Speaker : Husney Parvez Sarwar (IIT Kharagpur)

Date : 27th December, 11:30-12:30

Venue : Ramanujan Hall.

Abstract. We shall discuss the cancellation of symplectic modules and the

splitting of symplectic modules.

The symplectic cancellation can be thought of as a projective module

cancellation which is a recent result of Fasel.

The symplectic splitting is similar to Murthy's splitting theorem.

To prove the cancellation and splitting, we shall carefully analyze the

Postnikov tower in the A^1 homotopy category

Then we shall prove the vanishing of top cohomology with coefficients in

some homotopy sheaf.

As an another application of the vanishing result, we answer partially a

question of Mrinal Das about

the isomorphism of (d-1)-th Euler class group and (d-1)-th Chow group.

This is based on a joint work with Rakesh Pawar.

Algebraic Groups seminar

Thursday, 28 December 2023, 4 pm

====================

Venue: Ramanujan Hall

Host: Shripad Garge

Speaker: Chayan Karmakar

Affiliation: IIT Bombay

Title: Differentials & Smooth Points - IV

Abstract: We study the notion of Lie algebra of a linear algebraic group. 

Speaker : Husney Parvez Sarwar (IIT Kharagpur)
Date/ Time : 29th December, 11:30-12:30
Venue : Ramanujan Hall
Title : THE THIRD HOMOLOGY OF SYMPLECTIC GROUPS AND
ALGEBRAIC K-THEORY

Abstract : We improve the homology stability range for the 3rd integral
ho mology of symplectic groups over commutative local rings with infinite
residue field. As an application, we show that for local commutative rings
containing an infinite field of characteristic not 2 the symbol map from
Milnor-Witt K-theory to higher Grothendieck-Witt groups is an isomorphism
in degrees