Geometry and Topology seminar
Speaker: Sudarshan Gurjar, IIT Bombay
Title: Kodaira Embedding Theorem 
Time, day and date: 11:30:00 AM - 12:30:00 PM, Monday, October 27
Venue: Ramanujan Hall
Abstract: This is the fourth talk in the series. After briefly recalling the previous lectures, I will complete the proof of the theorem.

Student Seminar
Speaker: Neeraj Rawat, IIT Bombay
Host: Santanu Dey
Title: One phase Stefan problem in one dimension
Time, day and date: 2:00:00 PM – 2:45:00 PM, Monday, October 27
Venue: Room 113

Student Seminar
Speaker: Sayantan Sinha, IIT Bombay
Host: Santanu Dey
Title: TBA
Time, day and date: 2:45:00 PM – 3:30:00 PM, Monday, October 27
Venue: Room 113

Analysis seminar
Speaker: Prof. S. Thangavelu
Host: Sanjoy Pusti
Title: On Hardy's inequality for fractional powers of the sublaplacian
Time, day and date: 11:00:00 AM – 12:15:00 PM, Tuesday, October 28
Venue: Ramanujan Hall
Abstract: In these lectures we plan to give an introduction to Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group. We will recall the case of the standard Laplacian on $ \R^n $ and give a proof of Hardy's inequality for $ (-Delta)^s $ using extension problem and trace Hardy inequality. We will then develop necessary background for studying the modified extension problem for the sublaplacian, establish an analogue of trace Hardy inequality and deduce Hardy's inequality.

Student Seminar
Speaker: Samiun Ali Molla, IIT Bombay
Host: Keshav Aggarwal
Title: Bounds for Riemann zeta in the critical strip
Time, day and date: 11:30:00 AM – 12:10:00 PM, Tuesday, October 28
Venue: Room 114

Student Seminar
Speaker: Divye Goyal, IIT Bombay
Host: Keshav Aggarwal
Title: Distribution of zeros of Riemann zeta
Time, day and date: 12:15:00 PM – 12:55:00 PM, Tuesday, October 28
Venue: Room 114

Special Colloquium
Speaker: Uwe Franz, Universite Marie et Louis Pasteur, France
Host: Sutanu Roy
Title: What can Levy processes tell us about compact quantum groups?
Time, day and date: 4:00:00 PM - 5:00:00 PM, Tuesday, October 28
Venue: Ramanujan Hall
Abstract: Schurmann has defined Levy processes on involutive bialgebras, a generalization of the notion of Levy processes with values in groups or semigroups, to the setting of noncommutative stochastic processes. This talk will provide an introduction to these processes. We will then apply this theory to compact quantum groups in the sense of Woronowicz, and discuss how Levy processes can provide geometric information, like a spectral dimension or a notion of connected component of the unit, on these quantum spaces.

Mathematics Colloquium
Speaker: Mayukh Mukherjee, IIT Bombay
Title: A \Delta-criterion, Green geometry and the strong Liouville property on groups
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, October 29
Venue: Ramanujan Hall
Abstract: We develop a unified framework linking harmonic function growth, random-walk geometry, and heat kernel asymptotics on finitely generated groups. The central analytic device is a potential theory-based boundary functional whose vanishing characterises strong Liouville property, and we give general heat-kernel envelope conditions that force vanishing without requiring sharp two-sided estimates. This yields new, checkable criteria for strong Liouville on broad classes of groups (including polynomial growth and many subGaussian settings). In the opposite direction, we prove that on exponentially growing groups $\Delta$ does \emph{not} decay on balls (under mild on-diagonal bounds), forcing the existence of non-constant positive harmonic functions. On the geometric side, we show that a trivial Martin boundary collapses the Green geometry and the Green speed vanishes along any path with finite word-speed. Two speed results refine the picture on nilpotent groups. First, there are natural heavy-tail regimes with speed vanishing in probability. Second, under a uniform cone lower bound on jump directions, any positive word-speed implies finite first moment - and by symmetry the drift is then zero almost surely.

This is based on joint work with Soumyadeb Samanta and Soumyadip Thandar

Student Seminar
Speaker: Sourav Khatua, IIT Bombay
Host: Santanu Dey
Title: Morita Equivalence and C*-Correspondence and its application to Graph C*-algebras
Time, day and date: 2:00:00 PM – 2:45:00 PM, Thursday, October 30
Venue: Room 113

Commutative Algebra seminar
Speaker: Sayed Sadiqul Islam, IIT Bombay
Host: Tony Puthenpurakal
Title: ON THE MATLIS DUALS OF LOCAL COHOMOLOGY MODULES
Time, day and date: 4:00:00 PM - 5:00:00 PM, Thursday, October 30
Venue: Ramanujan Hall
Abstract: Let R be a regular local ring of positive characteristic. Let M be a local cohomology module H^i_I(R)​ for any non-zero ideal I of R. We show that if M is non-zero then the support of D(M), where D is the Matlis-dual functor, is the whole Spec(R). The proof is due to Lyubeznik and Yildirim and uses techniques from F-module theory.

Topology and Related Topics Seminar
Speaker: Omkar Ramdas, IIT Bombay
Host: Rekha Santhanam
Title: An introduction to Lawvere theory and their applications
Time, day and date: 11:00:00 AM – 12:00:00 PM, Friday, October 31
Venue: Room 105
Abstract: Lawvere theory is a unique categorical framework which unifies the ideas of algebraic structures like groups, rings, etc into one category using their "logical signatures". I am planning to give two talks on this.
In this first talk, I'll cover the logical prerequisites needed and then we'll go on to define what Lawvere theories are. This talk will be very basic and accessible to all.

Analysis seminar
Speaker: Prof. S. Thangavelu
Host: Sanjoy Pusti
Title: On Hardy's inequality for fractional powers of the sublaplacian
Time, day and date: 4:00:00 PM – 5:15:00 PM, Friday, October 31
Venue: Ramanujan Hall
Abstract: In these lectures we plan to give an introduction to Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group. We will recall the case of the standard Laplacian on $ \R^n $ and give a proof of Hardy's inequality for $ (-Delta)^s $ using extension problem and trace Hardy inequality. We will then develop necessary background for studying the modified extension problem for the sublaplacian, establish an analogue of trace Hardy inequality and deduce Hardy's inequality.