## Friday, April 11, 2008

### (Math) seminars during April 14-18

We have a seminar and a colloquium during April 14-18

Colloquium:
----------
Speaker: M. Boratynski,
University of Bari, Italy
Date and Time: Tuesday, April 15, 2008 at 4 p.m.

Title: Invariant tubular neighborhood theorem for affine
varieties''
Venue: Ramanujan Hall

Abstract

The topic of the talk is the algebraic geometry analogue of the
Invariant tubular neighborhood theorem which concerns the action
of compact Lie groups on differential manifolds.
=============================================================

Seminar
------
Title: A graphical method to compare the efficiencies of cluster
randomized designs
Speaker: Prof. Siuli Mukhopadhyay
Department of Mathematics, IIT-B
Time: 3-4 pm
Date 15 April
Room 113

Abstract

The purpose of this talk is to compare efficiencies of several cluster
randomized designs using the method of quantile dispersion graphs (QDGs).
A
cluster randomized design is considered whenever
subjects are randomized at a group level but analyzed at the individual
level. A prior knowledge of
the correlation existing between subjects within the same cluster is
necessary to design these cluster
randomized trials. Using the QDG approach we are able to compare several
cluster randomized designs
without requiring any information on the intracluster correlation. For a
given design, quantiles of
the power function are obtained for several effect sizes. The quantiles
depend on the intracluster
correlation present in the model. The dispersion of these quantiles over
the
space of the unknown
intracluster correlation is determined, and then depicted by the QDGs. Two
applications of the
proposed methodology are presented.

Tony J. Puthenpurakal
Convener
SCC

## Tuesday, April 8, 2008

### update on todays seminar

Hi
Todays seminar by Dr. A. Garge will be held at Room 216 (Old Ramanujam
Hall) at 4 pm

Tony

## Monday, April 7, 2008

### update: (math)seminars during April 7-11 (fwd)

The seminar will be held on Tuesday, April 8, 4 to 5 pm

## Sunday, April 6, 2008

### (math)seminars during April 7-11

We have one seminar this week

Title: The Steinberg formula for orbit spaces
Speaker: Dr. Anuradha Garge
IIT-Bombay
Time: 4 to 5 pm
Venue: Room no: 113, Maths Department

Abstract:
The orbit space of unimodular rows of size $n$
(denoted by $\Um_n$) modulo elementary action has
been an object of study for both topologists and algebraists.
L. N. Vaserstein and W. van der Kallen showed that in certain cases,
depending on the dimension of the ring,
the orbit space admits a group structure and this can be explained
using the Vaserstein and universal weak Mennicke symbols. These will
be detailed in the talk.

Throughout this talk, for us $R$ will be a commutative ring with unity.
For a map $\Um_n (R) \stackrel{\varphi}{\longrightarrow} A$,
$A$ an abelian group, we say that the Steinberg formula holds if
for $1 \leq i \neq j \leq n, \lambda \in R$,
\begin{itemize}
\item $\varphi (a_1, \ldots, a_n) = \varphi (a_1, \ldots, a_i+ \lambda a_j, a_{i+1}, \ldots, a_n)$.

\item $\varphi (a_1, \ldots, a_i, \ldots, a_n) + \varphi (a_1, \ldots, (1 - a_i), \ldots, a_n) = ~~~~~~~~$
$~~~~~~~~~~~~~~~~~~ \varphi (a_1, \ldots, a_i(1- a_i), \ldots, a_n).$
\end{itemize}

The aim of this talk is to show that the Steinberg formula holds
for the Vaserstein symbol and the weak Mennicke symbol. The main
feature is that this formula holds for the above symbols
independent of the dimension assumptions on the ring.

Tony J. Puthenpurakal
Convener
SCC

## Friday, March 28, 2008

### (Math) seminars during March 31- April 4

We have two seminars next week

1. Title: Sequences of 0's and 1's: Hahn Properties

Speaker: Dr. Maria Zeltser,
Tallin University, Estonia

Day, Date and Time: Tuesday, April 1, 2008, 4.00-5.00 p.m.

Venue: Ramanujan Hall, Dept. of Mathematics

2. Title: Gorenstein Approximation, Dual Filtrations and Applications

Speaker: Dr. Tony J. Puthenpurakal,
Department of Mathematics, IIT-Bombay

Day, Date and Time: Tuesday, April 1, 2008, 2:30-3:30p.m.

