| Date and Time |
Speaker |
Title |
Abstract |
| |
|
|
|
| 27 April 2011, 3PM |
Chandrasheel Bhagwat, TIFR Mumbai |
On spectral analogues of strong multiplicity one theorem |
The classical strong multiplicity one theorem due to Atkin and Lehner states that, if f and g are newforms for some Hecke congruence sub-
group \Gamma_0(N) such that the eigenvalues of the Hecke operator at a prime p are equal for all but finitely many primes p then f and g are equal. In this
talk, I will talk about analogues of the strong multiplicity theorem in the context of the representation theoretic, function theoretic and length spectra
of compact locally symmetric Riemannian manifolds. This is joint work with Prof. C. S. Rajan. |
| 23 April 2011, 11:30 AM |
Anupam Singh, IISER Pune |
Characters of GL_n(q) |
In this lecture we see how to construct characters of GL_n(q) based on the classical work of Green |
| 23-24 April 2011, 10AM |
Anuradha Garge, CBS Mumbai |
Mennicke symbols and reciprocity laws |
This series of two talks will be based on a paper of Suslin. We will prove that if A is a Noetherian, regular ring of dimension at most two and I is an ideal of A, then there is a one-to-one correspondence between I-reciprocities and Mennicke symbols.
Knowledge of basic commutative algebra will be assumed |
| 22-24 April 2011, 4PM |
Shripad Garge, IIT Mumbai |
Chevalley Groups |
I plan to give a series of lectures on Robert Steinberg's notes on Chevalley groups.
We begin by discussing the basic theory of root systems.
Then we will do theory of Chevalley basis and, if there is time, we will see the construction of Chevalley groups |
| 22 April 2011, 2:30 PM |
Rabeya Basu, IISER Pune |
Bruhat decomposition |
TBA |
| 15 April 2011, 4PM |
Narayana, CRL Pune |
Multilevel Monte Carlo approach to the simulation of multidimensional stochastic differential equations |
Multilevel Monte Carlo methods(MMCM) inherently reduce variance. We use MMCM to the simulation of multidimensional SDEs. Also we apply
our results to quant finance for pricing the derivatives. This is joint work with K.S. Mallikarjuna and J. Venkateswaran, IEOR,
IITB. |
| 8 April 2011, 4PM |
Ashish Tendulkar, IIT Chennai |
Analyzing Bio-molecules using Graphs, Geometric Invariants and Machine Learning |
The focus of the talk will be on analysis of protein structures using geometric, machine learning and graph theoretic techniques and its implications in functional site predictions. Proteins are versatile bio-molecules made up of amino acids and are involved in many cellular functions. They function through an arrangement, known as functional site, of a small number of spatially proximal amino acid residues (typically three to six) in the structure. Given a new protein, biologists are interested in determining its functional site using suitable experimental techniques. In doing so, they are faced with enormous number of choices due to combinatorial explosion and it is just not feasible to evaluate these choices exhaustively because of excessive time and resource requirements. To overcome the problem, we developed a method that provides the biologists with a small list of most likely functional sites, which will serve as a useful guide while designing their experiments.
In our scheme, we represent each protein structure as an unweighted undirected graph with amino acid residues being the nodes. The nodes are connected with an edge if the corresponding amino acid residues are spatially proximal in the structure. Each functional site is represented as a clique in this set up. We extract candidate functional sites from each protein using Bron-Kerbosch clique finding algorithm. Now, the objective is to determine most likely functional sites from a large number of candidate sites. The work is founded on the well characterized biological knowledge that the functionally important substructures are conserved and recur in functionally related proteins. We represent the candidate functional sites using geometric invariants, which remain unchanged upon transformations like rotation and translation. The candidate sites are grouped, using machine learning techniques, based on their similarity in a space spanned by geometric invariants. The recurring candidate sites are analyzed to provide a rank list of possible functional sites to the experimental biologists. Finally, I will present some examples of successful application of this method in novel proteins. |
| 30 March 2011, 4PM |
Dr. Manoj Yadav, HRI Allahabad |
Central automorphisms of finite $p$-groups |
In this talk, I'll first survey results on central automorphisms of finite $p$-groups and then show that it is not easy
to put general structure on finite $p$-groups having abelian automorphism groups. It may be very difficult even in the case when the automorphism
group is elementary abelian.
|
| 28 March 2011, 4PM |
Dr. Manoj Yadav, HRI Allahabad |
Automorphisms of finite groups |
In the first half of my talk, I would discuss about automorphisms of finite $p$-groups. Mainly the progress on the
questions which arose by the following famous result of W. Gaschutz: Theorem. Every non-abelian finite $p$-group has an outer automorphism
of $p$ power order.
