Seminars, Colloquia, and Conferences
2017 Norbert Wiener Lectures
Ken Ono
Asa Griggs Candler Professor, Department of Mathematics and Computer
Science, Emory University
Polya's program for the Riemann Hypothesis and related problems
(December 78, 2017)
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Public Lecture
Why does Ramanujan, "The man who knew infinity," matter?
Thursday, December 7, 5:00pm; Crane Room, Paige Hall
Reception: 4:30pm; Crane Room
Abstract:
This lecture is about Srinivasa Ramanujan, "The Man Who Knew
Infinity." Ramanujan was a selftrained twotime college dropout who
left behind 3 notebooks filled with equations that mathematicians
are still trying to figure out today. He claimed that his ideas came
to him as visions from an Indian goddess. This lecture is about why
Ramanujan matters. The speaker was an Associate Producer of the film
"The Man Who Knew Infinity" (which starred Dev Patel and Jeremy
Irons) about the life of Ramanujan. He will share clips from the
film.
Colloquium
Polya's program for the Riemann Hypothesis and related problems
Friday, December 8, 12:30pm; Crane Room, Paige Hall
Reception: 1:30pm; Crane Room
Abstract:
In 1927 Polya proved that the Riemann Hypothesis is equivalent to
the hyperbolicity of Jensen polynomials for Riemann's Xifunction.
This hyperbolicity has only been proved for degrees d=1, 2, 3. We
prove the hyperbolicity of 100% of the Jensen polynomials of every
degree. We obtain a general theorem which models such polynomials by
Hermite polynomials. This theorem also allows us to prove a
conjecture of Chen, Jia, and Wang on the partition function. This is
joint work with Michael Griffin, Larry Rolen, and Don Zagier.
Colloquium
Can't you just feel the moonshine?
Friday, December 8, 4:00pm; BromfieldPearson 101
Reception: 5:00pm; BromfieldPearson, Clarkson Conference Room
Abstract:
Borcherds won the Fields medal in 1998 for his proof of the
Monstrous Moonshine Conjecture. Loosely speaking, the conjecture
asserts that the representation theory of the Monster, the largest
sporadic finite simple group, is dictated by the Fourier expansions
of a distinguished set of modular functions. This conjecture arose
from astonishing coincidences noticed by finite group theorists and
arithmetic geometers in the 1970s. Recently, mathematical physicists
have revisited moonshine, and they discovered evidence of
undiscovered moonshine which some believe will have applications to
string theory and 3d quantum gravity. The speaker and his
collaborators have been developing the mathematical facets of this
theory, and have proved the conjectures which have been formulated.
These results include a proof of the Umbral Moonshine Conjecture,
and Moonshine for the first sporadic finite simple group which does
not occur as a subgroup or subquotient of the Monster. The most
recent Moonshine (announced here) yields unexpected applications to
the arithmetic elliptic curves thanks to theorems related to the
Birch and SwinnertonDyer Conjecture and the Main Conjectures of
Iwasawa theory for modular forms. This is joint work with John
Duncan, Michael Griffin and Michael Mertens.
The Norbert Wiener Lectures were initially funded by an anonymous gift to the Department of Mathematics. All talks are free and open to the public.
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