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. Faculty in related areas: Mitya Boyarchenko and Stephen DeBacker (representation theory);  Igor Dolgachev, William Fulton, Robert Lazarsfeld, Mircea Mustaţă, and Karen Smith (algebraic geometry);  Harm Derksen and Gopal Prasad (algebraic groups);  Michael Zieve (algebra). Postdocs: Djordje Milicevic, Lan Nguyen Graduate students (advisor): Ernest Brooks (Prasanna), Elizabeth Chen (Lagarias), Johnson Jia (Skinner), Andrey Mishchenko (Lagarias), Julian Rosen (Lagarias), Xinyun Sun (Conrad), Benjamin Weiss (Lagarias) Former faculty: Kannan Soundararajan (2000-2007),  Brian Conrad (2000-2008),  Chris Skinner (2000-2007),  Trevor Wooley (1991-2007),  David Masser (1983-1992),  James Milne (1969-1999),  Donald J. Lewis (1957-1996),  William J. LeVeque (1949-1971). Courses The following full-year graduate courses are offered in alternating years: analytic number theory (Math 675/775)  (taught in 2009 by Hugh Montgomery)  and algebraic number theory and class field theory (Math 676/776)  (to be taught in 2010-2011) We also offer a range of courses on advanced topics in number theory. In Fall 2009, Kartik Prasanna is teaching a course on Iwasawa theory. In Winter 2010, Jeff Lagarias will teach a course on Diophantine approximation, and Michael Zieve will teach a course on the arithmetic of dynamical systems. Previous year's topics include: elliptic curves, Diophantine problems, 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. Special lecture series: Annual event in which a distinguished visitor gives three talks on a current research topic in number theory. In Winter 2010, Matt Baker will lecture 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. Student Arithmetic Seminar: Student organized; lectures by graduate students. Recent Graduates