Colloquia Posters

Department of MathematicsIndian Institute of Technology Bombay

Department Colloquium

Speaker:

Prof. T. N. VenkataramanaSchool of Mathematics

TIFR Mumbai

Title: Monodromy of certain cyclic covers of the pro-jective line.

Abstract:We give a very brief overview of the Deligne Mostow (DM) theory and show thatin contrast to the DM situation, the monodromy group for most of the cyclic covers of theprojective line is an arithmetic group of a certain unitary group.

Date :Wednesday, November 18, 2015

Time :16:00 - 17:00Venue :Ramanujan Hall, Dept. of Mathematics



Speaker:

Prof. Indranil BiswasSchool of Mathematics

TIFR Mumbai

Title: A construction of a universal connection.

Abstract: Let G be a Lie group. We give a new construction of a universal G-connection.This is a joint work with Jacques Hurtubise and James D. Stasheff.

Date : Wednesday, November 4, 2015

Time : 16:00 - 17:00Venue : Ramanujan Hall, Dept. of Mathematics



Speaker:

Prof. K. V. SubrahmanyamChennai Mathematical Institute

Chennai

Title: Invariants of several matrices under SL(n) ×SL(n)-action.

Abstract: Let R(m,n) denote the ring of invariant polynomial functions of the SL(n)×SL(n) action on m tuples of matrices. We describe the ring of relations (the second fun-damental theorem) among these invariants. We also describe the S(m) × S(m)-modulestructure of the invariant ring, where S(m) denotes the symmetric group on [m], and alsothe module structure for the diagonal action of S(m). We describe another natural relationamong the invariants which we believe will be useful to give an upper bound on the degreein which the ring of invariants is generated. We give an algorithm to detect when a tupleof matrices is in the null cone of this action, which runs in time polynomial in the degree inwhich the invariant ring is generated. This algorithm rides on an algorithm of Gurvits, and ouranalysis is based on a novel use of blow-ups of matrices, which we will outline. We will alsostate some recent developments, a polynomial time algorithm for the same problem by twoindependent groups of researchers. This is joint work with Gabor Ivanyos and Youming Qiao.

Date :Wednesday, October 28, 2015




Speaker:

Prof. Sandeep JunejaSchool of Technology and Computer Science

TIFR Mumbai

Title: Large deviations, selecting the best populationand multi-armed bandit methods.

Abstract: Consider the problem of finding a population amongst many with the smallestmean when these means are unknown but population samples can be generated. Typically, byselecting a population with the smallest sample mean, it can be shown that the false selectionprobability decays at an exponential rate. Lately researchers have sought algorithms thatguarantee that this probability is restricted to a small δ in order log(1/δ) computational timeby estimating the associated large deviations rate function via simulation. We show that suchguarantees are misleading. Enroute, we identify the large deviations principle followed by theempirically estimated large deviations rate function that may also be of independent interest.Further, we show a negative result that when populations have unbounded support, any policythat asymptotically identifies the correct population with probability at least 1 − δ for eachproblem instance requires more than O(log(1/δ)) samples in making such a determinationin any problem instance. This suggests that some restrictions are essential on populationsto devise O(log(1/δ)) algorithms with 1 − δ correctness guarantees. We note that underrestriction on population moments, such methods are easily designed. Further, under similarrestrictions, sequential methods from multi-armed bandit literature can also be adapted todevise such algorithms.

Date : Wednesday, October 14, 2015




Speaker:

Prof. Radhika GanapathyTIFR Mumbai

Title: Applications of the Deligne-Kazhdan philoso-phy to the Langlands correspondence for split classicalgroups.

Abstract: The Deligne-Kazhdan theory loosely says that the complex representation theoryof Galois groups and split reductive groups over a local field of characteristic p can be viewedas the limit, as the ramification index tends to infinity, of the representation theory of thesegroups over local fields of characteristic 0. In this talk, I will explain how this method can beused to prove the local Langlands correspondence for split classical groups over a local field ofcharacteristic p (with some restrictions on the characteristic) using the corresponding result ofArthur in characteristic 0. This is joint work with Sandeep Varma.

Date : Wednesday, October 7, 2015




Speaker:

Prof. M. VanninathanTIFR Centre For Applicable Mathematics, Bangalore

Title: The G-closure Problem.

Abstract: The G-closure problem whose origin is in Material Science, seeks to know allpossible material behaviour that one can obtain by mixing the known materials in a givenvolume proportion. In my talk, I discuss one situation where it arises and its resolution. Inparticular, I present mathematical notions and ideas involved in its resolution. Lastly, I mentionhow things can be generalized to more complicated situations. Efforts are made to keep thetalk accessible to non-specialists.

Date : Wednesday, September 30, 2015




Speaker:

Prof. Pralay ChatterjeeThe Institute of Mathematical Sciences, Chennai

Title: Abstract homomorphisms of linear algebraicgroups.

Abstract: We will talk about abstract group homomorphisms between groups of rationalpoints of linear algebraic groups (not necessarily reductive) over some specific fields. We willrecall some past works, go through some examples and describe some new results.





Speaker:

Dr. Ritwik MukherjeePostdoctoral fellow

TIFR Mumbai

Title: Enumerative Geometry of rational cuspidalcurves on del-Pezzo surfaces.

