Room 217

Research Methodology seminars

First year JRF

IMSc

Title :Quiver representation
Speaker: R. Jayakumar
Time: 10:00 - 10:45
Abstract :
In this seminar presentation, we will talk the categorical aspect of
quiver representation and the indecomposable representations. We
will also discuss Gabriel’s Theorem which allows
to determine the quivers with finitely many indecomposable
representations. If time permits we will sketch the proof of
Gabriel’s Theorem.


Title: L. Vasserstein's solution of Serre's problem on Projective Modules
Speaker: Arpit Kansal
Time: 11:00-11:45
Abstract:In $1958$,J.P.Serre proved that every finitely generated
projective module $M$ over
$k[x_1,...,x_n]$(for $k$ field) is stably free i.e. it becomes free
after adding a finitely generated
free module.Assuming this result of Serre I will present L.
Vasserstein's proof of Serre's problem which
says that every finitely generated projective module over
$k[x_1,...,x_n]$ is in fact free.

Title:- The Inverse Galois Problem for Finite Abelian Group.
Speaker: Satyam Kumar
Time: 11:45-12:30

Abstract:-The Inverse Galois Problem asks that " Whether any finite
group can be realized as the Galois group of some extension
$K/\mathbb{Q}$. In this presentation i will show that the answer to
the inverse Galois problem is yes for finite abelian groups and
dihedral groups.