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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 Dec. 14, 2005)

Research

My primary research interest is analytic number theory. More specifically, I work on problems in automorphic forms. Below is a list of recent publications and preprints. Collaborative work with Dan Bump can also be found in the Papers section of his home page:

Weyl group multiple Dirichlet series and Gelfand-Tsetlin patterns (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.

Weyl Group Multiple Dirichlet Series IV: The stable twisted case (with D. Bump and S. Friedberg), To appear in AIM volume on Eisenstein series.

Weyl Group Multiple Dirichlet Series III: Connections with Eisenstein series (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

Student Research at Stanford

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.

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Teaching at MIT

During Spring '07, I'll be teaching 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 am teaching 18.786: Topics in Algebraic Number Theory on "Reciprocity Laws." Eventually, Problem Sets will be linked from here. I hope to have the first problem set up by Friday, Sept. 29.

Teaching at Stanford ('03-'06)

During the 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:

Math 51: Linear Algebra and Differential Calculus of Several Variables

For the Spring quarter, 2005, I taught just one course:

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

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:

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

Mihran Papikian and I co-chaired the Stanford Number Theory Seminar for the 2003-2004 academic year. A schedule can be found here:

Number Theory Seminar, Spring '04

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