webcal

Time:

11:30am - 12:30pm

Location:

Ramanujan Hall

Description:

Title: Uncertain Compression and Graph Coloring
Speaker: Madhu Sudan (Harvard)

The classical task of compression, made famous by the works of Shannon and
Huffman, asks the question: Given a distribution on possible messages, how
can one build a dictionary to represent the messages so as to
(approximately) minimize the expected length of the representation of a
random message sampled from this distribution. Given the centrality of
compression as a goal in all, natural or designed, communication, we
introduce and study the uncertain compression problem. Here the goal is to
design a compression scheme that associates a dictionary to each
distribution such that messages can be recovered even by receivers that do
not know the distribution exactly, but only know them approximately.
Understanding the limits of uncertain compression leads to intriguing
challenges and in particular leads to the challenge of understanding the
chromatic number of an explicit family of graphs. In this talk we will
describe some of the graphs, and attempts to bound their chromatic number.

Based on joint works with Badih Ghazi, Elad Haramaty, Brendan Juba, Adam
Kalai, Pritish Kamath and Sanjeev Khanna.

Time:

2:30pm

Location:

Ramanujan Hall

Description:

Speaker: Akshaa Vatwani, University of Waterloo

Title : Variants of equidistribution in arithmetic progressions

Abstract: It is well known that the prime numbers are equidistributed in
arithmetic progressions. Such a phenomenon is also observed more generally
for a class of multiplicative functions. We derive some variants of such
results and give a few applications. We also discuss an interesting
application that relates to the Chowla conjecture on correlations of the
Mobius function, and show its relevance to the twin prime conjecture.

Time:

3:30pm - 5:30pm

Location:

Room 215, Department of Mathematics

Description:

Speaker: Prof. Mahan Mj (TIFR Mumbai)

Title: Non-arithmetic lattices

Abstract: We shall describe a construction of non-arithmetic lattices in SO(n,1)
following Agol.

Time:

4:00pm

Location:

Ramanujan Hall

Description:

Speaker: Dr. Swarnava Mukhopadhyay

Title: Conformal blocks, strange duality and the moduli space of curves.

Abstract: Conformal blocks are refined invariants of tensor product of
representations of a Lie algebra that give a special class of vector
bundles on the moduli space of curves. In this talk, I will introduce
conformal blocks and explore connections to questions in algebraic
geometry and representation theory. I will also focus on some ``strange"
dualities in representation theory and how they give equalities of divisor
classes on the moduli space of curves.

Time:

3:30pm

Location:

Room 215, Department of Mathematics

Description:

Title. Compact Complex Surfaces

Abstract: We will start with some general results about compact complex
manifolds of dimension 2 (including non-algebraic ones) like intersection
theory, Hodge Index Theorem, Riemann-Roch Theorem...The goal is to outline
the classification of minimal smooth projective surfaces, and describe the
main properties of surfaces in each class. Due to time constraints almost
no proofs will be given

Time:

4:00pm - 5:00pm

Location:

Ramanujan Hall

Description:

Speaker: Dr. Jotsaroop Kaur, IISER Bhopal

Title: Localisation of Bochner Riesz means on sets of positive Hausdorff
dimension in R^d

Abstract is attached.

Time:

4:00pm - 5:00pm

Location:

Ramanujan Hall

Description:

Speaker: Dr. Debanjana Mitra, (Postdoc, Virginia Tech.)
Title: Control theory in partial differential equations,

Abstract:

I shall discuss on control problems governed by the partial differential
equations-mainly compressible Navier-Stokes equations,
visco-elastic flows. I shall mention some of the basic tools applicable to
study the control problems.
We mainly use spectral characterization of the operator associated to the
linearized PDE and Fourier
series techniques to prove controllability and stabilizability results.
I shall also indicate how the hyperbolic and parabolic nature of equations
affects their main controllability results.
Then some of our recent results obtained in this direction will be
discussed.