The following two question arise naturally: Question one: How big the Sylow $p$-subgroup of $Aut(G)$ could be for
a finite $p$-group $G$, where $Aut(G)$ denotes the group of all automorphisms of $G$?
Question two: Does every non-abelian finite $p$-group have an outer automorphism of order $p$?
In the last half of my talk, I'll talk about automorphisms of abelian extensions of finite groups. Results on automorphisms of abelian
extensions of finite $p$-groups shall be of great use in the study of Question one above. |
| 15 and 16 March 2011 |
Amit Deshpande, Microsoft Research, Bangalore |
Approximability of subspace approximation |
Given a data set of points in large dimensions, the subspace approximation problem asks for a linear subspace that "fits" these
points well. In this talk, we'll focus on particular subspace-fits defined using l_p norms, which generalize the ordinary least-squares
fits. We'll give approximation algorithms for these problems based on semidefinite/convex relaxation and randomized rounding. Moreover,
we'll show that it's hard to do any better (unless Khot's Unique Games Conjecture is false). The talk will be self-contained and geared to a
broad audience with only basic knowledge of linear algebra and probability. |
| 18 February 2011, 4PM |
Prof. Rajaram Bhat, ISI Bangalore |
Dilations Of Completely Positive Maps |
The classical Sz. Nagy dilation of contractions on Hilbert spaces to isometries/unitaries has been found to be very useful.
Here we talk about a generalization of this result to completely positive (CP) maps. CP maps are `information
channels' of quantum information theory. |
| 17 February 2011, 4PM |
Prof. Rajaram Bhat, ISI Bangalore |
Invariants |
This lecture is about the use of `invariants' in Mathematics through some simple examples.
It is a very useful concept and is used in practically every field of mathematics. |
| 8 February 2011, 4PM |
Prof. Vavilov, St.Petersburg State University, Russia |
Efficient Generation Of Simple Groups |
TBA |
| 7 February 2011 at 4PM 9 Feb at 12 Noon |
Dr. Gerald, TIFR Mumbai |
The Riemann-Hilbert correspondence and extensions of flat vector bundles |
Starting from a first order linear differential equation on a Riemann
surface one obtains a linear representation of its fundamental group. That
this, actually, goes both ways for non-compact such is the content of the
Riemann-Hilbert correspondence. The first talk shall focus on establishing
the relevant facts and its statement. The second talk will aim at a
generalisation of the concepts involved to the case of complex analytic
spaces culminating in a glimpse into the problem of extending flat
analytic vector bundles to certain compactifications of such.
|
| 4 February 2011, 12 Noon |
Lakshmi Ramachandran, HeyMath! Chennai |
Presentation about HeyMath! |
HeyMath! |
| 27-28 January 2011, 4PM |
Prof. C. Pandu Rangan, IIT Chennai |
The joy of Algorithms |
Algorithm design is at the heart of computer science.
It is a healthy mix of mathematics, programming, engineering and of course creative thinking.
The purpose of this series is to give an enticing introduction to the topic, motivate and inspire young minds
to face challenges and offer guidelines and insight for creating good solutions to problems.
The required prerequisites are pen, paper and a bit of curiosity!!!.
The talk is suitable for all audience of all branches of knowledge with age 16+... |
| 20 January 2011, 4PM |
Dr. Ayan Mahalanobis |
The MOR cryptosystems |
The discrete logarithm problem is one of the oldest cryptographic primitive in use today.
In this talk we will talk about the discrete logarithm problem, and public key cryptosystems based on the
discrete logarithm problem.
Very similar cryptosystems can be built using the automorphism group of finite groups.
