| Date and Time |
Speaker |
Title |
Abstract |
| |
|
|
|
| 17 April 2010, 11AM |
Supriya Pisolkar, TIFR Mumbai |
Local Fields |
We will begin with the definition of discrete valued fields. Local fields are
special examples of such fields.
After discussing important properties like Hensel's lemma, we will study types of extensions of local fields.
If time permits we will also see the the statement of local class field theory. |
| 16 April 2010, 3PM |
Amit Hogadi, TIFR Mumbai |
The Brauer group of a field. |
This talk will start with definition of central simple algebras
and some elementary properties of Brauer group of a field. Towards the end we will see
some interesting problems and conjectures which are still open. |
| 07-09 April 2010, 3PM |
Prof. Akhil Ranjan, IIT Bombay |
Differential Geometry of Curves and Surfaces in R3 |
Abstract |
| 05 April 2010, 11AM |
A. Chandrashekaran |
Linear and semidefinite linear complementarity problems. |
In this talk we will see a brief introduction to the linear complementarity
problems (LCP) and the semidefinite linear complementarity problems(SDLCP).
We begin with the definition of (LCP) and illustrate it with some examples. Then we move to the
SDLCP's. Here we give some examples of SDLCP's and we show how SDLCP's includes LCP as its special case.
We also discuss the difficulties that we will face when working with SDLCP's compared to LCP's.
Finally we will see few results from my earlier research work. |
| 24 March 2010, 3PM |
Nageswara Rao |
Simulations for modelling population balance equations
of particulate process using discrete particle model. |
Not received yet |
| 22,23 March 2010, 3PM |
Rama Mishra |
Galois Theory for Differential Equations. |
Abstract |
| 15, 16 March 2010, 3PM |
Vivek Mallick |
Projective Spaces, Grassmannians and Gaussian binomials. |
In this talk we define grassmannians over a finite
fields. We go on to find out the cardinality of these finite sets. We
show that the cardinality have properties similar to those of binomial
coefficients. |
| 09 March 2010, 3PM |
Sreekar Vadlamani, Technion, Israel |
Wiener space and the geometry of random fields |
This talk is broadly divided into two parts:
In the first part, we shall study some geometric aspects of the Wiener space.
In particular, we shall extend the well known (for the old-school Statisticians,
and the old-German-school Geometers) "Tube formula", to the case of infinite
dimensions, using the infinite dimensional calculus set forth by L. Gross and
P. Malliavin.
Then, in the second part, we shall use the results obtained in the first part, to
understand the geometry of random fields defined on smooth manifolds. |
| 05 March 2010, 12 Noon |
Sankaran Viswanath, IISc Bangalore |
Constant Term Identities |
In his 1962 study of the statistical theory of energy levels of complex nuclei,
Freeman Dyson was led to conjecture an identity for the associated Boltzmann partition function in closed form.
Over the next 3 decades, this "constant term identity" has been progressively generalized and its connections to
Lie algebras and associated structures unearthed. I will narrate parts of this story, including a recently discovered
relation to polynomial analogs of weight multiplicities in representations of affine Lie algebras. |
| 25 February 2010 , 2PM |
Rabeya Basu, IISER Kolkata |
A Problem of J.P.-Serre on Projective Modules |
In 1956, J.P.-Serre posed a problem on projective modules.
During 60's many Indian mathematicians of Tata Institute were motivated by this problem and showed their profound
contributions. In 1958, C.S. Seshadri gave a proof for a special case.
It took 20 years to get the general solution of the problem. Finally,
it was proved by Daniel Quillen and Andrei Suslin Independently in 1976.
Now it is known as Quillen-Suslin Theorem. In this talk I will discuss few problems related to the above famous result. |
| 23 February 2010, 3 PM |
Aparajita Dasgupta, IISc Bangalore |
The Twisted Laplacian, the Laplacians on the Heisenberg Group
and SG Pseudo-Differential Operators |
Abstract |
| 19 February 2010, 3PM |
Amit Bose |
Two case studies on what controls a neuron's firing properties |
Neurons convey signals throughout the nervous system by firing
action potentials which are large voltage deviations from a resting state. In
many cases, a neuron needs to receive input from other neurons in order to
produce an action potential. In this talk, I will discuss two examples of this
situation. The first involves coincidence detection where a neuron must
calculate the time difference between distinct inputs and display a firing rate
that is inversely related to this difference. This problem is related to how
animals localize sound sources. The second example involves sustained
activity in a working memory model. In this situation, a neuron is recruited
into an ongoing activity pattern if and only if it receives a number of sufficiently
strong inputs in a short enough window of time. Mathematical models for both
phenomena will be presented. The analysis of these models relies on tools
from non-linear dynamical systems. |
| 18 February 2010, 3PM |
S. K. Sahoo, IIT Madras, Chennai |
Quasihyperbolic Distance and Quasiconformal Mappings
Notes of the talk |
Quasihyperbolic distance is a generalization of the hyperbolic distance, in the sense that
they are equal in the upper half plane of the complex plane.
