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.