List of speakers and abstracts

Date and Time: Monday 8th Jan, 4- 5pm

Venue: Ramanujan Hall

Speaker: Anusha Krishnan

Affiliation:  University of Münster

Title: Toral symmetries of homogeneous ancient Ricci flows

Abstract: Ricci flow solutions that are defined for all negative times, are called ancient, and have a special significance since they arise as blowup limits at singularities of the flow. Several instances in the literature suggest that ancient solutions to the Ricci flow have a higher degree of symmetry than initially assumed. In recent work (joint with F. Pediconi and S. Sbiti), we show that under certain assumptions, collapsed homogeneous ancient solutions to the Ricci flow have additional toral symmetry.

Date and Time: Feb 9, 4pm - 5pm

Venue: Ramanujan Hall

Speaker: Debraj Chakrabarti

Affiliation: Central Michigan University, Mt. Pleasant, MI

Title: Projection operators on Bergman spaces of Reinhardt domains.

Abstract: It is a famous result of M. Riesz that the Szegö projection operator, initially defined as the orthogonal projection from the space of square integrable functions on the circle to the Hardy space of the disc extends continuously as a projection operator from $L^p(T)$ onto $H^p(D)$. There is a long history of similar results in the setting of Bergman spaces, and a long list of domains where an analogous statement does not hold in the Bergman setting. We try to understand the geometric distinction between the Hardy and the Bergman situations on Lebesgue spaces, and propose a new projection operator on Reinhardt domains which is expected to have better mapping properties. We verify that the new operator satisfies Lebsegue space estimates in some situations where the Bergman projection operator does not satisfy such estimates. This is joint work with Luke Edholm of the University of Vienna.

Date and Time: March 1, 4pm - 5pm

Venue: Ramanujan Hall

Speaker: Saikat Mazumdar

Affiliation: IITB

Title: Taming explosions by blowing up.

Abstract: In this talk, I will consider the question of compactness of (approximate) solutions to some Yamabe-type problems. We will see that by appropriately blowing up the singularities a finer analysis often reveals some analytical or geometric rigidity, thereby ruling out explosions. This establishes uniform bounds which implies compactness (in the appropriate topology) and gives existence and non-existence results. 

Date and Time: March 7, 4pm - 5pm

Venue: Ramanujan Hall

Speaker: Dhriti Ranjan Dolai

Affiliation: IIT Dharwad

Title: The central limit theorem (CLT) for integrated density of states (IDS) of discrete random Schrodinger operator (Anderson model on lattice)

Abstract: Abstract  

Date and Time: March 15, 5pm - 6pm

Venue: Ramanujan Hall

Speaker: Niranjan Balachandran

Affiliation: IITB

Title: Title: What is the Polynomial method?

Abstract: The solution of the Erdos distinct distances Problem in 2014 was
the culmination of a new and powerful method that has since then also been
exploited in settling many problems in Combinatorics, and Fourier Analysis
as well.

We shall take a combinatorial perspective here and look at the solutions
to 3 problems: the Finite Kakeya Conjecture, the Szemeredi-Trotter
theorem, and a partial solution to the distinct distances problem. It will
also be instructive to know what does NOT constitute the application of
the Polynomial method.

Date and Time: March 22, 4:30pm - 5:30pm

Venue: Ramanujan Hall

Speaker: Niranjan Balachandran

Affiliation: IITB

Title: What is the Polynomial method?

Abstract: This is the second talk of the series. We will discuss the Szemeredi-Trotter theorem.

Date and Time: April 5, 4pm - 5pm

Venue: Ramanujan Hall

Speaker: Prachi Mahajan

Affiliation: IITB

Title: The Squeezing function & the Fridman invariant

Abstract: The squeezing function and its dual, the Fridman invariant, are biholomorphic invariants, both of which capture the coarse metric geometry of the given domain. I will describe some results on the squeezing function and Fridman invariant such as their boundary behavior, their utility in classifying the unit ball under various hypotheses, and estimates near the boundary of the given domain. In the second part, I will compare this pair of invariants by showing that they are both equally capable of determining the boundary geometry of a bounded domain if their boundary behaviour is apriori known. 

Date and Time: April 30, 4pm - 5pm

Venue: Ramanujan Hall

Speaker: Mayukh Mukherjee

Affiliation: IITB

Title: Spectra of negatively curved Riemannian manifolds

Abstract: We discuss various issues surrounding the spectra of complete Riemannian manifolds (and sometimes orbifolds) of non-positive curvature. These include, among other topics, absolute and (absence of) singularly continuous spectra, small eigenvalues and eigenfunction decay. This describes previous (and ongoing) joint work with Ballmann and Polymerakis.