NCTS(South)/ NCKU Math Colloquium


DATE2010-05-06¡@16:10-17:00

PLACER204, 2F, NCTS, NCKU

SPEAKERProf. Winnie Li §õ¤å­ë±Ð±Â¡]NCTS & Penn. State University¡^

TITLEThe Riemann Hypothesis

ABSTRACT The purpose of this talk is to survey and compare the Riemann Hypothesis occurring naturally in different areas of mathematics. We begin by discussing the historical development of the classical RH in number theory, its broad generalizations, implications, and approaches. It is a million dollar open problem.
RH also occurs in other context, where its truth is known. In algebraic geometry the Riemann Hypothesis for zeta functions attached to curves and varieties defined over finite fields was established. Its proof may inspire an approach to proving the classical RH.
On the combinatorical side, the zeta functions attached to graphs are analogous to zeta functions for curves. But the RH only holds for graphs with extremal spectral property, called Ramanujan graphs.