Venue: Ramanujan Hall, Dept. of Mathematics

Abstracts
==========

1. Abstract for Dr. Zeltser's talk
---------------------------------------------------
The main idea of the talk is the following: for a given sequence
space we have a property which is satisfied for a simple and small
subset of it -- for the set of all sequences of 0's and 1's in this
space. We ask whether the whole space has this property.

For example, in 1922 Hahn proved that if an (infinite) matrix
sums all sequences of 0's and 1's, then it sums all bounded
sequences. (In summability the term
sums''
means that the matrix transforms the given sequence to a convergent
sequence.) So if the matrix maps the set of all 0-1 sequences to the space
of all convergent sequences $c$, then it also maps the space of all
bounded sequences to $c$.

We would like to study whether this result remains true if we replace the
space of all bounded sequences by any sequence space $E$ and the set of
all 0-1 sequences by the set of all 0-1 sequences in $E$. In this case we
say that $E$ has the matrix Hahn propoerty. We consider also two
generalizations of this notion.

2. Abstract for Dr. Puthenpurakal's talk
---------------------------------------------------
We give a two step method to study certain questions regarding associated
graded module of a \CM \ module \wrt \ an $\m$-primary ideal $\A$ in a
complete Noetherian local ring $(A,\m)$. The first step, we call it
Gorenstein approximation, shows that it suffices to consider the case when
both $A$, $\GA = \bigoplus_{n \ge 0} \A^n/\A^{n+1}$ are Gorenstein and
$M$ is a maximal \CM \ $A$-module. The second step consists of analyzing
the classical filtration $\{ \Hom_\A(M,\A^n) \}_{\nZ}$ of the dual
$\Hom_A(M,A)$. We give many applications of this point of view. For
instance we show that if $(R,\n)$ is \CM \ then the a-invariant of
$G_\n(R)$ is $-\dim R$
\ff \ $R$ is regular local. We also extend to modules a result of Ooishi
relating symmetry of $h$-vectors and the Gorenstein property of associated

Tony J. Puthenpurakal
Convener
SCC

## Wednesday, March 19, 2008

### Seminars during March 24-28

Popular Lecture Series
=======================
Title:
An Investor's Martingale Walk

Speaker:
Prof. M. G. Nadkarni, Emeritus Professor, University of Mumbai
Venue: Ramanujan Hall
Date: Friday 28 March
Time: 5:15 pm

Abstract:

I will explain what is a martingale in a very elementary manner, using
just sets
and functions, explain how martingale appear in Business Mathematics,
and discuss a consequence which is rarely mentioned in Business
Mathematics texts.

This talk may be of interest to students and teachers of Mathematics
and Statistics, as well as the mathematically inclined persons in

Prof. M. G. Nadakarni obtained his Ph.D. in Mathematics from Brown
University,
USA in 1965. He has taught at Washington University, St. Louis
(1965-66), the University of Minnesota (1966-1968), ISI Calcutta
(1968-1980), and the University
of Mumbai (1980-1999). Currently he is an Emeritus Professor at the
University of Mumbai. Prof. Nadkarni is a Fellow of the Indian
National Science Academy as well as the Indian Academy of Sciences
and the Maharashtra Academy of Sciences. His research interests
include Ergodic Theory, Harmonic
Analysis, and Probability Theory. He has authored or coauthored over
50 research
publications and two books.

Thanks
Tony Puthenpurakal
Convener
SCC

## Friday, March 14, 2008

### no seminars during March 17 to 21.

Hi
There is no seminars next week

Thanks
Tony

## Friday, March 7, 2008

### seminars during March 10-14

We have two colloquims and a seminar next week.

Golden Jubilee Colloqium series in Mathematics
========================================

Speaker : Prof. Manjul Bhargava
Princeton University
Title: Gauss Composition Laws and their applications
Date : Monday 10 March 2008
Time : 2:30 p.m.
Venue : Ramanujan Hall (Room 214)

Abstract: In 1801 Gauss laid down a remarkable law of composition on
integral binary quadratic forms. This discovery, known as Gauss
composition, not only had a profound influence on elementary number
theory but also laid the foundations for ideal theory and modern
algebraic number theory. Even today, Gauss composition remains one of
the best ways of understanding ideal class groups of quadratic fields.

The question arises as to whether there might exist similar laws of com-
position on other spaces of forms that could shed light on the structure
of other algebraic number rings and fields. In this talk we describe
several such higher analogues of Gauss composition, and we discuss
some of their recent applications.

