1. Number Theory Seminar.
Speaker: Aditi Savalia (IIT Bombay)
Title: Spectral theory of automorphic forms
Time, Day and Date: 11:30 a.m., Monday, September 2
Venue: Room 215, Department of Mathematics
Abstract: We'll discuss Sections 1.5 and 1.6 of Iwaniec's Topics in Classical Automorphic Forms.

2. Commutative Algebra Seminar.
Speaker: R. V. Gurjar (TIFR Mumbai (retired))
Title: Local Analytic Geometry
Time, Day and Date: 12:30 p.m., Tuesday, September 3
Venue: Room 215, Department of Mathematics

Abstract:

LAG is mainly local study of complex analytic varieties. So it is useful for understanding algebraic varieties in a small Euclidean neighborhood of a point. Some part of the theory is just local algebra, particulaly local analytic rings. The theory is quite non-trivial and rich because of results of Cartan, Hamm, Hironaka, Milnor, Mumford, Oka, Remmert, Scheja, Stein, Thullen, Le dung Trang, Whitney,....It is important for singularity theory, from analytic, geometric, and topological viewpoints. No sheaf cohomology is used.

3. Harmonic Analysis Seminar.
Speaker:  Iswarya Sitiraju (Louisiana State University)
Title: ANALYTIC WAVEFRONT SETS OF SPHERICAL
DISTRIBUTIONS ON THE DE SITTER SPACE
Time, Day and Date: 10:30 a.m., Wednesday, September 4
Venue: Online (Zoom): https://meet.google.com/kmo-osxt-zqh

Abstract: In this work, we determine the wavefront set of certain eigendistributions of the Laplace-Beltrami operator on the de Sitter space. Let G' = {O}_{1,n}(R) be the Lorentz group, and let H' = {O}_{1,n-1}(R) ' be its subset. The de Sitter space dS^n is a one-sheeted hyperboloid in R^{1+n} isomorphic to G'/H'. A {\it spherical distribution} is an H'-invariant eigendistribution of the Laplace-Beltrami operator on dS^n. The space of spherical distributions on the de Sitter space with eigenvalue \lambda, denoted by {D}'_{\lambda}, has dimension 2. We construct a basis for the space of positive-definite spherical distributions as boundary values of sesquiholomorphic kernels on the crown domains, which are open complex domains in dS^n_{C} containing dS^n on the boundary.

We then characterize the analytic wavefront set for such distributions.

4. Number Theory Seminar.
Speakers: Aditi Savalia
Title: Spectral Theory of Automorphic Forms
Time, Day and Date: 11:30 a.m., Wednesday, September 4
Venue: Room 215, Department of Mathematics

Title: Operads and Infinite loop space theory

Time, Day and Date: 11:30 a.m,  Wednesday 4th September 2024.

Venue: Ramanujan hall

Host: Rekha Santhanam

Speaker: Sahin Mandal

Abstract:
 This is the second talk in the  series of talks  on Opera’s and Infinite
loop space theory. In this talk we will see the definition of operads and
various examples.

Colloquium:
Speaker: Ayan Bhattacharya (IIT Bombay)
Title: Persistence of heavy-tailed sample averages: principle of infinitely many big jumps
Time, Day and Date: 4:00 p.m., Wednesday,  September 4
Venue: Ramanujan Hall, Department of Mathematics

6. Analysis Seminar:
Speaker: Utsav Dewan (ISI Kolkata)
Title: Boundary exceptional sets for radial limits of positive superharmonic functions on Harmonic manifolds
Time, Day and Date: 4:00 p.m., Thursday,  September 5
Venue: Ramanujan Hall, Department of Mathematics
Abstract: By classical Fatou (resp. Littlewood) type theorems in various setups, it is well-known that positive harmonic (resp. superharmonic) functions have non-tangential (resp. radial) limits at almost every point on the boundary. In this talk, in the setting of non-positively curved Harmonic manifolds of purely exponential volume growth, we will see some size estimates of the exceptional sets of points on the boundary at infinity, where a suitable function blows up faster than a prescribed growth rate, along radial geodesic rays, in terms of its Hausdorff dimension or Hausdorff outer measure.

 Complex Algebraic Surfaces Seminar:
Speaker: Ronnie Sebastian (IIT Bombay)
Title: Birational maps
Time, Day and Date: 3:30 p.m., Thursday,  September 6
Venue: Room 114, Department of Mathematics
Abstract: We will continue with Chapter 2 in Beauville's book.

1. Number Theory seminar

Time, Day, Date :  11:30 am, Monday 9th Sept

Venue : Room 215

Speaker : Suraj Panigrahy

Title : Tate's thesis learning seminar

Abstract : We will discuss section 1.8 from the book of Goldfeld--Hundley.
We prove an adelic Poisson summation formula.
 

