## Saturday, January 26, 2008

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thanks to an exhaustive two year study of Riemann's unpublished notes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