2. Statistics Seminar
==================
Speaker: Prof. B.K. Sinha,
Indian Statistical Institute, Kolkata
Title: Statistical Surveillance: Issues, Models and Methods with
Applications
Date and Time: March 11th(Tue)3.00pm-4.30pm
Venue: Ramanujan Hall, Department of
Mathematics, IIT Bombay

Abstract:

Surveillance is the art and science of online monitoring of a process to
detect changes [in the process], if any, as quickly as possible and at the
same time, to keep desired control on the false alarms. Most of the
processes being stochastic in nature, there are many challenging
statistical issues involved. Also there are numerous application areas
wherein surveillance is a major concern. For example, issues in medical
sciences [complicated cases of pregnancies] and public health [emission of
radiation from hazardous pollutants in air / surface / water] have widely
attracted the attention of researchers. Security issues may often be
challenging and these are taking an alarming shape in some countries in
recent times. It is suggested that continuous time monitoring is easier to
handle than discrete time monitoring.
Since the processes need to be monitored over [discrete / continuous] time
domains, longitudinal models play a fundamental role in any critical study
of surveillance. There can be instances of a .sub-optimal. record as
against an expected .generic. record at one point of time which needs
immediate detection. Also this can lead to a false alarm altogether.
Detecting a .true. change scenario as against a .false alarm. scenario has
posed challenging statistical issues.
Characterizing surveillance in statistical terms is an exercise in
statistical inference using sequential observations arising out of a
process wherein the nature of statistical hypotheses are continuously
changing. Moreover, the twin issues of .detection. of a true shift and
keeping a .control on false alarm. need to be addressed. There are a
number of alternative strategies to meet these objectives, mainly from the
point of view of data-use. Simpler but less efficient methods use most
recently available data, thereby simplifying the data analysis and meeting
one or the other of the stated objectives. These methods are suitable for
detection of .large. changes. Other methods use the entire available data
and naturally seek to provide better results on the surveillance issues.
Also important is the concept of .weighted. observations, since most
recent data are likely to gain more importance in the study of
surveillance.
Detecting a .true. change [immediately after it has taken place] and
again, at the same time, controlling a .false. signaling [about such a
change] are the twin requirements for a sound statistical technique to
meet. Most research have centered around these two points of concern.
Traditional statistical procedures do not necessarily take into account
the time point of alarm nor the delay in alarms. Statistical evaluation of
a surveillance method rests on computation of the chance of successful
detection of a true change along with that of expected delay for such
detection. Also it rests on the chance of raising a false alarm.
The concept of a baseline has also gained importance in the study of
surveillance. If it is too low, too many false alarms might surface up. On
the other hand, if it is too high, it will slower the detection process.
There is thus a strong ground for studying the aspect of robustness of
statistical surveillance procedures.
Surveillance may create a fundamentally different situation [for its
detection] when more than one changes occur in the process. In this talk,
I will review the literature on this fascinating topic.

3. Popular Lecture Series in Statistics
=======================================
Speaker: Prof. B.K. Sinha
Indian Statistical Institute, Kolkata
Title: On Some Statistical Aspects of Agreement Among Measurements
Date and Time: March 13th(Thur) during 3.00-4.00pm
Venue: Ramanujan Hall, Department of Mathematics, IIT Bombay.

Abstract:

One of the important aspects of interest for researchers in scientific
investigations may be to objectively examine the inter-observer variation
in quantitative and/or qualitative studies. Similar interest may exist in
examining the variation in a variable between two measurement techniques,
the established one and the test one. As an attempt in this direction,
scientists unknowingly may rely on inappropriate agreement analysis such
as simple correlation/association analysis, instead of examining known
limitations of such analysis in this regard.

This technical and, yet, popular talk is aimed at discussing
methodologically appropriate techniques used in agreement analysis, with
real data sets.

Tony Puthenpurakal
Convener
SCC.

## Wednesday, March 5, 2008

### update on Prof Shastri's lecture

Prof. Shastri's lecture today has been rescheduled. It will be held on
Friday (7/3/08) at 5:15
pm in room number 113.

Tony
Convener
SCC

## Tuesday, March 4, 2008

### update: additional seminars this week

We have an additional seminar and colloquium this week

Seminar
=========

Title:
Three popular concentration inequalities in
probabilistic combinatorics.

