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


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
Date and Time: March 11th(Tue)3.00pm-4.30pm
Venue: Ramanujan Hall, Department of
Mathematics, IIT Bombay


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
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.


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

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.


Tuesday, March 4, 2008

update: additional seminars this week

We have an additional seminar and colloquium this week


Three popular concentration inequalities in
probabilistic combinatorics.

Prof. Anand Srivastav, University of Kiel, Germany

Day & Date:
Wednesday, March 5, 2008


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

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

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

Tony J. Puthenpurakal