Commutative Algebra Seminar
Speaker: Sayed Sadiqul Islam, IIT Bombay
Host: Tony J Puthenpurakal
Title: Zariski Closedness of Supports of Local Cohomology Modules
Time, day and date: 11:30:00 AM – 12:30:00 PM, Monday, September 07
Venue: Room 215
Abstract: These talks are based on two recent papers, one by Katzman and Zhang and the other by Gintz and Zhang, concerning the Zariski closedness of supports of local cohomology modules in prime characteristic.

We shall show that the support of H_I^i(R/gR) is Zariski closed when R is a regular ring of prime characteristic and g is an element R . We shall also discuss an extension of this result to the case in which R has finitely many isolated singular points. Furthermore, we shall prove that if f_1 and f_2 form a regular sequence, then the support of H_I^j(R/(f_1,f_2)) is Zariski closed.

APS
Speaker: Aditya DSS, IIT Bombay
Host: Ayan Bhattacharya
Title: Growth of regularly varying branching random walks
Time, day and date: 8:15:00 AM – 9:15:00 AM, Tuesday, September 08
Venue: Conference Room
Abstract: We consider branching random walks (BRWs) with real-valued displacements having regularly varying tails, allowing the tail behavior of the displacements to vary across generations. We study the exponential growth of the BRW through its maximal position when the underlying genealogical tree is generated by a supercritical Bienaymé–Galton–Watson process with finite mean. We show that the growth exhibits a phase transition depending on the indices of regular variation of the displacement tails. We further investigate the fluctuations of the maximal position by establishing a weak limit for the appropriately normalized maximal position in the (n)-th generation.

APS
Speaker: Suraj Panigrahy, IIT Bombay
Host: Kummari Mallesham
Title: Short Second Moment of GL(2) L-Functions via Trivial Delta
Time, day and date: 10:00:00 AM – 11:00:00 AM, Tuesday, September 08
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1oeypbYUwezzQrOGejnRLBFsaBPFKwHUh/view?usp=sharing

Special Colloquium
Speaker: Pu Zhao Kow, National Chengchi University
Host: Suman Kumar Sahoo
Title: On scattering behavior of corner domains with anisotropic inhomogeneities
Time, day and date: 3:00:00 PM – 4:00:00 PM, Wednesday, September 09
Venue: Ramanujan Hall

Video Call: https://meet.google.com/ztk-bwit-ioy

Abstract: We investigate the scattering and non-scattering behavior of an anisotropic, inhomogeneous Lipschitz medium at a fixed wave number under a single incident field. By relating the anisotropic non-scattering problem to a Bernoulli-type free boundary problem, we leverage techniques from free boundary theory to show that any anisotropic medium with a Lipschitz, but not C1,α, boundary scatters all incident waves satisfying a non-degeneracy condition [1]. For degenerate incident waves, the outcomes fall into two categories [2]: In the first, we show that in two dimensions, piecewise C1 or convex penetrable obstacles with corners (and in higher dimensions, obstacles with edge points) always produce nontrivial scattering. In the second, we prove that piecewise C 1 obstacles with corners in two dimensions (or with edge points in higher dimensions) whose angles are not rational multiples also generate nontrivial scattering for any incoming wave. This is a joint work with Mikko Salo and Henrik Shahgholian.

APS
Speaker: Bittu Singh, IIT Bombay
Host: Rekha Santhanam
Title: On Equivariant Formality of G-equivariant Sapces and Maps
Time, day and date: 10:00:00 AM – 11:00:00 AM, Thursday, September 10
Venue: Ramanujan Hall
Abstract: Triantafillou and Scull developed an equivariant rational homotopy theory in which the rational $G$-homotopy type of a simply $G$-connected space is encoded by a suitable functor taking values in commutative differential graded algebras (CDGAs). When the rational $G$-homotopy type of a $G$-space is completely determined by the associated cohomology diagram, the space is called equivariantly formal. This perspective naturally leads to the study of formal maps, namely maps whose rational homotopy-theoretic information is, up to the appropriate notion of equivalence, determined by their induced maps in cohomology. In this talk, we discuss formality of spaces and maps in the equivariant setting. 

Algebraic Groups Seminar
Speaker: Sabyasachi Dhar, IIT Bombay
Host: Shripad M. Garge
Title: F-rank and the duality functor
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, September 10
Venue: Room 215
Abstract: F-rank and the duality functor from Digne-Michel, Chapter 7

Plancherel measure
Speaker: Dipendra Prasad, IIT Bombay
Title: Plancherel measure
Time, day and date: 5:00:00 PM – 6:15:00 PM, Friday, September 11
Venue: Room 215
Abstract: Waldspurger, J.-L. La formule de Plancherel pour les groupes p-adiques (d'après Harish-Chandra). (French) [The Plancherel formula for p-adic groups (after Harish-Chandra)] J. Inst. Math. Jussieu 2 (2003), no. 2, 235–333.