We will begin our Popular Lecture series in Mathematics for this semester on Monday, 6 August, 2018.
Sudarshan Gurjar will be speaking at Ramanujan Hall at 5:15 PM on the following topic.
Title: Applications of Analysis and Topology to Commutative Algebra
Abstract: In this talk, I will discuss two applications of analysis and
topology in constructing counterexamples to certain questions in
commutative algebra. The talk will be fairly elementary and accessible to
M.Sc students.
Time:
5:00pm-6:30pm
Location:
Ramanujan Hall
Description:
Seminar: CACAAG.
Time: 5-6:30 pm, Tuesday, August 07, 2018.
Venue: Ramanujan Hall.
Speaker: Dr. Samir Shukla.
Title: An introduction to some graph coloring complexes
Abstract: Graph complexes are simplicial complexes arising from graphs. In
this talk we mainly focus on two types of complexes: Neighborhood
complexes and Hom complexes. The topology of these complexes are closely
related to the chromatic number of the underlying graphs. We give a brief
survey of the research have been done with respect to them in recent
years. We also discuss some open problems related to them.
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.
Time:
4:00pm
Location:
Room No. 215 Department of Mathematics
Description:
Title: Introduction to Symplectic Geometry
Abstract: In this second talk of the series I will continue the discussion
on symplectic manifolds. I will introduce the moment map and use it to
construct quotients of symplectic manifolds under certain actions of lie
groups.