2. Online IPDF Seminar (Statistic)

Time, Day and Date : 4:00 pm, Monday 9th Sept

Joining link : https://meet.google.com/wvi-fjaw-hzk

Speaker: Ritik Soni

Affiliation: Central University of Punjab

Title : On some fractional stochastic processes

3. Local Analytic Geometry (Commutative algebra seminar)

Time, Day, Date: 12:30 pm, Tuesday 10th Sept

Speaker: R.V. Gurjar

Venue: Room 215

Title: Local Analytic Geometry

Abstract: Same as last week

4.  Number Theory Seminar

Day, Date and Time :  Wednesday, 11th September at 11:30 am

Venue: Room 215

Speaker: Aditi Savalia

Title: Spectral theory of automorphic forms

Abstract : We'll discuss Sections 2.1 and 2.2 of Iwaniec's '' Topics in
Classical Automorphic Forms."

5. Pre-Synopsis of Parvez Rasul (Hybrid mode)

Time, Day and Date : 3:30 pm, Wednesday, 11th September

Venue : Ramanujan Hall

Online link : https://meet.google.com/kmo-osxt-zqh

Title: Irreducibility of nested Hilbert and Quot schemes

Abstract : We will begin with a survey of known results on nested Hilbert
Schemes of smooth projective surfaces and Quot schemes on curves. After
this we will mention some new results related to these, which are part of
the thesis of the speaker. If time permits, we will illustrate some of the
ideas which go into the proofs.

6. Complex Algebraic Surfaces

Day, Date and Time : Thursday 12th Sept, 3:30 pm

Venue: Room 114

Speaker : Ronnie Sebastian

Title: Birational maps

Abstract : We will continue with Chapter 2 of Beauville's book.

7.  Algebraic Geometry Seminar

Day, Date and Time: Friday 13th Sept, 2:00 pm

Venue : Room 215

Speaker: Kaushik Khamari

Title : Reducibility of Hilbert Schemes

Abstract : In this second talk, we will explain Iarrobino's proof of the
reducibility of Hilbert schemes.
 

1. APS seminar

Time, Day and Date: Tuesday 17th September, 3:30 pm

Speaker: Priyanka Sen

Venue : Room 113

Title : Large sample behaviour of high-dimensional Kendall's correlation
matrices with dependence

Abstract : The limiting spectral distribution (LSD) of Kendall's
correlation matrix has been established in the literature under conditions
of row dependence. However, the assumptions used in prior works are
non-interpretable and difficult to validate, especially in non-Gaussian
settings. In this talk, we shall discuss the same under more interpretable
assumptions that are easier to visualize and can be validated in a wider
range of non-Gaussian models. Moreover, we shall discuss the joint
convergence of multiple Kendall's correlation matrices and the LSD of
polynomials formed from these matrices. This significantly extends the
existing results in the study of the high-dimensional random matrices.

Title: Matricial Ranges and Extremal Marginal States

Time: Tuesday, 17th September 2024, 5:00 pm - 6:00 pm

Venue: Room 105, Department of Mathematics, IIT Bombay

Abstract: The objective of this talk is twofold. Firstly, we will discuss
a long-standing open problem describing the matricial ranges of the Jordan
block of size three. Secondly, we will discuss various classes of extremal
marginal states that attain the Choi-rank bound given by K. R.
Parthasarathy.
 

2. Algebraic Groups Seminar

Day, Day and Time : Tuesday 17th Sept, 5:00 pm

Speaker: Shripad Garge

Venue : Ramanujan Hall

Title: Parabolic subgroups in reductive groups

Abstract : Let $G$ be a reductive group and $B$ a Borel subgroup in $G$.
We use Bruhat decomposition in $G$ to describe all parabolic subgroups
containing the Borel subgroup $B$.

3. Complex Algebraic Surfaces

Day, Date and Time : Thursday 19th Sept, 3:30 pm

Speaker: Ronnie Sebastian

Venue : Room 105

Title: Ruled Surfaces

Abstract : Following Chapter 3 in Beauville's book, we begin the study of
ruled surfaces.
 

4. Algebraic Groups Seminar

Day, Date and Time : Friday 20th Sept, 4:00 pm

Venue : Room 215

Speaker : Saad

Title : Nilpotent Conjugacy Classes

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

1.  Number Theory seminar

Time, Day, Date :  11:30 am, Monday 23th Sept

Venue : Room 215

Speaker : Keshav Aggarwal

Title : Tate's thesis learning seminar

Abstract : We will finish chapter 1 and begin chapter 2 of
Goldfeld--Hundley. This talk will finish the proof of adelic Poisson
summation formula, and start with its application to derive the functional
equation of the Riemann zeta function.

