Annual Progress Seminar

Monday, 30th September 2023, 11:00-11.30 am

Time, Day, Date :  11 am,  Monday, 30th September

Venue : Room 216

Speaker : Pallab Kumar Sinha

Title : A Multi-Region Discrete Time Chain Binomial Model for Infectious
Disease
Transmission

Abstract : We explore a multi-category disease model to study about how
disease spreads in neighbouring geographical regions. Simulation results
and real data results based on a UK measles data is used for illustration
purposes.
 

1. Number Theory Seminar
Speaker: Keshav Aggarwal (Department of Mathematics, IIT Bombay)
Title: Tate's thesis
Time, Day and Date: 11:30 a.m. - 1:00 p.m., Monday, September 30
Venue: Room 215

Abstract: We will start chapter 2 of Goldfeld--Hundley. Here, we'll define automorphic representations for GL(1) and apply the adelic Poisson summation formula to derive the functional equation of the Riemann zeta function.

Annual Progress Seminar

Monday, 30th September 2023, 11:30 am-12.00 pm

Venue: Room 216, Department of Mathematics

Speaker: Niphadkar Shubham Sanjay

Title: Optimality of Multivariate Crossover Design in Correlated Setup

Abstract: We consider multivariate crossover designs with correlation
between responses. In order to account for correlation between responses,
we consider the proportional and the generalized Markov-type of covariance
structures. We investigate efficiency using various structures for the
variance-covariance matrix within the response, namely the exponential,
gaussian and Mattern(1.5) structures. We prove that an orthogonal array
design of type I and strength 2 is A-, D- and E-optimal for the direct
effects under the proportional covariance structure. We propose the mixed
effects model using subject effects as random effects and obtain
the structure of the information matrix for the direct effects.

PreSynopsis Seminar:

Speaker: Akash Yadav (Department of Mathematics, IIT Bombay)

Title: Archimedean Integral Representations and Poles of $L$-functions

Time, Day and Date: 3:00 - 4:00 p.m., Monday, September 30

Venue: Conference Room, Department of Mathematics

2. Annual Progress Seminar
Speaker: Hamidul Ahmed (Department of Mathematics, IIT Bombay)
Title: Complete Nevanlinna-Pick Dirichlet series kernel and multiplier variety
Time, Day and Date: 3:00 - 4:00 p.m., Monday, September 30
Venue: Ramanujan Hall, Department of Mathematics

Abstract: In this talk, we will concentrate on Dirichlet series kernels, which are also complete Nevanlinna Pick (CNP) kernels. We will start with a characterization of such kernels. It is known that every CNP space is isometrically isomorphic to the Drury-Arveson space restricted to its smallest multiplier-variety. Therefore, determining the smallest multiplier-variety is crucial in our context. McCarthy and Shalit have shown that if we take CNP Dirichlet series kernels corresponding to d natural numbers which are log independent, then the smallest multiplier-variety is the full ball, and thus the RKHS corresponding to such Dirichlet series kernels are isometrically isomorphic to the Drury-Arveson space. In this talk, we will completely determine smallest multiplier-varieties for any CNP Dirichlet series kernels.

Combinatorics Seminar
Speaker: Anand Srivastav (Kiel University, Germany)
Title: Chromatic number of randomly augmented graphs
Time, Day and Date: 4:00 - 5:00 p.m., Monday, September 30
Venue: Room 114

Chayan will present his 4th APS in the Ramanujan Hall at 4 pm today.
Tea and snacks after the talk.

Title: Character values at elements of order 2.

Abstract: We aim to compute the character values of highest weight representations for
classical groups of types An, Bn, Cn, and Dn at specific conjugacy classes of order
2. We will demonstrate that these character values can be expressed either as
a product involving the dimensions of two highest weight representations from
classical subgroups, along with an additional constant term, or as an alternating
sum of products of the dimensions of two highest weight representations from the
classical subgroups, also accompanied by an extra constant term.

4. Commutative Algebra Seminar
Speaker: R. V. Gurjar (TIFR, Mumbai (retired))
Title: Local Analytic Geometry
Time, Day and Date: 12:30 - 2:00 p.m., Tuesday, October 1
Venue: Room 215, Department of Mathematics
 

Combinatorics Seminar
Speaker: Anand Srivastav (Kiel University, Germany)
Title: Chromatic number of randomly augmented graphs
Time, Day and Date: 4:00 - 5:00 p.m., Tuesday, October 1
Venue: Room 114

Abstract: https://drive.google.com/open?id=1EQxBeQKYytlkBAHQf7gaTpgLzzr36WAh

Algebraic Groups Seminar
Speaker:  Shripad Garge (Department of Mathematics, IIT Bombay)
Title: Geometric questions related to the Bruhat decomposition II
Time, Day and Date: 4:00 - 6:00 p.m., Tuesday, October 1
Venue: Ramanujan Hall, Department of Mathematics
Abtract: We study some geometric aspects of the Bruhat decomposition.

Speaker: Dr Renu Joshi, IISER Bhopal

Time, Day and Date: 2.30 pm, Thursday, October 3, 2024.

Google Meet Link: https://meet.google.com/fqv-owns-ydv

Title: The Schur Multiplier and Non-inner Automorphism Conjecture

Abstract: The Schur multiplier M(G) of a finite group G is defined as H^2(G, ℂ×), where ℂ× is the trivial G-module. Several authors have determined upper bounds on the order, rank, and exponent of M(G). If G is a p-group of a maximal class of order p^n and 4 ≤ n ≤ p+1, we demonstrate that the Schur multiplier M(G) is an elementary abelian p-group. Additionally, the case n = p+1 answers a question raised by Primož Moravec.

In 1973, Berkovich asked if every finite non-abelian p-group has a non-inner automorphism of order p, for any prime p. This problem is solved in the positive direction for several classes of p-groups. In 2017, it was proven for p-groups of co-class 3 for p≠3. Consequently, the following question arises: Does the non-inner automorphism conjecture hold for finite 3-groups of co-class 3? Our current work focuses on 3-groups of co-class 3. We will discuss our progress and findings in this direction.

Complex Algebraic Surfaces
Speaker: Ronnie Sebastian (Department of Mathematics, IIT Bombay)
Title: Ruled Surfaces
Time, Day and Date: 3:30 - 5:00 p.m., Thursday, October 3
Venue: Room 114, Department of Mathematics

Abstract: We will continue with Chapter 3 in Beauville.

Algebraic Groups Seminar
Speaker: Deep Makadiya (Department of Mathematics, IIT Bombay)
Title: Nilpotent conjugacy classes
Time, Day and Date: 4:00 - 5:30 p.m., Friday, October 4
Venue: Room 215, Department of Mathematics

Abtract:We will continue the analysis of nilpotent conjugacy classes using the book by Collingwood and McGovern.