Speaker:
Prof. Anand Srivastav, University of Kiel, Germany

Day & Date:
Wednesday, March 5, 2008

Time:

Lecture 1: 3.00 PM - 3.50 PM
Tea Break: 3.50 - 4.10 PM
Lecture 2: 4.10 PM - 5.00 PM

Colloquium
==========
Speaker: Prof. H. N. Mhaskar ,
Department of Mathematics, California State University, Los
Angeles,

Title: EDGE DETECTION AND LOCAL APPROXIMATION USING SPECTRAL DATA
Date: 7 March 2007
Time: 4.00-5.00 p.m
Venue: Ramanujan Hall

--------------------------------------------------------------------

Abstract for Prof Anand Srivastav's talks:
======================================
We will give an introduction to concentration inequalities
(i.e. estimation of large deviations) for sums of independent
and partially dependent random variables in a discrete
setting and their impact on some combinatorial problems,
like discrepancy of 2-colorings of hypergraps, lattice
approximation and subgraph counting. In the first lecture
the well-known Chernov-Hoeffding bounds are introduced.
In the second lecture we will discuss an inequality of
Svante Janson for a sum of partially dependent random variables. If
time permits, we will also discuss a lower tail
due to Janson, Luczak and Ruczinski is discussed.

These lectures shall be expository in nature.

------------------------------------------------------------------------------

Abstract for Prof. H. N. Mhaskar's talk
=======================================

We discuss the question of identifying local features of a function, such
as
the discontinuities in its derivatives, membership in local smoothness
classes,
etc., given global information about the function in the form of its
Fourier
coefficients with respect to an orthonormal system. We present a unifying
theme for some of the recent work on trigonometric and algebraic
polynomial
frames on the circle, the unit interval, the Euclidean sphere, and a
smooth
manifold in general. Applications include direction finding in phased
array
antennas, estimation of the velocity of the gulf stream, and
semi-supervised
learning of hand written digits.

Tony J. Puthenpurakal
Convener
SCC

## Friday, February 29, 2008

### seminars during March 3 to 7

Next week the following seminars are scheduled.

Year-long programme in Topology
------------------------------
Title : 3 manifolds,
Speaker : A.R.Shastri,
Time : 5:15 - 6:15 pm,
Venue : Room no 113,
Date : 3/3/2008 (monday) and 5/3/2008 (wednesday)

Tony

Convener
SCC

## Thursday, February 28, 2008

### update

Todays additional colloquium is at 5:15 pm and not at 4:40 pm as
previously announced

## Wednesday, February 27, 2008

We have one more Colloquium this week. Msc students/Research scholars are
encouraged to attend

Department Colloquium
=====================

Speaker: Prof. Mario Ahues, LAMUSE,
Department of Mathematics
University of St-Etienne, France

Title: Iterative Refinement: Theory and Applications

Venue: Ramanujan Hall

Time: 4:40pm to 5:40 pm
Date: 28 Feb
Abstract:

If an abstract problem is put in the form of a functional
equation and if a numerical algorithm is available to produce an
initial approximation of the exact solution, then a sequence of
approximations can be built using only the numerical algorithm. Under
rather mild hypotheses, this sequence of approximations
is convergent to the exact solution of the abstract problem. Some examples
of specific application are: linear and nonlinear integral
equations including eigenvalue problems, computation of the Hermitian
positive definite square root of an Hermitian positive definite matrix and
Sylvester equations.

## Friday, February 22, 2008

### seminars during Feb 25-29

We have five talks during the week Feb 25-29

1.
Colloquium talk:
----------------
Speaker: A. Joseph Kennedy
Title: Combinatorial Representation Theory
Date: February 26, 2008 (Tuesday)
Time: 4:30 to 5:30 pm
Venue: Ramanujan Hall

Abstract:

Let G be a group of linear transformations on a finite
dimensional vector space V. Then G acts diagonally on
V^k, the k-th tensor power of V. The basic problem is
to know how does V^k decompose into irreducible
representations of G. One way of studying this problem
is to consider the algebra of all linear
transformation on V^k that commute with the G-action,
called centralizer algebra of G. A large class of
Diagram algebras (whose basis consist of diagrams with
certain multiplication) arises in this way as the
centralizer algebras of different groups. This
provides the connection between the representation
theory and related combinatorics. The main part of
this talk is to discuss this aspect in detail.

2.
Seminar talk:
---------------
Speaker: A. Joseph Kennedy
Title: Partition Algebras
Date: February 28, 2008 (Thursday)
Time: Time 3 to 4 pm
venue: room no 105

Abstract:

In the early 1990's, the partition algebra appeared
independently in the works of P. Martin and V. F. R.
Jones. Their work on the partition algebra stemmed
from studies of Potts models and related problems in
statistical mechanics. In 1993, Jones considered the
partition algebra P_k(n) as the centralizer algebra of
the symmetric group S_n acting on V^k, where V is the
permutation module for S_n. This talk mainly
discusses the above work and its continuation by me.

