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Graduate
Program in Number Theory
at the University of Michigan
The
department has long maintained
a vigorous graduate program
in number theory. However the department has recently lost the faculty members B. Conrad (Stanford), C. Skinner (Princeton), K. Soundararajan (Stanford), and T. Wooley (Princeton). It is actively rebuilding faculty in this area.
Faculty
Permanent:
- J.C. Lagarias
- Algebraic and analytic number theory, Diophantine approximation.
- H.L.
Montgomery
- Analytic
number theory, distribution
of prime numbers,
Fourier analysis,
analytic inequalities,
probability.
Faculty
in related areas include: S. DeBacker
(representation theory), I.
Dolgachev (algebraic
geometry), W. Fulton
(algebraic geometry),
R. Lazarsfeld (algebraic
geometry), Mircea Mustata (algebra/algebraic geometry),
G. Prasad (arithmetic
of algebraic groups).
Courses
The
following full-year courses
are offered in alternating
years
- analytic
number theory (Math 675/775)
and
- algebraic
number theory and class
field theory (Math 676/776)
We also offer
a range of courses on advanced
topics in number theory.Topics
of recent courses include:
elliptic curves, Diophantine
problems, Hida theory, transcendence
theory, spectral theory of
modular forms, Galois representations
and modular forms, automorphic
forms on algebraic groups.
Seminars
- 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."
- Number
Theory: Weekly
research seminar with
outside speakers on topics
in all areas of number
theory.
- Student
Number Theory: Student
organized; lectures by
graduate students.
Current Thesis Students (Advisor)
Jonathan Bober (Lagarias),
Leo Goldmakher (Soundararajan), Wansu Kim (Conrad), Craig Spencer
(Wooley), Xinyun Sun (Conrad), Ben Weiss (Lagarias).
Recent
Graduates
Mahesh Kumar Agrawal
Dissertation: P-Adic L-functions for GSp(4) x GL(2)
Advisor, year: Skinner, 2007
First position:
Matthew
Smith
Dissertation; On solution-free sets for simultaneous additive equations
Advisor, year: Wooley, 2007
First position: University of Georgia (Postdoc)
Bryden Cais
Dissertation: Compatabilities , correspondences, and integral structure in p-adic cohomology
Advisor, year: Conrad, 2007
First position:
CRM Postdoctoral Fellow
Rizwanur
Khan
Dissertation: Non-vanishing of the symmetric square L-function
Advisor, year: Soundararajan, 2007
First position: UCLA (Assistant Adjunct Professor)
Trevor Arnold
Dissertation: Anticyclotomic Iwasawa Theory for Modular Forms
Advisor, year: Skinner, 2006
First position: University of Washington Postdoc
Krzysztof Klosin
Dissertation: Congruences among automorphic forms on the unitary group U(2,2)
Advisor, year: Skinner, 2006
First position: Cornell, Visiting assistant professor
Sreekar
Shastry
Dissertation:
J_1(n) has connected fibers
Advisor, year: Conrad, 2005
First position: Tata Institute (Bombay)
Peng Gao
Dissertation:
n-level densities of zeros
of quadratic Dirichlet
L-functions
Advisor, year: Soundararajan/Montgomery,
2005
First position: AIM/Montreal
Jim Brown
Dissertation:
Sato-Kurokawa lifts and
L-values
Advisor, year: Skinner, 2004
First position: Ohio State University
Tong Liu
Dissertation:
Potentially good reduction
of Barsotti-Tate groups
Advisor, year: Conrad, 2004
First position: Univ. of Penn.
Tobias Berger
Dissertation:
Eisenstein ideal for imaginary
quadratic fields
Advisor, year: Skinner, 2004
First position: Cambridge University
Mihran Papikian
Dissertation:
Optimal elliptic curves
and degree conjecture over
function fields
Advisor, year: Conrad, 2003
First position: Stanford
Tsz Ho Chan
Dissertation:
Pair correlation and distribution
of prime numbers
Advisor, year: Montgomery, 2002
First position: AIM
Michael Knapp
Dissertation:
Forms in many variables
over p-adic fields
Advisor, year: Wooley, 2000
First position: Univ. of Rochester
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