These cryptosystems are called MOR cryptosystems. We will talk about MOR cryptosystems in general and one
particular instance using the group of unitriangular matrices over finite fields. |
| 04 January 2011, 4PM |
Prof. S. R. S. Varadhan, Courant Institute of Mathematica Sciences, New York University |
Entropy, relative entropy and the study of rare events. |
In many situations a precise evaluation of the probabilities of rare events,
which are very small are nevertheless important. Relative entropy plays a crucial role in the
calculation of these small probabilities. We will look at examples that explain why and how. |
| 03 January 2011, 4PM |
Dr. John Augustine, Nanyang Technological University, Singapore |
Aligning Individual and Societal Interests in
Broadcast Games Via Subsidies |
Abstract |
| 15 December 2010, 11 AM |
Dr Clare D'cruz, CMI Chennai |
Depth of Blowup Rings |
TBA |
| 3 December 2010, 3PM |
Dr. Kavita Sutar, Northeastern University |
A short Introduction to Representations of Quivers |
Abstract |
| 24 November 2010, 4PM |
Dr. Ashwin Vaidya, Montclair State University |
Paradoxes in Fluid Mechanics |
Classical and modern physics have long known to display several phenomena that defy intuitive understanding. Such phenomena are labeled 'paradoxes', among them are some famous ones such the twin paradox, the Schroedinger's cat, Maxwell's demon, Stokes paradox etc. The term 'paradox' must merely be taken to mean that linear thinking does not suffice and that non-linear or more sophisticated models are required for proper understanding of the phenomena. In this talk, we will focus on some newly discovered paradoxes in fluid mechanics such as the orientation paradox (a sedimenting body falls differently in a Newtonian versus a non-Newtonian fluid), the flight time paradox (in a potential flow around an obstacle, fluid particles sufficiently near the obstacle can travel faster than fluid particles infinitely far away from the obstacle) and the bouncing ball paradox (a sphere sedimenting in a doubly stratified fluid can arrest, or even bounce, in the bottom layer even if the density of the sphere is larger than that of the bottom layer). We will discuss our experimental work in this regard and also provide a theoretical resolution to these problems. |
| 22 November 2010, 11 AM |
Dr. Anisa M.H.C. |
Shape Optimization Problems |
A typical shape optimization problem is, as the name suggests, to find the shape which is optimal in the sense that it minimizes a certain cost functional while satisfying given constraints. Mathematically, to find a domain O that minimizes a functional J(O) possibly subject to a constraint of the form G(O) = 0. In other words, it is about minimizing a functional J(O) over a family F of admissible domains O. In many cases, the functional being minimized depends on the solution of a given partial differential equation defined on the variable domain. I will talk about one such shape optimization problem in the Euclidean space $\mathbb{E}^n$ and its generalization to certain other Riemannian manifolds and other configurations.
|
| 22 November 2010, 2PM |
Prof. Eknath Ghate, TIFR Mumbai |
Modular Endomorphism Algebras |
For the past several years, the speaker and his collaborators have been trying to understand why certain primes show up as primes of
ramification of the endomorphism algebra of the geometric object attached
to a modular form. I will explain some recent advances which allow us to identify these primes in many cases as the primes for which the slopes of the adjoint lift of the form have odd parity. |
| 19 November 2010, 4:30 PM |
Prof. Manindra Agrawal, IIT Kanpur |
The P not equal to NP Hypothesis |
The classes P and NP were formally defined about 50 years ago although intuitively
they have been understood for much longer. The class P is captures the set of all those problems that can be
efficiently solved using some mechanized process (including computers). And the class NP captures all the problems
whose solutions can be efficiently verified by a mechanized process. Note that it may be inefficient to compute
the solution of a problem in NP; what is required is that once a possible solution is given, it is easy to verify
its correctness. An example of such a problem is solving Sudoku puzzle on an n2 x n2 grid
(in place of typical 9 x 9 grid). It can be very difficult to find a solution, but it is straightforward to
verify the correctness of a given solution.
It has been conjectured that P not equal to NP; that is, there are problems whose solutions are easy to verify but
hard to compute. Intuitively, this appears to be true; for example, in mathematics, finding a proof of a statement is
generally much harder than verifying the correctness of the proof. However, there exists no formal proof of the hypothesis
despite intense efforts to find one. The hypothesis is considered to be one of the most important unresolved questions in
mathematics and computer science.
In this talk, I will define the two classes and describe two major obstacles that have been encountered while
attempting to find a proof of the hypothesis. These obstacles rule out a large number of approaches by proving that
these approaches cannot resolve the hypothesis. The first of these obstacles is relativization. In this, we assume that a
certain algorithm can be executed freely without incurring any time penalty. Baker, Gill, and Solovay [1]
(see also http://en.wikipedia.org/wiki/Oracle_machine) showed that there is an algorithm relative to which P not equal to NP
and there is another relative to which P = NP. Hence any proof technique that works relative to all algorithms cannot
resolve the hypothesis.
The second obstacle is natural proofs. Razborov and Rudich [2] (see also http://en.wikipedia.org/wiki/Natural_proof)
showed that most of the known proofs that separate two classes of problems satisfy certain properties and called them
natural proofs. Further, they showed that, under a widely believed assumption, natural proofs cannot separate P from NP.
I would also outline a new approach, based on pseudorandom generators, that holds promise to circumvent these obstacles.
|
| 15-16 and 19 November 2010, 12 Noon |
Prof. Alladi Sitaram, IISc Bangalore |
A quick introduction to Fourier series |
TBA |
| 26 October 2010, 12 Noon |
Dr. Debraj Chakrabarti, IIT Bombay |
Several Complex Variables are better than just One. |
Complex analysis in one variable is a cornerstone of Mathematics.