We study the quasihyperbolic distance on arbitrary proper subdomains of the real Euclidean spaces with
dimension at least two.
We consider certain geometric properties of arc lengths and characterize
domains (open and connected sets) in terms of the quasihyperbolic distance
where the geometric properties hold. In the sequel, we investigate
invariance properties of such domains under quasiconformal mappings. |
| 6, 7 February 2010, 10AM - 5PM |
Professor Rajeev Karandikar, Cranes Software International Ltd, Bangalore |
Introduction to Statistics |
(from the organiser) These will be Marathon interactive discussion sessions to introduce statistics
to the undergraduate students. The aim will be to see how one can apply simple statistical ideas to solve many
problems. |
| 3 February 2010, 3 PM |
Krishnendu Gongopadhyay, ISI Kolkata |
On the Existence of an Invariant Non-degenerate Bilinear Form under a Linear Map. |
Let $V$ be a vector space over a field $F$ of characteristic different from $2$.
Let $T: V --> V$ be an invertible linear map. We shall discuss an answer to the following question in this talk:
When does $V$ admit a $T$-invariant non-degenerate symmetric (resp. skew-symmetric) bilinear form?
Along the way we shall apply our result to give a characterization of the real elements in the general linear group $GL(n, F)$. |
| 2 February 2010 3PM |
Saikat Chatterjee, S.N. Bose National Centre for Basic sciences |
Parallel transport on the path space and category theory |
A p-form on path space PM can be constructed from a p-form and a p+1-form on
the space M. Similarly from a Lie algebra valued 1-form A and a Lie algebra
valued 2-form B on Principal fiber bundle one can construct a connection on
path space bundle. But a single group is not sufficient for non Abelian
description of surface holonomy ("No go" theorem)! Introducing another group
one can define a 'consistent' surface holonomy for the non Abelian case.
This introduction of a second group leads to an interesting categorical
picture of the surface holonomy. As in pathspace a 'point'is basicaly
a 'path' in base space, path space formalism can be very useful to study
dynamics of an extended object like string. |
| 3 February 2010, 5PM |
Vijay Patankar, Microsoft Research, Bangalore |
Factoring polynomials and Abelian Varieties |
An irreducible polynomial with integer coefficients can factor modulo p
for every prime p. We study a geometric analogue of this phenomenon in the context of Abelian varieties. |
| 27, 28 January 2010, 3PM |
Rama Mishra, IISER Pune |
Topological Quantum Field Theory (TQFT) |
A topological quantum field theory (TQFT) is an, almost, metric independent quantum field theory that
gives rise to topological invariants of the background manifold. This is a nice interplay between Topology and Algebra.
We will see that in dimension 2, the category of 2d TQFTs are in one to one correspondence with the category of
Commutative Frobenius Algebras. |
| 20, 21 January 2010, 3PM |
Anupam Kumar Singh, IISER Pune |
Orthogonal and Symplectic Groups |
We will define Orthogonal and Symplectic groups and study some of it's properties. |
| 12 January 10, 3PM |
Prof. S. M. Bhatwadekar, TIFR Mumbai |
Completion of Unimodular Rows over Integers |
Abstract |
| 08 January 10, 3PM |
Professor Mahesh Nerurkar, Rutgers University |
on Lyapunov Exponents |
Not recieved Yet |
| 10 December 09, 3PM |
Abhijit pal |
Trees of Spaces and Cannon-Thurston Maps.
|
In this talk, we will first introduce trees of strongly relatively hyperbolic spaces and then
we will prove that if X is a tree of relatively hyperbolic spaces satisfying some conditions, then, for a vertex spaces
Y, a Cannon-Thurston map exists for the embedding i:Y -> X, i.e., i can be extended continuously to their boundaries.
Using same technique, for the above short exact sequence of relatively hyperbolic groups, we can prove that a
Cannon-Thurston map for the inclusion i:K -> G exists. |
| 09 December 09, 1PM |
Abhijit pal |
Relative Hyperbolicity and Quasi-Isometric section. |
In this talk, we will introduce hyperbolic and strongly relatively hyperbolic spaces (groups).
