Commutative algebra seminar

M.Sc. project presentation

Monday, 17 July, 11 am

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Venue:  Ramanujan Hall
Host: J. K. Verma
Speaker: Pradyumna Datta, IIT Bombay

Title: Syzygies of toric ideals  and integer programming
Abstract: We shall present algorithms to find integer solutions of linear Diophantine equations using computations of syzygies of toric ideals using Grobner bases of polynomial ideals.

Mathematics Colloquium:

Date and time: Monday, July 17, 4:00 p.m. 

Venue: Ramanujan Hall, Department of Mathematics

Host: Ravi Raghunathan

Speaker:  Subhajit Jana 

Affiliation:  Queen Mary's College

Title: Analytic Newvectors and moments of central L-values

Abstract: 

A reciprocity formula usually relates certain moments of two different families of L-functions that apparently have no connections between them. The first such formula was due to Motohashi who related a fourth moment of Riemann zeta values on the central line with a cubic moment of certain automorphic central L-values for GL(2). 

In the first talk, we describe some instances of reciprocity formulas both in low and high-rank groups and give certain applications to subconvexity and non-vanishing of central L-values. This talk will be partly based on a few joint works with Nunes and Blomer--Nelson.

Number Theory Seminar:

Date and time: Tuesday, July 18, 4:00 p.m

Venue: Ramanujan Hall, Department of Mathematics

Host: Ravi Raghunathan

Speaker:  Subhajit Jana 

Affiliation:  Queen Mary's College

Title: Analytic Newvectors and moments of central L-values

Abstract: In the second talk, we describe the concept of analytic newvectors and how they can be used for asymptotic evaluation of moments of central L-values in the conductor aspect. This talk will be partly based on joint work with Nelson.

Algebraic Groups seminar

Tuesday, 18 July 2023, 4.30 pm

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Venue: Room 114

Host: Shripad Garge

Speaker: Dibyendu Biswas

Affiliation: IIT Bombay

Title: Diagonalizable groups and tori

Abstract: We resume our seminar with a quick review of the first two chapters of Springer's book.

Time permitting, the third chapter will be discussed.

Mathematics Colloquium

Wednesday, July 19, 4 pm

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Venue: Ramanujan Hall

Host: Ravi Raghunathan

Speaker: Shreyasi Datta, Univ. of Michigan

Title: S-arithmetic Diophantine Approximation

Abstract: Diophantine approximation deals with quantitative and qualitative aspects of approximating numbers by rationals. A significant breakthrough by Kleinbock and Margulis in 1998 was to study Diophantine approximations for manifolds using homogeneous dynamics. After giving an overview of recent developments in this subject, I will talk about Diophantine approximation in the S-arithmetic set-up, where S is a finite set of valuations of rationals.

Dynamics, geometry and Number Theory Seminar
Thursday, July 20, 4 pm
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Venue: Ramanujan Hall
Host: Ravi Raghunathan
Speaker: Shreyasi Datta

Title: Quantitative Simultaneous Approximation (Seminar talk)

Abstract: One of the most fascinating problems in number theory is to study rationals that are close to a specific curve, more generally, close to a manifold. Showing that given a nice
decaying function, the points on any 'curved' manifold approximated at this function's rate are 'pnegligible' was a long-standing problem.  In recent ground-breaking work (arXiv:2105.13872), Beresnevich and Yang solved this problem.

In this talk, we will explain an effective version of their result. This is based on the work https://arxiv.org/abs/2209.14196.