3.
Popular Lecture Series Talk
----------------------------
Speaker: Professor Jaikumar Radhakrishnan
School of Technology and Computer Science
Tata Institute of Fundamental Research, Mumbai
Title: List-decoding Reed-Solomon codes
Date: 29 February 2008
Time: 5:05-6 pm
Venue: Ramanujan Hall

Abstract: We will introduce the notion of list-decoding, and
discuss the list-decoding algorithms of Sudan, and Guruswami &
Sudan for list-decoding Reed-Solomon codes. We will then describe
some results on the limits of list-decoding. The talk will
involve mainly linear algebra and should be accessible to a
general mathematical audience.

4&5.
Year-Long Programme in Topology
-------------------------------
Speaker : A.R. Shastri,
Topic : 3 - manifolds,
venue : room no 113,
Days : Monday (25/02/2008) and Wednesday (27/02/2008)
Time : 5:15 - 6:15 pm

Thanks

Tony J. Puthenpurakal
Convener
SCC

## Saturday, January 26, 2008

### Re: Maths Dept Seminar and colloquium for the week Jan28 toFeb3

Update

Prof. P. Zvengrowski's colloquium "Riemann and his Zeta Function"
will be held from 4:30 to 5:30 and not at 4 to 5 as announced earlier.

Thanks

Tony

### Maths Dept Seminar and colloquium for the week Jan28 toFeb3

We have three department colloquiums and two seminars for the week Jan28
toFeb3

1. Title: Real Elements in Spin Groups
Speaker: Anupam Kumar Singh,
IMSc, Chennai
Venue: Ramanujan Hall
Date: Jan 28
Time: 4 to 5pm
Abstract: Let $G$ be an algebraic group defined over a field $k$. We call
an element $t$ in $G(k)$ real if there exists $g$ in $G(k)$ such that
$gtg^{-1}=t^{-1}$. The question is to classify real elements in a
Semisimple Algebraic Group. In this talk, along with known results, we
sketch the proof in the case of Spin groups.

2. Title: Spectrum and Arithmetic
Speaker: Professor C. S. Rajan,
TIFR Mumbai
Venue: Ramanujan Hall
Time: 4 to 5pm
Date: Jan 29

Abstract: We will discuss the relationship between spectrum and arithmetic
especially in the context of locally symmetric spaces. In this context we
raise some conjectures and give some partial evidence that the arithmetic
and the spectrum of such spaces should mutually determine each other.

3. Title: Riemann and his Zeta Function
Speaker: P. Zvengrowski
University of Calgary
Venue: Ramanujan Hall
Time: 4 to 5pm
Date: Jan 31
Abstract:
This talk will take an historical/mathematical perspective to the
Riemann zeta function $\zeta(s)$
and the famed Riemann Hypothesis (RH), generally considered the most
important and probably most difficult unsolved question in
mathematics. Riemann wrote a single paper of just 8 pages on the
subject, in 1859. The RH is stated there but
it is not at all clear from this paper tha
(a) Riemann thought it was important,
(b) Riemann had any evidence whatsoever to make his conjecture.
Some sixty odd years after his death answers to these questions became
clearer,
thanks to an exhaustive two year study of Riemann's unpublished notes
by Karl
Ludwig Siegel. In this talk we shall examine the methods that Riemann
likely used to study the zeros of $\zeta(s)$, compute a few zeros
ourselves by these very same methods, and if time permits mention
briefly some of the major developments
since the time of Siegel's study.

4. Title : Vector bundles, flag manifolds and Stiefel manifolfds
Speaker : Peter Zvengrowski
Venue : Room no 113, Maths Department,
Time : 5:00 - 6:15 pm,
Date : 28/01/2008 (monday) and 30/01/2008 (wednesday)

Abstract

In this seminar we shall start we an introduction to vector bundles, from
the definition and a few examples to some of the basic properties. The
example of most interest to us will be the tangent bundle of a smooth
manifold. This will be studied first (briefly) for the case of a flag
manifold, following K.Y.Lam. Then the special case of Stiefel manifolds
will be examined in some detail, including the theorem of Sutherland that
$V_{n,r}$ is parallelizable (has trivial tangent bundle) for $r \geq 2$.
The associated projective Stiefel manifolds $X_{n,r}$ will also be
studied. An attempt will be made to keep the lectures as self contained as
possible, although the techniques used range from geometry to homotopy
theory to K-theory.

Tony J. Puthenpurakal
Convener
SCC