Faculty

Permanent:

• B. Conrad
  • Algebraic number theory; arithmetic geometry.
• K. Soundararajan
  • Analytic number theory, distribution of prime numbers
• H.L. Montgomery,
  • Analytic number theory, distribution of prime numbers, Fourier analysis, analytic inequalities, probability.
• C. Skinner
  • Algebraic number theory;arithmetic of L-values.
• T. Wooley
  • Analytic number theory, diophantine equations.

Faculty in related areas include: I. Dolgachev (algebraic geometry), W. Fulton (algebraic geometry), R. Lazarsfeld (algebraic geometry), S. DeBacker (representation theory), G. Prasad (arithmetic of algebraic groups).

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, rigid-analytic geometry, Galois representations and modular forms, automorphic forms on algebraic groups, and alterations.

• 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.

Mahesh Agarwal (Skinner), Trevor Arnold (Skinner), Bryden Cais (Conrad), Ellen Eischen (Skinner), Leo Goldmakher (Soundararajan), Jia Johnson (Skinner), Rizwanur Khan (Soundararajan), Wansu Kim (Conrad), Kris Klosin (Skinner), Joe Rabinoff (at Stanford; Conrad), Sreekar Shastry (Conrad), Matthew Smith (Wooley), Craig Spencer (Wooley), Xinyun Sun (Conrad)

Recent Graduates

Sreekar Shastry

Dissertation: J_1(n) has connected fibers
Advisor, year: Conrad, 2005.
First position: Tata Institute (Bombay).

Dissertation: n-level densities of zeros of quadratic Dirichlet L-functions
Advisor, year: Soundararajan/Montgomery, 2005.
First position: AIM/Montreal.

Dissertation: Sato-Kurokawa lifts and L-values
Advisor, year: Skinner, 2004.
First position: Ohio State University.

Dissertation: Potentially good reduction of Barsotti-Tate groups
Advisor, year: Conrad, 2004.
First position: Univ. of Penn.

Dissertation: Eisenstein ideal for imaginary quadratic fields
Advisor, year: Skinner, 2004.
First position: Cambridge University.

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.