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CATEGORIES:Lectures & Presentations
DESCRIPTION:Speaker: Professor Ken Ono (University of Virginia)\n\nTitle: V
ariants of Lehmer’s conjecture\n\nAbstract: Generating functions are centr
al devices and tools in arithmetic geometry\, combinatorics\, number theory
\, physics\, and representation theory. Amazingly\, such generating functio
ns often turn out to be examples of modular forms. Despite many deep develo
pments in the arithmetic geometric and analytic aspects (e.g. Deligne’s pro
of of the Weil Conjectures\, the development of Galois representations\, Bi
rch and Swinnerton-Dyer Conjecture\, to name a few) of modular form theory\
, some of the seminal questions about these generating functions remain ope
n. Perhaps the most prominent of these is Lehmer’s Conjecture on the nonvan
ishing of Ramanujan’s tau-function. In joint work with J. Balakrishnan\, W.
Craig\, and W.-L. Tsai\, the speaker has obtained the first results that e
stablish that many integers are never modular form coefficients. This lectu
re is geared to a very general audience and begins with a historical survey
of illustrating the importance of modularity.
DTEND:20240419T211000Z
DTSTAMP:20240622T145302Z
DTSTART:20240419T201000Z
GEO:35.957579;-83.925751
LOCATION:Ayres Hall\, Room 124
SEQUENCE:0
SUMMARY:Colloquium
UID:tag:localist.com\,2008:EventInstance_45552061768087
URL:https://calendar.utk.edu/event/colloquium_5293
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