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