Graduate workshop on zeta functions, L-functions and their applications; Summer 2009, Orem, UT

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ABSTRACT Principal Investigator: Baker, Roger C.Proposal Number: DMS - 0910714 Institution: Brigham Young University Title: Graduate workshop on zeta functions, L-functions and their applicationsThe Graduate Workshop on Zeta Functions, L-functions and Their Applications will be held at Utah Valley University on June 1-4, 2009. NSF funds will be used for travel and lodging for 20 participants including plenary speakers and students. The Riemann zeta function has gained enormous importance in the eyes of number theorists since its properties (expressed in terms easily understandable to a modern undergraduate studying complex analysis) were developed by Riemann in a renowned lecture in Berlin in 1859. Since then, the function has been used to prove the fundamental theorem on the distribution of prime numbers, and many other important results in number theory. The Dirichlet L-functions, and other zeta functions and L-functions invented since that time by Dedekind, Hecke, Artin and others, have vastly extended the range of application of Riemann's ideas, yet many conundrums remain about their properties. The workshop will have three sets of lectures by experts in the field: Brian Conrey, Ram Murty and Steve Gonek. Also, there will be about 16 talks by junior mathematicians and senior researchers. The three principal lecturers will discuss the ideas of zeta functions and L-functions beginning with the Riemann zeta function and Dirichlet L-functions, Dedekind zeta functions, and L-functions of number fields. They will also introduce automorphic L-functions, Artin L-functions and L-functions of varieties. Introductory concepts and results will be given in some detail. Modern topics such as the Birch-Swinnerton-Dyer conjecture and the random matrix approach to results and conjectures concerning zeta functions and L-functions will also be outlined. It is highly desirable to give graduate students working in number theory a broad picture of the state of the art in this subject area. The major component of the conference is the involvement of graduate students. This includes a certain number of talks reserved for graduate students who have results in the area to report. In addition, the conference will provide an opportunity for graduate students to interact with established researchers. This interaction will be promoted by scheduling breaks in which the participants will be encouraged to break up into groups to discuss research ideas. At the end of the workshop there will be a round table discussion on open problems and directions for future research. This will help stimulate the interest of graduate students and new PhDs.