October 2016
Public Access Category: All |

- Time:
- 11:00am - 12:30pm
- Location:
- Room 216, Maths Building
- Description:
- Commutative algebra seminar

Title: Depth of higher associated graded modules

Abstract: Let (A,m) be a Noetherian local ring with depth(A) > 1, I an

m-primary ideal, M a finitely generated A-module of dimension r, and G_n,

the associated graded module of M with respect to I^n. We will discuss a

necessary and sufficient condition for depth (G_n) > 1 for all

sufficiently large. This talk is based on a paper by Tony Joseph

Puthenpurakal (Ratliff-Rush filtration, regularity and depth of higher

associated graded modules: Part I )

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Parabolic bundles in positive characteristic.

Abstract: In this talk algebraic parabolic bundles on smooth projective

curves over algebraically closed field of positive characteristic is

defined. We will show that the category of algebraic parabolic bundles is

equivalent to the category of orbifold bundles defined in. Tensor, dual,

pullback and pushforward operations are also defined for parabolic

bundles.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Mathematics Colloquium

Title: Brauer-Thrall Conjectures and Commutative Algebra

Abstract: Brauer-Thrall conjectures for representation theory of Artin algebra's

was proved many years ago (in 1968). However the techniques invented by Auslander to prove this conjecture has found more applications than just proving

the original conjectures. These techniques have been extended in commutative algebra to study Maximal Cohen-Macaulay modules over Cohen-Macaulay isolated singularities. I will also discuss a result of mine in this direction.

Poster: http://www.math.iitb.ac.in/~seminar/colloquium/colloq-05-oct-16.pdf

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Victoria Hoskins from Freie University Berlin.

Title : Stratifications in moduli theory

Abstract

Many moduli spaces in algebraic geometry are constructed as quotients of algebraic varieties by a reductive group action using geometric invariant theory. In this talk we explain two such examples: moduli of coherent sheaves on a projective variety and moduli of quiver representations. In both cases, we introduce and compare two stratifications: a Harder-Narasimhan stratification associated to the notion of stability for the moduli problem and a stratification coming from the geometric invariant theory construction. In nice cases, these stratifications can be used to give recursive formulas for the Betti numbers of the moduli spaces.

Poster: http://www.math.iitb.ac.in/~seminar/colloquium/colloq-13-oct-16.pdf

- Time:
- 11:00am - 12:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Matrix Scaling and Applications

Abstract: When can the rows and columns of a non-negative square

matrix be scaled so that it becomes doubly stochastic? In 1964,

Sinkhorn proposed and analyzed a natural iterative procedure that

produces such a scaling when possible. In this talk, we will see this

procedure and see some algorithmic and (if time permits) combinatorial

applications.

- Time:
- 2:30pm - 4:00pm
- Location:
- Room 113
- Description:
- The h-cobordism theorem -1

Abstract: I will outline a proof of the h-cobordism theorem in these two lectures

- Time:
- 2:30pm - 3:30pm
- Location:
- Room No. 216
- Description:
- The h-cobordism theorem -1

Abstract: I will outline a proof of the h-cobordism theorem in these two lectures

- Time:
- 11:00am - 12:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Spanning trees of the hypercube

Abstract: We will give a combinatorial proof of a product formula for the

number of spanning trees of the n-dimensional hypercube. The proof we will

present is a simplified version of the proof given by Bernardi.

- Time:
- 2:00pm - 3:00pm
- Location:
- Ramanujan Hall
- Description:
- Spekar: Viji Z. Thomas, IISER Thiruvananthapuram

TITLE:* Schur Multiplier and Bogomolov Multiplier.

*Abstract*: We will prove that the second stable homotopy group of the

Eilenberg Maclane space is completely determined by the Schur multiplier.

Then we will discuss about the Schur multipliers of Noetherian groups. Time

permitting, we will also discuss Noether's Rationality problem. All of the

above will be shown as an application of a group theoretical construction.