Algebraic geometry seminar

Date

Tuesday, 26 March, 11.30 am

Venue

Room 215

Host

Sudarshan Gurjar

speaker

Nitin Nitsure

Affiliation

Bhaskaracharya Pratishthana

Title

Galois descent and Galois cohomology: examples and calculations.

Abstract

We will begin by recalling the calculus of Galois descent, and its translation into Galois cohomology classes for twisted forms. After that, we will look at common examples, involving Galois twisted forms of algebraic groups, Brauer Severi varieties, and vector bundles (Hilbert 90). The final example will be the Galois twisted from over reals of a non-separated affine line with doubled origin. This twisted form is an algebraic space which is not a scheme.

Topology and Related Topics Seminar

Date

Tuesday 26  March, 2:30 pm

Venue

Ramanujan Hall 

Host

Rekha Santhanam

speaker

Sudarshan Gurjar 

Affiliation

IIT Bombay 

Title

 Vector bundles and Characteristic Classes

Abstract

This is the second talk in the series of three talks. We will give an introduction to the characteristic classes of a vector bundle. Characteristic classes are invariants of a vector bundle taking values in the singular cohomology of the base and satisfying the obvious functoriality property with respect to pullback. They are the measure of the non-triviality of the vector bundle.
The background assumed will depend on the audience present.

Commutative Algebra Seminar

Date

Tuesday, 26 March 2024, 4-5 pm

Venue

Room 215

Host

Tony J. Puthenpurakal

speaker

R. V. Gurjar

Affiliation

IIT Bombay

Title

Some more results about Brieskorn-Pham singularities-II

We will discuss the following results. (1) Classification of 3-dimensional factorial B-P singularities by U.Storch. (2) Classification of affine B-P 3-folds which admit a non-trivial action of the additive group G_a (equivalently, a non-zero locally nilpotent derivation on their coordinate ring) by M. Chitayat. (3) Classification of affine B-P 3-folds which are rational (i.e. their function field is a purely transcendental extension of the ground field) by M Chitayat.