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.

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.

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.

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.

We study the localisation of Bochner Riesz means on sets of positive Hausdorff measure in R^d by making use of the decay of the spherical means of Fourier Transform of fractal measures. We study the localisation of Bochner Riesz means on these sets corresponding to the Torus T^d as well.

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.

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.

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.

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.

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