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Number Theory at the University of Michigan
Faculty:
- Jeff Lagarias
- Algebraic and analytic number theory, Diophantine approximation.
- Hugh
Montgomery
- Analytic
number theory, distribution
of prime numbers,
Fourier analysis,
analytic inequalities,
probability.
- Kartik Prasanna
- Arithmetic of automorphic forms and periods, special values of L-functions, Iwasawa theory.
- Michael Zieve
- Algebraic number theory and arithmetic geometry, especially Galois theory and arithmetic dynamics.
Faculty
in related areas: Mitya Boyarchenko and Stephen DeBacker
(representation theory);
William Fulton,
Robert Lazarsfeld,
Mircea Mustaţă, and
Karen Smith
(algebraic geometry);
Harm Derksen and
Gopal Prasad (algebraic groups).
Postdocs:
Burcu Baran,
Daniel Fiorilli,
Ben Linowitz,
Ruochuan Liu,
and
Danny Neftin.
Graduate students (advisor):
Hunter Brooks (Prasanna), Adam Kaye (Prasanna), Sijun Liu (Zieve), Alex Mueller (Zieve),
Hieu Ngo (Lagarias), Suchandan Pal (Prasanna),
Julian Rosen (Lagarias),
Zach Scherr (Zieve), and Ari Shnidman (Prasanna).
Former faculty:
Brian Conrad (2000-2008),
Chris Skinner (2000-2007),
Kannan Soundararajan (2000-2007),
Trevor Wooley (1991-2007),
David Masser (1983-1992),
James Milne (1969-1999),
Donald J. Lewis
(1957-1996),
William J. LeVeque (1949-1971).
Conferences:
In May 2011, we hosted a workshop on
L-functions, Galois representations, and Iwasawa theory.
In November 2010, we hosted the
Midwest Number Theory Day and the
Midwest Number Theory Conference for Graduate Students.
Electronic resources:
Go here for links to e-journals
and other electronic resources for
number theorists. These links should work both from on-campus and off-campus.
Courses:
The
following full-year graduate courses
are offered in alternating
years:
- analytic
number theory (Math 675/775)
and
- algebraic
number theory and class
field theory (Math 676/776) (taught in Winter 2013 by Jeff Lagarias)
We also offer
a range of courses on advanced
topics in number theory.
Previous year's topics include:
elliptic curves, complex multiplication, Diophantine
problems,
Diophantine approximation,
arithmetic of dynamical systems,
Iwasawa theory,
Hida theory, transcendence
theory, spectral theory of
modular forms, Galois representations
and modular forms, and automorphic
forms on algebraic groups.
Seminars:
- Group Theory/Lie Theory/Number
Theory: Weekly
research seminar with
speakers from around the world on topics in number
theory and related areas.
- Michigan Lectures in Number Theory:
Annual event in which a distinguished visitor gives three talks on a current
research topic in number theory. In Winter 2010,
Matt Baker lectured
on applications of potential theory on the Berkovich projective line to
problems in arithmetic dynamics.
- Learning
seminar: Weekly student
lectures on a common
theme under guidance
of faculty for the duration
of the year. Past topics
include Gross-Zagier
formula, Shimura varieties,
torsion in elliptic curves,
complex multiplication
in abelian varieties,
and Serre's conjecture.
- Working seminar: Weekly sessions in which students and
faculty work their way through a paper, topic, or problem. This differs from the Learning seminar in that the
talks are less formal and more interactive, and the emphasis is on audience understanding rather than
quantity of material covered.
- Student
Arithmetic Seminar: Student
organized; lectures by
graduate students.
Previous graduates
Recent
postdocs
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