My primary research interest is analytic number theory. More specifically, I work on problems in automorphic forms. Here's a list of recent publications and preprints:
- Twisted Stable Weyl Group Multiple Dirichlet Series (with D. Bump and S. Friedberg), In preparation. (Generalizes W.G.M.D.S. II and proves a special case of a conjecture in W.G.M.D.S. III)
- Mean Values for Cubic Dirichlet L-functions, In preparation. (This will be a reworking of material done in my Ph.D. thesis, linked here as a PDF file.)
- Weyl Group Multiple Dirichlet Series III: Connections with Eisenstein series (joint with D. Bump, S. Friedberg, and J. Hoffstein), To appear in Annals of Math.
- Residues of Weyl Group Multiple Dirichlet Series associated to GL(n+1) (with Daniel Bump), To appear in Proc. Symp. Pure Math.
- Weyl Group Multiple Dirichlet Series II: The Stable Case (joint with D. Bump and S. Friedberg), To appear in Invent. Math. (now available through Springer online)
- Weyl Group Multiple Dirichlet Series I (joint with D. Bump, G. Chinta, S. Friedberg, and J. Hoffstein), To appear in Proc. Symp. Pure Math.
- On Kubota's Dirichlet Series (with Daniel Bump), To appear in J. Reine Angew.
- Cubic twists of GL(2) automorphic L-functions, (joint with Sol Friedberg and Jeff Hoffstein), Invent. Math. 160 (2005) no. 1, 31-58
- Non-vanishing twists of GL(2) automorphic L-functions, (joint with A. Bucur, G. Chinta, S. Frechette and J. Hoffstein), IMRN (2004) no. 78, 4211-4239
Bob Hough, Stanford Class of '07, wrote a comprehensive Summer Research Journal on Gauss sums, culling from Ireland and Rosen; Berndt, Evans, and Williams; and papers of Weil, Yamamoto, etc. with some original synthesis.
Carl Erickson, Stanford Class of '07, has been working on behavior of the Riemann Zeta Function in the critical strip. The resulting article appeared in the Stanford Undergraduate Research Journal and can be found in the Spring 2005, Issue 4 of SURJ.
This Spring quarter, 2006, I am teaching two courses:
- Math 152
- Math 249B - An Introduction to Langlands Program
During the Fall quarter, 2005, I taught Math 51 and Math 248, an introduction to automorphic forms, co-taught with Dan Bump. The course website for Math 51 can be found at:
For the Spring quarter, 2005, I taught just one course:
During Winter quarter, 2005, I taught two courses:
For the Fall quarter, 2004, I taught Math 52: Integral Calculus of Several Variables, a course on integration techniques culminating in the theorems of Stokes, Gauss, and Green.
During Spring quarter, 2004, I was on leave.
During Winter quarter, 2004, I taught two courses:
Math 109: Applied Group Theory, an introduction to group theory focusing on groups as measures of symmetry.
Math 248B: Algebraic Number Theory, covering basic introduction to automorphic L-functions.
During Fall quarter, 2003, I taught also Math 51: Linear Algebra and Differential Calculus of Several Variables. Click on the link for the web page.
This year, I am applying for tenure-track jobs for Fall, 2006. Here is a list of my job materials (Last Updated: December 14, 2005)
Teaching Statistics for my courses taught at Stanford University, together with some student comments from the same evaluations.
Here are some links to teaching ratings by Brown University's "Critical Review," a student run ratings magazine (for the two courses that I taught as a graduate student):
Stanford Representation Theory Seminar 2005-2006
The topics of this seminar range from arithmetic applications of automorphic representations to combinatorics related to Lie algebra representations. A schedule for this year's seminar can be found at:
Old Seminar Links
This year, the number theory seminar is jointly run between Stanford and AIM (American Institute of Mathematics). More information about the seminar can be foound at the following link:
Nat Thiem and I co-chair the Stanford Representation Theory Seminar for the academic year 2004-2005. A preliminary webpage is here:
Mihran Papikian and I co-chaired the Stanford Number Theory Seminar for the 2003-2004 academic year. A schedule can be found here:
Department of Mathematics, Bldg. 380
Stanford, CA 94305
Email: brubaker "at" math "dot" stanford "dot" edu
Last change: September 7, 2005.