Speaker : Professor Peter Zvengrowski, University of Calgary Title : Riemann and his Zeta Function Time : 4:30 p.m., Thursday, Jan 31, 2008 Venue : Ramanujan Hall, Department of Mathematics, IIT Bombay 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 that Riemann thought it was important, 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years after his death answers to these questions became clearer, thanks to an exhaustive two year study of Riemann's unpublished notes by Karl Ludwig Siegel.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