It was discovered early in the twentieth century that in many respects, holomorphic functions of
several complex variables have properties very different from those of a single variable. Since then,
the work of Hartogs, Cartan, Oka, Grauert, Kohn, Hormander and others have clarified the main properties
of functions of several complex variables. In this expository talk, we discuss some of these new features, and the some of the ways the study of complex
analysis in several variables illuminates the classical theory of one complex variable. |
| 19 October 2010 11 AM |
Prof. B. Sury, ISI Bangalore |
The ubiquity of the modular group. |
The group of unimodular matrices is omnipresent - we demonstrate this
through its very diverse appearances. A knowledge of advanced number theory or advanced group theory is not
a pre-requisite to understand the talks, but the aim is also to capture the interest of those who have such knowledge. |
| 18 October 2010, 3PM |
Prof. Shripad M. Garge, IIT Bombay |
Gelfand models for finite Coxeter groups. |
A Gelfand model for a finite group G is a complex linear representation of G that
contains each irreducible representation of G exactly once. It is interesting to find ``natural'' Gelfand
models for classes of groups. We describe two methods of obtaining Gelfand models for finite groups and
compare them for finite Coxeter groups. |
| 18 October 2010, 12 Noon |
Prof. B. Sury, ISI Bangalore |
A modern Indian method. |
Starting with Brahmagupta from the 7th century and continued by
Jayadeva and Bhaskara from the 11th and 12th centuries, the Indians
had discovered the marvellous method to completely solve a problem
whose special cases were posed later in the 17th century by Fermat as
a challenge to the English mathematicians! We discuss this ancient
method. |
| 14 October 2010, 3PM |
Dr Sreekar Shastry |
Integral Structures on Some Moduli Problems in Number Theory and Applications |
The problem of classifying elliptic curves with additional structure gives rise to an algebraic curve defined over Q. Such curves play a central role in the development of modern number theory. We would like to extend these curves so that they are defined over all of Z; the resulting arithmetic surface is called an integral model. The central difficulty arises the additional structure involves the prime p --- e.g. the classification of pairs (E,x) with x an element of E which is of order p in the group law on E. The reduction mod p of the integral model is then a singular variety. The entire theory just alluded to has a profound analogy in the case of the function field F_q(t), the field of rational functions in one variable over a finite field. In this case the role of elliptic curves is played by Drinfeld modules of rank 2.
After giving some background and context, I will explain an earlier result of mine which uses these structures to determine the component group of the Neron model of the Drinfeld modular Jacobian J_1(n) in the function field case. In the number field case, these models are related to modular forms and in that way to a work in progress. I hope to convince the audience that, in the number field case at least, it is possible and quite natural that singular varieties in characteristic p could be related to modular forms (which are complex analytic functions). |
| 29 September 2010, 3 PM (POSTPONED!!!) |
Nirmala Sankaran, HeyMath Chennai |
Career in Math Education (not final yet!!) |
TBA |
| 29 September 2010, 10 AM |
Prof. Siva Athreya, ISI Bangalore |
Probability undergraduate summer projects and more. |
The speaker will make an effort so that talks will be accessible to students.
The talks will focus on Probability theory motivated from other sciences.
In each talk one open problem will be stated. |
| 28 September 2010, 12 Noon |
Prof. Siva Athreya, ISI Bangalore |
Life sciences: randomness as a theme line. |
TBA |
| 27 September 2010, 12 Noon |
Prof. Siva Athreya, ISI Bangalore |
Statistical physics: view from a probability lense. |
TBA |
| 6 September 2010, 12 Noon |
Tanmay Deshpande, University of Chicago |
Geometric representation theory on unipotent groups |
I will briefly describe the theory of character sheaves on unipotent algebraic
groups (over fields of positive characteristic) developed by V. Drinfeld. I will begin by recalling some
facts from classical representation theory of finite groups and then describe how these concepts can be
geometrized to the case of a unipotent algebraic group.
