Thu, August 22, 2019
Public Access Category: All |
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- Time:
- 11:30am-12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- 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.
- Time:
- 2:00pm-3:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- 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.
- Time:
- 3:45pm-4:45pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- 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.