Time:

5:00pm - 6:00pm

Location:

Ramanujan Hall

Description:

Title: Heaps and applications
Speaker: K N Raghavan
Affiliation: The Institute of Mathematical Sciences (IMSc)

Abstract: This talk is based on the recently concluded 19-lecture course by Xavier Viennot at IMSc, and is meant as publicity for the videos
(freely and perpetually accessible) of those lectures on the Matscience Youtube channel. The lectures are jam-packed with new and elegant proofs of well known results, myriad applications--- from graph theory to Lie algebras and their representations to statistical physics and even quantum gravity---and open problems
of varying difficulty. We will take a tour through the basic definition, the main technical results, and some applications.

Time:

3:30pm

Location:

Room 215, Department of Mathematics

Description:

Prof R V Gurjar

Compact Complex Surfaces

Abstract. We will start with some general results about compact complex manifolds of dimension 2 (including non-algebraic ones) like intersection theory, Hodge Index Theorem, Riemann-Roch Theorem...The goal is to outline the classification of minimal smooth projective surfaces, and describe the main properties of surfaces in each class. Due to time constraints almost no proofs will be given.

Time:

4:00pm

Location:

Ramanujan Hall

Description:

Speaker : C S Rajan (TIFR Mumbai)

Title: A universal Torelli theorem for elliptic surfaces

Abstract: Given two semistable
elliptic surfaces over a curve $C$ defined over a field of
characteristic zero or finitely generated over its prime field, we
show that any compatible family of effective isometries of the
N{\'e}ron-Severi lattices of the base changed elliptic surfaces for
all finite separable maps $B\to C$ arises from an isomorphism of the
elliptic surfaces. Without the effectivity hypothesis, we show that
the two elliptic surfaces are isomorphic.

We also determine the group of universal automorphisms of a semistable
elliptic surface. In particular, this includes showing that the
Picard-Lefschetz transformations corresponding to an irreducible
component of a singular fibre, can be extended as universal
isometries. In the process, we get a family of homomorphisms of the
affine Weyl group associated to $\tilde{A}_{n-1}$ to that of
$\tilde{A}_{dn-1}$, indexed by natural numbers $d$, which are closed
under composition.

Time:

9:30am - 10:30am

Location:

Room 215, Department of Mathematics

Description:

Speaker: Rajiv Kumar

Title: Herzog-Kuhl Equations and its Applications - I

Abstract: In these talks, we will see relations between Hilbert series of a module and its graded Betti numbers. This gives relations between the
graded Betti numbers of a modules which are known as Herzog-Kuhl equations. As an application, we show that the property of R being Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay R-module of finite projective dimension.

Time:

10:30am - 11:30am

Location:

Room 215, Department of Mathematics

Description:

Speaker: Jai Laxmi

Title: Tate Resolutions - I

Abstract: Let S be a Noetherian ring, and R = S/I. It is always possible to construct a differential graded algebra (DG-algebra) resolution of R over S due to a result of Tate. If R is the residue field of S, then
Gulliksen proved that such a DG-algebra resolution is minimal. We shall discuss the construction of the Tate resolution in our talk.

Time:

11:00am

Location:

Ramanujan Hall

Description:

Speaker: Venkitesh S.I. (IITB)

Title: The Szemeredi-Trotter Theorem

Abstract:

Given a finite set of points P in R^2 and a finite family of lines L
in R^2, an incidence is a pair (p,l), where p\in P, l\in L and p is a
point in l.

The Szemeredi-Trotter Theorem states that the number of incidences is
atmost a constant multiple of (|L||P|)^{2/3} + |L| + |P|. We give a
proof by Tao, which uses the method of cell partitions.

Time:

4:00pm - 5:00pm

Location:

Ramanujan Hall

Description:

Speaker: Prof. Eknath Ghate (TIFR)

Title: Reductions of Galois Representations: Act 1.5

Abstract: We shall describe recent progress on the question of writing
down the reductions of certain local Galois representations. We shall
focus on the case of half integral slopes (especially slope 3/2)
where the behaviour of the reduction is both more complicated and
more interesting.

Our proof uses the mod p Local Langlands Correspondence to reduce the
problem to computing the reductions of certain locally algebraic
representations of GL_2 of the p-adics on certain functions on
the underlying tree.