We will give two definitions of a relatively hyperbolic space (due to Gromov and Farb). We will define nearest point
projections and discuss several properties of it. For a short exact sequence of finitely generated groups
1 -> K -> G -> Q -> 1, we will prove that if K is relatively hyperbolic and G
preserves cusp subgroups of K, then there exists a quasi-isometric section from Q to G.
|
| 23 November 2009, 4PM |
Prof. Rajeeva Karandikar, Cranes Software Bangalore |
Opinion polls, Exit polls and Early seat projections |
How can talking to a few thousand people enable one to predict the mood of the Nation?
This is the question I will focus on and talk about opinion polls, exit polls in Indian context.
I will share my experiences over the last 10 years.
No specific background in Statistics or Mathematics is assumed (other than Class 12 Maths). Notes |
| 11-13 November 2009, 11 AM - 12 Noon |
Prof. N. Raja, TIFR, Mumbai |
An Introduction to the Axiomatic Method |
Yet to recieve |
| 28 October 2009, 11 AM - 1PM |
Prof. Gautam Bharali, IISc Bangalore |
Analytic Continuation in Several
Complex Variables |
Notes |
| 26 October 2009, 3 PM |
Prof. Gautam Bharali, IISc Bangalore |
Analytic Continuation in Several
Complex Variables |
The theory of functions in several complex variables is
challenging
because of several unexpected phenomena that have no analogues in
one variable. One such phenomenon is that there exists domains in
C^n, n>1, for which EVERY holomorphic function defined on this
domain analytically continues past the boundary. Demonstrating this
is quite easy, and requires nothing more than an understanding of
Cauchy's integral formula and Laurent series.
In the first lecture, we shall recapitulate some of the one-variable
results that shall be exploited later -- and this lecture will be
accessible to all students who have seen some complex analysis. The
second lecture will be devoted to the phenomenon mentioned above, and
will be based on entirely elementary tools. The third lecture will
be concentrate on some new results on the theme of analytic
continuation.
|
| 21 October 2009, 3 PM |
Prof. G. Misra, IISc Bangalore |
Invariants for linear transformations |
We show how to extract unitary invariants for a linear
transformation from the unitary invariants for its restrictions
to a family of (finite dimensional) subspaces. Often it is possible
to (holomorphically) glue these subspaces and produce a holomorphic
Hermitian vector bundle. Then one sees that the invariants for the
restriction operators and the invariants for the holomorphic Hermitian
vector bundle determine each other. |
| 20 October 2009 |
Prof. Amit Kulshrestha, IISER Mohali |
Group Theory and Puzzles |
Notes |
| 06 October 2009, 3 PM |
Prof. Siddhartha Gadgil, IISc Bangalore |
Coarse geometry and Curvature : A glimpse into the work of Mikhail Gromov. |
Coarse Geometry is the study of geometry `seen from far away'.
We will explain what coarse geometry is as well as classical and
coarse notions of curvature. We also discuss related geometric notions
of approximating by finite sets and taking limits of metric spaces.
This lecture will be informal and accessible. Only a basic
knowledge of Calculus is assumed (even that in only part of the talk). |
| 21 September 2009, 4 PM |
Prof. K. Srinivas, IMSc, Chennai |
Summation of Arithmetical Fuctions |
Given a counting function $f$, one would like to know how to estimate $ \sum_{n\leq x} f(n)$. For
example, if $ f(n)=1$ when $n$ is prime, and $0$, otherwise, then one is asking how many primes are there upto $x$. We
shall discuss this problem. |
| 14 September 2009, 4 PM |
Dr. Shanta Laishram, Universit of Waterloo, Canada |
Irreducibility of generalized Schur Polynomials |
Abstract |
| 17 July 2009, 3:30 PM |
Dr. Rama Mishra |
Introduction to Knot Theory |
We will introduce Knot invariants. |
| 10 July 2009, 3 PM |
Dr. Rama Mishra |
Introduction to Knot Theory |
We will continue the introductory lecture on Knot Theory. |
| 01 July 2009, 3 PM |
Dr. Rama Mishra |
Introduction to Knot Theory |
We will continue the introductory lecture on Knot Theory. |
| 26 June 2009, 3 PM |
Dr. Rama Mishra |
Introduction to Knot Theory |
We will introduce Knots in the first lecture. |