#### 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.

Done