APS
Speaker: Imran Hussain (IIT Bombay)
Host: Saikat Mazumdar
Title: Rigidity results for the Q curvature equation on Einstein manifolds
Time, day and date: 11:30:00 AM – 12:30:00 PM, Monday, September 15
Venue: Ramanujan Hall
Abstract: In this seminar, we classify the constant Q-curvature conformal metrics(cQcc metrics) on Einstein manifolds. We show that on Einstein manifolds cQcc metrics are rigid in the sense that if (M,g) is Einstein then cQcc metrics in the conformal class of g are all of the form "a times g" where "a" is constant

Seminar
Speaker: Prof. Sanghoon Kwon (Catholic Kwandong University, Republic of Korea)
Host: Dipendra Prasad
Title: Non-uniform quotient of Bruhat-Tits buildings: spectral geometry and representation theory
Time, day and date: 2:30:00 PM, Monday, September 15
Venue: Room 105
Abstract: In this talk, we explore the rich interplay between the geometry of Bruhat–Tits buildings and the spectral theory of their non-uniform arithmetic quotients over global function fields. Beginning with an introduction to the Bruhat–Tits tree for PGL2 and higher dimensional buildings for groups, we investigate how these combinatorial and geometric objects give rise to Ramanujan complexes through the theory of automorphic representations.
We emphasize non-uniform lattices arising from function fields, highlighting how Eisenstein series and the residual spectrum contribute to the spectral decomposition. Special attention will be paid to the structure of the Laplacian spectrum on these quotients and the role of the Hecke operators. No special background is assumed. Part of this presentation is based on the joint work with Soonki Hong.

APS
Speaker: Bittu Singh (IIT Bombay)
Host: Rekha Santhanam
Title: Equivariant formal spaces and maps
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, September 17
Venue: Ramanujan Hall
Abstract: D. Sullivan developed a framework for studying rational homotopy theory, in which the rational homotopy type of a space is characterized by commutative differential graded algebras (CDGAs). In this work, we explore the equivariant version of rational homotopy theory, where the equivariant rational homotopy type of a $G$-space is encoded in terms of functors to CDGAs. An especially interesting situation occurs when the rational homotopy type of a space can be completely determined by its cohomology algebra—a property known as formality. This perspective extends further: maps induced on cohomology may determine maps between rational spaces, and such maps are called formal maps.

APS
Speaker: Hamidul Ahmed, IIT Bombay
Host: Bata Krishna Das
Title: Multiplier varieties and multiplier algebras of CNP Dirichlet
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, September 18
Venue: Ramanujan Hall
Abstract: In this talk, I will explore complete Nevanlinna–Pick (CNP) Dirichlet series kernels and the isomorphism problem for their multiplier algebras. To begin with, I will briefly recall key results from my earlier APS presentation, where we identified the multiplier variety as the common zero set of certain polynomials, before presenting new developments. We shall examine the isomorphism problem for a significant class of CNP Dirichlet series kernels, and show that any algebraic isomorphism in this class is automatically an isometric isomorphism.  In particular, we shall address an open question posed by McCarthy and Shalit, resolving it in the negative.