Ben Brubaker Assistant Professor Department of Mathematics MIT Room 2-267 Cambridge, MA 02139 Phone: Fax: (617) 253-4079 (617) 253-4358 Email: brubaker@math.mit.edu not so current CV (as linked PDF) (last updated Fall, 2007)

Research

My primary research interest is analytic number theory. More specifically, I work on problems in automorphic forms and their generalizations on arithmetic covering groups. This work is supported by NSF grant DMS-0702438, a focused research group grant with the NSF (DMS-0652529), and beginning in the Fall, 2009, by an NSF CAREER grant. Below is a list of recent publications and preprints. Collaborative work with Dan Bump, including many supporting materials on multiple Dirichlet series, can also be found in the Papers section of his home page:

• Whittaker coefficients of metaplectic, parabolic Eisenstein series (with S. Friedberg), In preparation.
• Schur polynomials and the Yang-Baxter equation (with D. Bump and S. Friedberg), Preprint.
• A crystal definition of symplectic multiple Dirichlet series (with J. Beineke and S. Frechette), Preprint.
• Weyl group multiple Dirichlet series of Type C (with J. Beineke and S. Frechette), Submitted for Publication.
• Weyl group multiple Dirichlet series, Eisenstein series, and crystal bases (with D. Bump and S. Friedberg), Submitted for Publication.
• Weyl group multiple Dirichlet series: Type A combinatorial theory (with D. Bump and S. Friedberg), Submitted for Publication.
• 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.)
• Gauss sum combinatorics and metaplectic Eisenstein series (with D. Bump and S. Friedberg), To appear in the Gelbart birthday conference volume.
• Twisted Weyl group multiple Dirichlet series: the stable twisted case (with D. Bump and S. Friedberg), Eisenstein series and applications 1--26. Progr. Math., 258, Birkhauser.
• Weyl Group Multiple Dirichlet Series III: Eisenstein series and twisted unstable A_r (joint with D. Bump, S. Friedberg, and J. Hoffstein), Annals of Math. 166 (2007)
• Residues of Weyl Group Multiple Dirichlet Series associated to GL(n+1) (with Daniel Bump), Proc. Symp. Pure Math. 75 (2006)
• Weyl Group Multiple Dirichlet Series II: The Stable Case (joint with D. Bump and S. Friedberg), Invent. Math. 165 (2006), 325-355
• Weyl Group Multiple Dirichlet Series I (joint with D. Bump, G. Chinta, S. Friedberg, and J. Hoffstein), Proc. Symp. Pure Math. 75 (2006)
• On Kubota's Dirichlet Series (with Daniel Bump), J. Reine Angew. (2006) 598, 159-184
• Cubic twists of GL(2) automorphic L-functions, (joint with S. Friedberg and J. 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 78 (2004), 4211-4239

Graduate Students at MIT

I currently have 3 graduate students working with me. They are all graduating within the next year or so, at which point I'll be eagerly seeking students.

• Sawyer Tabony, 4th year, working on adelic treatments of metaplectic Eisenstein series.
• Catherine Lennon, 3rd year, working on hypergeometric function identities for traces of Hecke operators and trace of Frobenius for elliptic curves.
• Peter McNamara, 3rd year, working on Whittaker functions for metaplectic forms over local fields and connections to crystal bases.
  • Metaplectic Whittaker Functions and Crystal Bases, Peter McNamara, Submitted for publication

Undergradute Student Research at Stanford

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Teaching at MIT ('06 - present)

For Spring '09, I taught 18.786: Topics in Algebraic Number Theory on "Tate's Thesis," closely following the books of Ramakrishnan-Valenza ("Fourier Analysis on Number Fields" -- the actual name for Tate's thesis) and the classic Weil's "Basic Number Theory." There was no course website.

During Fall '08, I taught 18.01, first-year calculus, using Simmons. (See the Fall '09 course web page)

During Spring '08, I taught 18.784: The Mathematical Legacy of Ramanujan, a small seminar course. I hope to eventually put up students' final projects, which were outstanding and original.

For Fall, '07, I taught 18.781: Theory of Numbers, a first course in number theory using Niven, Zuckerman, and Montgomery, but also featuring special topics like cubic reciprocity based on the treatment in Ireland and Rosen's book.

During Spring '07, I taught 18.103: Fourier Analysis - Theory and Applications. This course covers Lebesgue measure and integration theory and Fourier analysis, using the book by Adams and Guillemin. We'll discuss applications to probability along the way, and if time permits, how both the probability and the Fourier analysis are used in modern analytic number theory.

For Fall '06, I taught 18.786: Topics in Algebraic Number Theory on "Reciprocity Laws."

Teaching at Stanford ('03 -'06)

• 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:

• Math 51: Linear Algebra and Differential Calculus of Several Variables

• Math 110: Applied Number Theory, a course on cryptography using number theory, field theory, and elliptic curves.

During Winter quarter, 2005, I taught two courses:

• Math 109: Applied Group Theory, an introduction to group theory focusing on groups as measures of symmetry.
• Math 263A: Lie Groups (course announcement here), an introductory course for graduate students.
  • 263A Homework 1 (pdf format)
  • 263A Homework 2 (pdf format)

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.

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Seminars at MIT and in the Boston Area

MIT STAGE Seminar, Seminar on Topics in Arithmetic, Geometry, Etc., run by Kiran Kedlaya. This page contains links to number theory conferences and workshops as well - MONDAYS, 1-3

MIT Lie Groups Seminar - WEDNESDAYS, 4:30

MIT Combinatorics Seminar - WEDNESDAYS AND FRIDAYS, 4:15

BU Algebra Seminar, which is secretly always about number theory - MONDAYS, 4:15

Old Seminar Links

Stanford Representation Theory Seminar 2005-2006

Representation Theory Seminar,'05-'06

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:

AIM/Stanford Number Theory Seminar, Fall '04

Nat Thiem and I co-chair the Stanford Representation Theory Seminar for the academic year 2004-2005. A preliminary webpage is here:

Representation Theory Seminar,'04-'05

Number Theory Seminar, Spring '04

Links

• MathSciNet.
• Stanford Math Department.
• Brown Math Department.
• Eric Weisstein's World of Mathematics An online mathematics encyclopedia.
• Food Network.

• Dan Bump, Stanford
• Jeff Hoffstein, Brown
• Sol Friedberg, Boston College
• Gautam Chinta, Lehigh
• Sharon Frechette, Holy Cross
• Alina Bucur, Brown

Last change: August 27, 2009.