## 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