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.