|
| 1 September 2010, 4 PM |
Dr. Anindya Goswami, INRIA Rennes, France |
Risk Sensitive Optimization of Portfolio Wealth in a Semi-Markov Modulated Market |
We address a portfolio optimization problem in a semi-Markov modulated market. We find the optimal portfolio selections by optimizing the risk sensitive criterion for both finite and infinite time horizon. We use a probabilistic method to establish the existence and uniqueness of classical solution of the HJB equation for finite horizon problem. For infinite horizon problem we obtained the optimal growth rate for Markovian subclass in terms of a maximal eigenvalue of an appropriate matrix, using Perron-Frobenius theorem. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem. |
| 9-11 August 2010 |
Prof. K. B. Athreya, Iowa State University |
Introduction to discrete probability theory. |
In these lectures we will propose a mathematical model(due to A.N. Kolmogorov) for studying random phenoemena that lead to finite or countably many outcomes. The notions of a sample space, sample points, events, probability distributions, random variables, random vectors, random sequences, joint distributions, means, variances, covarinaces, moments, laws of large numbers and the central limit theorem will be discussed. Examples will include coin tossing, card games, sports tournaments, statistical mechanics, finite population sampling . Extension to the uncountable case will be mentioned. A good background in basic counting and combinatorics will be good but not assumed. These lectures will NOT assume or use any measure theory but facility with calculus and analysis will be very useful. |
| 07/08/10 at 2:00 PM in Raman Hall |
Prof. John Coates, Cambridge University |
Primality testing and factorization. |
The lecture will give a non-technical discussion of the modern theory of both primality testing and factorization for large integers. |
| 06 August 2010, 4 PM |
Prof. A Raghuram, Oklahama State University, USA |
From Calculus to Number Theory: An introduction to the special
values of L-functions. |
An L-function is a function of one complex variable that is
attached to some interesting arithmetic or geometric data. The values
of such an L-function, at interesting points, give structural
information about the data to which it is attached. This talk will be
an introduction, via examples, to the subject of special values of
L-functions. I will begin by recalling some classical formulae which
one usually encounters in an advanced course in Calculus. These
formulae, when recast in modern language, are the prototypes of
special values of L-functions. Starting at an elementary level, I will build up toward
the conjectures of Deligne, which has guided a lot of research over
the last thirty years on this theme. Toward the end of my talk I will
give some idea of my own recent research on this subject. |
| 05 August 2010, 12 Noon |
Dr. Meera G. Mainkar, Dartmouth College, Hanover |
Anosov Automorphisms on Nilmanifolds |
Nilmanifolds admitting Anosov automorphisms play an important role in the theory of dynamical
systems. These nilmanifolds correspond to Anosov Lie algebras of which few examples were known. We will discuss
a combinatorial method using graphs of constructing Anosov Lie algebras. We will also describe some recent
examples constructed using algebraic number theory. This talk will be accessible to undergraduate students. |
| 21 July 2010 at 3PM |
Prof. G. Ravindra, University of Missouri, St. Louis |
On the algebra and geometry of sets defined by polynomials. |
In this lecture, I will address the following two questions:
- How many equations are needed to describe any algebraic subset.
- Given a "general" homogeneous polynomial F, does there exists a
matrix with polynomial entries, such that its determinant is some
power of F?
I will talk about some recent and ongoing work which provides answers
to these two questions. This talk will be accessible to senior
undergraduate and graduate students.
|
| 16 July 2010, 11AM |
Dr. Bala Krishnamoorthy, Washington State University |
Optimal Homologous Cycles, Total Unimodularity, and Linear Programming
|
Given a simplicial complex with weights on its simplices, and a
nontrivial cycle on it, we are interested in finding the cycle with
minimal weight which is homologous to the given one. A recent result
showed that this problem is NP-hard when the homology is defined
using binary coefficients, which is intuitive and easy to deal
with. In this paper we consider homology defined with integer
coefficients. We show that the boundary matrix of a finite
simplicial complex is totally unimodular if and only if the
simplicial complex is relatively torsion-free with the homology
defined relative to all pure subcomplexes of appropriate
dimensions. Because of the total unimodularity of the boundary
matrix, we can solve the optimization problem, which is inherently
an integer programming problem, as a linear program and obtain an
integer solution. Thus the problem of finding optimal cycles in a
given homology class can be solved in polynomial time. One
consequence of our result, among others, is that one can compute in
polynomial time an optimal (d-1)-cycle in a given homology class for
any triangulation of an orientable compact d-manifold or for any
finite simplicial complex embedded in d-dimensional space. Our
optimization approach can also be used for various related problems,
such as finding an optimal chain to a given one when these are not
cycles.
This is joint work with Tamal Dey at Ohio State University and Anil
Hirani at University of Illinois. The paper has been accepted to
STOC '10, and is available on arXiv: http://arxiv.org/abs/1001.0338.
|
| 26 May 2010, 3PM |
Dr. Sameer Chavan, IIT Kanpur |
Spectral Theory for Non-normal Hilbert Space Operators |
Abstract |