Thu, August 22, 2019
Public Access

Category: All

August 2019
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11:00am [11:30am] Aprameyo Pal : University of Duisburg-Essen, Germany
Number theory seminar. Speaker: Aprameyo Pal. Affiliation: University of Duisburg-Essen, Germany. Date and Time: Thursday 22 August, 11:30 am - 12:30 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: A central value formula of degree 6 complex L-series and arithmetic applications. Abstract: We prove an explicit central value formula for a family of complex L-series of degree 6 for GL2 × GL3 which arise as factors of certain Garret--Rankin triple product L-series associated with modular forms. Our result generalizes a previous formula of Ichino involving Saito--Kurokawa lifts, and as an application, we prove Deligne's conjecture about the algebraicity of the central values of the considered L-series up to the relevant periods. I would also include some other arithmetic applications towards subconvexity problem, construction of associated p-adic L function etc. This is joint work with Carlos de Vera Piquero.

2:00pm [2:00pm] Deepanshu Kush : IIT Bombay
Combinatorics seminar. Speaker: Deepanshu Kush. Affiliation: IIT Bombay. Date and Time: Tuesday 22August, 2:00 pm - 3:00 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: Normalized Matching Property in Random & Pseudorandom Graphs. Abstract: Normalized Matching Property (NMP) is a simple and natural generalization of the famous Hall's marriage condition for bipartite graphs, to the setting when the sizes of the two vertex classes are distinct. It is a well-studied notion in the context of graded posets and several well-known ones are known to have it (for instance the boolean lattice or the poset of subspaces of a finite dimensional vector space). However, in this talk, we will consider NMP with a 'random twist': if for every possible edge in a bipartite graph, we toss a coin in order to decide if we keep it or not, how biased must the coin be to expect to have NMP in the graph with high probability? We shall arrive at a sharp threshold for this event. Next, what can we say about explicit graphs that are known to behave 'random-like'? One of the earliest notions of a pseudorandom graph was given by Thomason in the 80s. We shall prove an 'almost' vertex decomposition theorem: every Thomason pseudorandom bipartite graph admits - except for a negligible portion of its vertex set - a partition of its vertex set into trees that have NMP and which arise organically through the Euclidean GCD algorithm.

3:00pm [3:45pm] Dr. P. V. Sukhatme Memorial Lecture: Rajeeva Karandikar (CMI)
Dr. P. V. Sukhatme Memorial Lecture. Speaker: Rajeeva Karandikar. Affiliation: Chennai Mathematical Institute. Date and Time: Thursday 22 August, 3:45 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: On Connections between Partial Differential Equations and Diffusion Processes. Abstract: In this talk we will describe connections between second order partial differential equations and Markov processes associated with them. This connection had been an active area of research for several decades. The talk is aimed at Analysts and does not assume familiarity with probability theory.