Colloquium 2:

Time, Day, Date: 24rd October, Thursday 4:00 pm

Venue ; Ramanujan Hall

Speaker: S. Ramanan

Title : Hyperelliptic curves and Geometry of quadrics

Abstract : There is a deep relationship between hyper-elliptic curves of
genus $g$ and quadric geometry in a projective space of dimension $2g +1$.
When $g = 2$,  this was investigated by Klein in the 19th century.
Narasimhan and I related this to the moduli of vector bundles. Usha and I
generalised the results to arbitrary genus. Recently I modified and
formulated the proofs in such a way that it would work over a number
field. This was used by Parimala Raman and Jaya Iyer to get
number-theoretic consequences. I propose to give a summary of my methods
which yield some additional consequences as well.
 

4. Commutative Algebra Seminar

Time, Day and Date : 24th October, Thursday, 4:00 pm

Venue : Room 215

Speaker : Samarendra Sahoo

Title : Primes associated to multigraded rings.

Abstract :  Let A be a Noetherian ring, I be an ideal, and M be a finitely
generated A-module. Brodmann(1979) proved that the set Ass(I^nM/I^{n+1}M)
and Ass(M/I^nM) are stable for large n. McAdam and Eakin(1979) proved that
if R is a standard graded Noetherian ring with R_0=A and M is a finitely
generated graded R-module then the set Ass_A(M_n) is stable for all large
n. In this series of talks, we will discuss a multigraded version of the
above result and its applications.
 

5. Analysis Seminar (Ricci flows)

Time, Day and Date: 24th October, Thursday, 5:30 pm

Venue : Ramanujan Hall

Speaker: Pradip Kumar Maity

Title : 2nd expository talk on Ricci flows

Abstract : We will continue with Ricci solitons. Then we shall move to
variation formulas. Next we will discuss briefly short time existence of
Ricci flow. After that  we will move to Maximum principal and its
consequences.