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.