Dedekind sums in geometry, topology, and arithmetic (09w5102)

Arriving in Banff, Alberta Sunday, October 11 and departing Friday October 16, 2009

Organizers

(San Francisco State University)

(University of Massachusetts Amherst)

Adam Sikora (State University of New York (SUNY) - Buffalo)

Objectives

The goal of the workshop is to bring together topologists, geometers,
and number theorists working in the above areas. The emphasis will be
on interaction between these groups of researchers, with the hopes of
engendering cross-fertilization and new and unusual collaborations.
All of the proposed participants are either active in these areas or
have professed interest in them. The large areas of overlap among the
topics above and the research interests of the proposed participants
means that the intimate setting of Banff is ideal for such a workshop.

The time is ripe for such a workshop. Although two-dimensional
Dedekind sums have been around since the 19th century and
higher-dimensional Dedekind sums have been explored since the 1950s,
it is only recently that such sums have figured prominently in so many
different areas. Moreover there have been conferences devoted to
individual topics under consideration, such as enumerating lattice
points in polytopes and special values of $L$-functions, but to date
there has not been a meeting emphasizing Dedekind sums as a unifying
theme between these subjects. Bringing together a group of
researchers will likely lead to significant breakthroughs in current
research programs, and may also uncover new connections between these
fields.