


Algebraic Geometry seminar
Date and Time: Thursday, 12 Jan 2023, 11.3012.45
Venue: Ramanujan Hall
Host: Sudarshan Gurjar
Speaker: Atharva Korde
Affiliation: University of British Columbia, Vancouver, Canada
Title: Gromov Witten invariants and Donaldson Thomas invariantsIII
Abstract: I will give an introduction to GromovWitten invariants (via algebraic geometry, rather than symplectic geometry) and DonaldsonThomas invariants. Then I will explain the GWDT correspondence, which relates these two sets of numbers for a CalabiYau threefold. If time permits, I will talk about quantum cohomology later, an idea of Kontsevich which is used to answer the question of counting the following GWinvariant – how many rational curves of degree d pass through 3d1 general points in the plane? The first talk will be less technical and accessible to anyway with minimal knowledge of algebraic geometry. The second talk will be more technical.
Seminar on Coding Theory
Date and time:: Thursday, 12th January 2023 at 2.30 pm
Venue: Ramanujan Hall
Speaker: Mahir Bilen Can
Affiliation: Tulane University, New Orleans, USA
Host: Sudhir Ghorpade
Title: Dual Higher Grassman Codes
Abstract: The Grassmann variety of kdimensional subspaces of an ndimensional vector space over a finite field with qelements can be thought of as the ``moduli space'' of all linear qary (n,k)codes. At the same time, each Grassmann variety naturally provides an algebraic geometry code via its Plucker embedding. The structure of Grassmann codes has been parsed by many researchers, most notably by Ghorpade. In this talk, we will discuss a fruitful generalization of the Grassmann codes by using the embeddings of Grassmannians into higher dimensional projective spaces. This new family of ``higher Grassmann codes'' has interesting connections with representation theory of SL_n over finite fields.
Commutative algebra seminar Date and time: Thursday, 12 January 2023, 4 pm Venue: Ramanujan Hall Host: Manoj Keshari Speaker: Soumi Tikedar, Diamond Harbour Women's University Title: On a question of Moshe Roitman and its applications Abstract: Let A be a ring of dimension d and P be a projective A[T]module of rank n. We say that p ∈ P is a unimodular element if there exists a homomorphism f in P* such that f(p) = 1. When n > d, then Plumstead proved that P has a unimodular element. But this is not the case for n=d and n< d. In this talk, we will discuss the following results: Theorem: Let A be a ring of dimension d containing an infinite field k, P be a projective A[T]module of rank n such that 2n is not less than d + 3 and singular locus of Spec(A) is a closed set V(J) with ht J is atleast d − n + 2. If P_f has a unimodular element for some monic polynomial f(T). Then P has a unimodular element. Next, we will discuss some applications of Roitman's question to define the Euler class group, which serves as an obstruction group to detect the existence of unimodular elements in the Projective module with certain conditions. In this talk, we associate a stably free module to the Euler class group and show that the vanishing of this is the precise obstruction having P unimodular element.