2. Local Analytic Geometry (Commutative algebra seminar)

Time, Day, Date: 12:30 pm, Tuesday 24th Sept

Speaker: R.V. Gurjar

Venue: Room 215

Title: Local Analytic Geometry

Abstract: Same as before

3. Algebraic Groups seminar

Time, Day and Date : 4:00 pm, Tuesday 24th Sept

Speaker: Chayan Karmakar

Venue : Ramanujan Hall

Title : Geometric questions related to the Bruhat decomposition

Abstract : We complete the description of parabolic subgroups, containing
a given Borel subgroup, in a reductive group and then study some geometric
aspects of the Bruhat decomposition.
 

4. Number Theory Seminar

Day, Date and Time :  Wednesday, 25th September at 11:30 am

Venue: Room 215

Speaker: Aditi Savalia

Title: Spectral theory of automorphic forms

Abstract : We'll discuss Sections 2.2 and 2.3 of Iwaniec's Topics in
Classical Automorphic Forms.
 

APS Seminar

Date and Time: 11:30 AM - 12:30 PM on 25th September, Wednesday

Venue: Ramanujan Hall

Speaker: Surajit Pal

Title: Unique Continuation Principle and its applications

Abstract: This seminar explores the relationship between Hatus Lemma and
unique continuation principle, highlighting how UCP can be used to prove
the conditions for stabilizability in the Hautus Lemma. The Hautus Lemma
provides necessary and sufficient conditions for the stabilizability of
linear systems. The unique continuation which states that any solution  of
an elliptic equation that vanishes in a small ball must be
identically zero.

Then we will try to give the argument how we can get unique continuation
principle for elliptic equation with constant, real-analytic coefficient
and later we will prove the unique continuation for little bit general
set-up using Carleman inequality.

Speaker: Unnati Nigam

Day, Date and Time: Wednesday, 25th September, 11.30 am 
Online mode: join at https://meet.google.com/viw-jwsy-zdr

Title: Modelling of quasi-periodic data 

Abstract:  Quasi (pseudo/approximate) periodic signals often occur in natural settings, particularly when a periodic signal is recorded with noise. In this seminar, we will present a new dynamical equation system to construct a family of Quasi-Periodic Gaussian Processes (QPGP). We will describe a computationally inexpensive algorithm for the maximum likelihood estimation of parameters based on dynamic equations. This approach also simplifies the signal forecasting. We will illustrate via a simulation study that the proposed QPGP estimation strategy is faster as well and more accurate than existing constructions. Unlike these existing models, the proposed approach extends to multiple families of kernels, which we illustrate by modeling sunspot data, carbon dioxide emissions data and ECG data with both periodic Mat\'ern and MacKay's covariance kernel. This shows the exclusive advantage of the new QPGP family proposed in this work.

Debapriya Ojha will give her 2nd APS as follows.

25 September, 2-3 pm, Ramanujan Hall

Title: Hilbert's 17th Problem

Abstract: We will see the general concept of orderings of arbitrary
fields. We then establish relations between sums of squares in a field
and orderings of the same field. Next, we try to enlarge an ordered
field by extending the order to the new elements. Finally, we will
discuss Hilbert's 17th problem about the representation of forms by sums
of squares and its solution by Emil Artin . As an application of this
theorem we get the "sign change criterion".

Google Meet joining info

Video call link: https://meet.google.com/tgz-psxc-riq

Pre-synopsis Seminar

Day, Date and Time : Thursday, 26th Sept, 10:00 am.

Venue : Ramanujan hall.

Speaker : Vikrant Desai.

Title : Ergodic control of degenerate diffusions and mean field games.

Abstract : We talk about small noise limit approach to study ergodic
control problems of controlled degenerate diffusions and investigate mean
field games.

5. Complex Algebraic Surfaces

Day, Date and Time : Thursday 26th Sept, 3:30 pm

Speaker: Ronnie Sebastian

Venue : Room 215

Title: Ruled Surfaces

Abstract : We will continue with Chapter 3 in Beauville.
 

Speaker: Amal Das

Time: 26 September, 4-5 pm

Venue:  Ramanujan Hall.

Title: Concentration phenomena for a Sobolev critical equation.

Abstract: In this report we will study a non-linear elliptic equation on a
bounded smooth domain in R^n with critical Sobolev exponent, the so called
Brezis-Nirenberg problem. The equation can be written in a variational
form and weak solutions can be obtained as the critical points, in
particular, minimizers of the corresponding energy functional. The core
issue is to show that there is no concentration and minimizing sequence
converges, which holds provided one is strictly below a threshold energy
level given by the best Sobolev constant in R^n.

Bittu Singh will be presenting his APS seminar tomorrow.

