Friday, April 11, 2008

(Math) seminars during April 14-18

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

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
Venue: Ramanujan Hall


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.

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


The purpose of this talk is to compare efficiencies of several cluster
randomized designs using the method of quantile dispersion graphs (QDGs).
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
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

Tuesday, April 8, 2008

update on todays seminar

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


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
Time: 4 to 5 pm
Venue: Room no: 113, Maths Department

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 $1 \leq i \neq j \leq n, \lambda \in R$,
\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) =
$~~~~~~~~~~~~~~~~~~ \varphi (a_1, \ldots, a_i(1- a_i), \ldots, a_n).$

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

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


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
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
graded rings.

Tony J. Puthenpurakal

Wednesday, March 19, 2008

Seminars during March 24-28

Popular Lecture Series
An Investor's Martingale Walk

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


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
Business School.

About the Speaker:

Prof. M. G. Nadakarni obtained his Ph.D. in Mathematics from Brown
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.

Tony Puthenpurakal

Friday, March 14, 2008

no seminars during March 17 to 21.

There is no seminars next week