Abstract: Enumerative geometry is a branch of mathematics that deals with the followingquestion: “How many geometric objects are there that satisfy certain constraints?” The simplestexample of such a question is “How many lines pass through two points?”. A more interestingquestion is “How many lines are there in three dimensional space that intersect four genericlines?”. An extremely important class of enumerative question is to ask “How many rational(genus 0) degree d curves are there in CP 2 that pass through 3d-1 generic points?” Althoughthis question was investigated in the nineteenth century, a complete solution to this problemwas unknown until the early 90’s, when Kontsevich-Manin and Ruan-Tian announced a formula.In this talk we will discuss some natural generalizations of the above question; in particular wewill be looking at rational curves on del-Pezzo surfaces that have a cuspidal singularity. Wewill describe a topological method to approach such problems in Enumerative Geometry.

Date :Wednesday, September 16, 2015




Speaker:

Prof. Rahul RoyTheoretical Statistics and Mathematics Unit

ISI Delhi

Title: The Brownian web

Abstract: The Brownian web is a system of coalescing Brownian motions starting fromevery point in the space-time R2. Various random network models scale to the Brownian weband as such many properties of these networks may be obtained from the Brownian web. Wepresent an overview of results in this area.

Date :Wednesday, September 9, 2015




Speaker:

Dr. Sivaguru RavisankarPostdoctoral fellow

School of Mathematics

TIFR Mumbai

Title: Boundary Geometry and Function Theory in Cn

Abstract: There is a deep interplay between boundary geometry and holomorphic functiontheory on domains in Cn, n > 1. This is quite unlike the situation in C and it leads to startlingnew phenomena in higher dimensions that are absent in the one dimensional setting. We willexplore several of these phenomena using concrete examples. The talk would be accessible tograduate (and advanced undergraduate) students - the only prerequisite being a first course incomplex analysis.





Speaker:

Prof. R. ParimalaArts & Sciences Distinguished Professor

Department of Mathematics and Computer Science

Emory University

Atlanta, USA

Title: Local-global principles for homogeneous spacesover function fields of p-adic curves

Abstract: We discuss some recent developments towards Hasse principle for homogeneousspaces under linear algebraic groups over function fields of p-adic curves.

Date : Wednesday, August 26, 2015




Speaker:

Prof. Krishna B. AthreyaDistinguished Professor

Department of Mathematics and Statistics

Iowa State University

Ames, USA

Title: Asymptotics of sums of powers of binomial co-efficients

Abstract: Polya and Szego posed in their famous 1925 book the problem of determiningthe growth rates of sums of powers of binomial coefficients. We solve this using probabilitytheory, elementary Fourier series and generalise this to the multinomial case as well. We shallalso provide yet another proof (7th or so) of Stirling’s formula.





Speaker:

Dr. Anand SawantMathematisches Institut der Universitat Munchen

Ludwig Maximilians Universitat

Munchen

Title: Rationality questions for algebraic groups andhomotopy theory of algebraic varieties

Abstract: The notion of R-equivalence, introduced by Manin in the 1970’s, has been veryuseful in the study of rationality properties of algebraic groups. We will begin with a briefintroduction to R-equivalence and discuss some open questions. In the 1990’s, Morel andVoevodsky developed a (motivic) homotopy theory for algebraic varieties in which the affineline plays the role of the unit interval. Classical results about R-equivalence combined withrecent works in motivic homotopy theory allow one to relate R-equivalence with A1-connectivityin certain algebraic groups. We will give an overview of some recent results in this direction,without going into technical details.





Speaker:

Prof. Abhijit ChampanerkarDepartment of Mathematics

College of Staten Island and The Graduate Center, CUNY

USA

Title: Density spectra for knots

Abstract: Knot theory has a fascinating history of using techniques from diverse fields ofmathematics. In this talk we will explore the interactions of knot theory, hyperbolic geometryand graph theory. We study two natural quantities: the volume density defined as the hyperbolicvolume of a knot complement per crossing number, a geometric invariant, and the determinantdensity defined similarly, a diagrammatic invariant. We will talk about recently discoveredinteresting relationships between the spectra of volume and determinant densities, and explorenatural questions motivated by these bounds. The techniques used in answering some of thesequestions involve an interesting blend of graphs, dimer models and circle packings, in additionto geometric techniques such as polyhedral decomposition and volume bounds. This is jointwork with Ilya Kofman and Jessica Purcell.





Speaker:

Prof. Jayadev AthreyaDepartment of Mathematics

University of Illinois

Urbana, USA

Title: The Erdos-Szusz-Turan distribution for equivari-ant point processes

Abstract:We generalize a problem of Erdos-Szusz-Turan on diophantine approximation toa variety of contexts, and use homogeneous dynamics to compute an associated probabilitydistribution on the integers. This is joint work with Anish Ghosh.

Date :Wednesday, July 29, 2015




Speaker:

Prof. M. Ram MurtyProfessor and Queen’s Research Chair

Department of Mathematics

Queen’s University

Kingston, CANADA

Title:

Consecutive Squarefull Numbers

Abstract:A natural number is called squarefull if whenever a prime p divides it, so does p2. Erdosconjectured that the number of squarefull numbers less than x is bounded by (log x)A forsome A positive. We will prove this conjecture assuming the ABC conjecture and also obtainsome unconditional results. We also relate this problem to the study of fundamental units inreal quadratic fields. This is joint work with Kevser Aktas.

Date : Wednesday, July 01, 2015


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Colloquia Posters