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thanks to an exhaustive two year study of Riemann's unpublished notes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

had

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