Central Florida)
Venue: Ramanujan Hall
Date & Time: Monday 13th August, 4-5 PM.
Title: Detecting odd holes
Abstract: The complexity of determining whether a graph has an induced odd
cycle of length at least 5 (odd hole) is unknown. In this talk, I will
describe a polynomial-time algorithm to do this if the input graph does
not contain the bull (a particular 5-vertex graph that turns out to be
important in the theory of induced subgraphs) as an induced subgraph.
This is joint work with Maria Chudnovsky.
Time:
5:00pm-6:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Seminar: CACAAG.
Time: 5-6:30 pm, Tuesday, August 14, 2018.
Venue: Ramanujan Hall.
Speaker: J. K. Verma
Title: Richard Stanley's solution of Anand-Dumir-Gupta conjecture about
enumeration of magic squares
Abstract: In 1973 Richard Stanley solved several conjectures about magic
squares
proposed by Harsh Anand, V. C. Dumir and Hans Raj Gupta. In his "Green
Book"
Stanley used the theory of Cohen-Macaulay and Gorenstein rings to solve
these
conjectures. I will sketch his solution assuming only basic commutative
algebra.
Title:
A Finite Field Nullstellensatz and the Number of Zeros of Polynomials over
Finite Fields.
Abstract:
In this series of two talks, we will begin by discussing some
Nullstellensatz-like results when the base field is finite, and outline the
proofs. Next, we will discuss a combinatorial approach to determining or
estimating the number of common zeros of a system of multivariate
polynomials with coefficients in a finite field. Here
we will outline a remarkable result of Heijnen and Pellikaan about the
maximum number of zeros
that a given number of linearly independent multivariate polynomials of a
given degree can have
over a finite field. A projective analogue of this result about
multivariate homogeneous polynomials
has been open for quite some time, although there has been considerable
progress in the last two
decades, and especially in the last few years. We will outline some results
and conjectures here,
including a recent joint work with Peter Beelen and Mrinmoy Datta.