August 2017
Public Access Category: All |

- 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.