Time, Day, Date :  4 Pm, Thursday, 26th Sept

Venue : Video call link: https://meet.google.com/bgc-qdgb-ny

Speaker : Bittu Singh

Title : Equivariant formality

Abstract : we explore the concept of the equivariant rational homotopy theory, which
provides a description of the equivariant rational homotopy type of a G-space in terms of Commutative differential graded algebra (CDGAs). A particularly interesting case arises when the homotopy type of the space can be derived from its cohomology algebra, a phenomenon known as formality.

6. APS Seminar

Day, Date and Time : Thursday 26th Sept, 5:00 pm

Venue : Rom 113

Speaker : Dibendu Pal

Title : Lie's third theorem

Abstract : We prove Sophus Lie's so-called third theorem that every finite
dimensional Lie algebra is the Lie algebra of a connected Lie group.

APS Seminar:

        * Title: Zeros of Quadratic Forms over Number Fields

        * Date:26th September, 2024 (Thursday)

        * Time:05:00 PM - 05:40 PM

        * Venue: Conference Room, Department of Mathematics, IIT Bombay

Lal Bahadur Sahu will present his first APS tomorrow. The details are as follows.

Time, Day, Date:  5:45 pm, Thursday, 26th September

Venue: Ramanujan Hall

Speaker: Lal Bahadur Sahu

Title: Clifford Algebra and Spinor Groups

Abstract: Using the theory of Clifford algebra, we will define the spinor groups Spin(n) and show that they form a double simply connected cover of the special orthogonal groups SO(n) for n>2.

Probability Seminar

Day, Date and Time : Thursday 26th Sept 3:00 pm

Venue : Ramanujan Hall

Speaker : Parthanil Roy

Title : Detailed Analysis of Phase Transition for Elephant Random Walks
with Two Memory Channels

Abstract : Random processes with strong memory and/or self-excitation
arise naturally in various disciplines including physics, economics,
biology, engineering, geology, etc. Memory can be multifaceted and can
arise due to interactions of more than one underlying phenomena. Many of
these processes exhibit superdiffusive growth due to the effect of
self-excitation. A class of one-dimensional, discrete-time such models
called “elephant random walk with n memory channels” was introduced and
discussed in a recent paper on statistical physics by Saha (2022). In
these models the information of n previous steps from the walker’s entire
history is needed to decide the future step. The aforementioned work
carried out a bunch of calculations, and conjectured a phase transition
from diffusive to superdiffusive regime based on some numerical
computations in the n=2 case. We have been able to prove these conjectures
rigorously and establish a few new transition boundaries beyond the
predicted ones. I shall present these results along with several open
problems. (This talk is based on a joint work with Krishanu Maulik and
Tamojit Sadhukhan.)

7. Algebraic Groups Seminar

Day, Date and Time : Friday 27th Sept, 4:00 pm

Venue : Room 215

Speaker : Akash Yadav

Title : Nilpotent Conjugacy Classes

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

Annual Progress Seminar

Day, Date and Time : Friday, 27th Sept, 4 pm.

Venue : Ramanujan hall

Speaker : Mayukh Choudhury

Title: Asymptotic Inferences in Generalized Linear Models

Abstract: This talk will be bifurcated into two segments. In the first
part, we will mainly indulge in "Asymptotic Properties of Cross-Validated
Lasso Estimator in GLM". This is precisely the continuation of our last
talk. The penalty parameter in LASSO, is generally chosen in a data
dependent way in practice. Among them, the K-fold CV is the most
celebrated one. So far we have defined the K-fold CV Lasso estimator
$\hat{\lambda}_{n,K}$ and explored its asymptotic properties in terms of
establishing the consistency of the sequence $n^{-1}\hat{\lambda}_{n,K}$
and boundedness of the sequence $n^{-1/2}\hat{\lambda}_{n,K}$ . However,
to justify the distributional convergence of LASSO estimator, we usually
need the convergence of the sequence $n^{-1/2}\hat{\lambda}_{n}$. Towards
that, we will prove the sequence $n^{-1/2}\hat{\lambda}_{n,K}$ is Cauchy
under some additional conditions. Now boundedness together with Cauchy
will serve our purpose. With this we will summarise and conclude this
segment.

In the later half, we will talk about "Large Dimensional CLT in GLM over
Convex Sets and Balls". We will aim to approximate the distribution of
properly centered and scaled GLM estimator with Gaussian random vector
under finite fourth moment condition uniformly over convex sets and
Euclidean Balls precisely when the dimension of the parameter vector, d
can grow with n. For class of measurable convex sets we obtain that d can
grow as o(n^{2/5}) and that for Euclidean Balls, we get d=o(n^{1/2}).
These are the best possible rates that we can have, which are similar to
the findings of Fang and Koike (2024). Lastly, we will prove the Bootstrap
approximation results for the distribution of properly centered and scaled
GLM estimator when the covariance matrix of the Gaussian random vector is
usually unknown.
 

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.