Professor of Mathematics, Stanford University
Daniel Bump's research is in representation theory.
Office Hours (Winter 2017)
Some previous classes
Class web page for 2016's
Math 263B (Crystal Bases).
Lectures and Web Resources
Multiple Dirichlet Series Workshop
- A Yang-Baxter equation
for Metaplectic Ice with Brubaker and Buciumas
- Matrix Coefficients and
Iwahori-Hecke algebra modules with Brubaker and Friedberg.
Schubert Eisenstein Series and Demazure Characters with Young-Ju Choie.
- Unique Functionals
and Representations of Hecke Algebras. With Brubaker and Friedberg,
dedicated to Jonathan Rogawski.
- Multiple Dirichlet Series.
Eisenstein Series with Young-Ju Choie.
- Factorial Schur Functions and the Yang-Baxter Equation with McNamara and Nakasuji.
Functions and Demazure Operators with Brubaker and Licata. (Dedicated to Steve Rallis).
- Eisenstein Series, Crystals and Ice with Brubaker and Friedberg
- Metaplectic Ice with Brubaker, Chinta, Friedberg and Gunnells
- Crystals of Type B and Metaplectic Whittaker Functions with Brubaker, Chinta, and Gunnells
- Coefficients of the n-fold theta function with Brubaker, Friedberg and Hoffstein.
Dedicated to S. J. Patterson.
- The Casselman Basis of Iwahori Fixed Vectors and the Bruhat Order with Nakasuji. To appear in the Canadian J. of Mathematics.
- Schur Polynomials and the Yang-Baxter Equation with Brubaker and Friedberg. To appear in Comm. Math. Phys.
- Integration on p-adic groups and Crystal bases with Maki Nakasuji. In
Proceedings of the AMS.
- Weyl Group Multiple Dirichlet Series,
Eisenstein Series and Crystal Bases, with Ben Brubaker and Solomon Friedberg. To appear in Annals of Mathematics.
- Weyl Group Multiple
Dirichlet Series: Type A Combinatorial Theory, with Ben Brubaker and
Solomon Friedberg. Preprint version. The published version is Annals of Mathematics Studies 175,
which contains more expository material than this preprint version.
- Gauss Sum
Combinatorics and Metaplectic Eisenstein series, with Ben Brubaker and
Weyl Group Multiple Dirichlet Series I, with Brubaker, Chinta,
Friedberg and Hoffstein.
Weyl Group Multiple Dirichlet Series II: The Stable Case
, with Ben Brubaker and Solomon Friedberg. To appear in
Weyl Group Multiple Dirichlet Series III: Eisenstein Series
and Twisted Unstable Ar, with Ben Brubaker, Solomon Friedberg
and Jeffrey Hoffstein. And here are two companion papers. The first,
Metaplectic Eisenstein Series on GL(3) contains two articles
with more details about some of the proofs. The second,
Gelfand-Tsetlin interpretation of Chinta's A5 polynomial
is only available as a TeX dvi file since this is a smaller
format than postscript or pdf. You should not print it since
it is very long.
Residues of Weyl Group Multiple Dirichlet Series Associated to
GL(n + 1) with Ben Brubaker.
Weyl Group Multiple Dirichlet Series IV: The stable
twisted case with Ben Brubaker and Solomon Friedberg.
On Kubota's Dirichlet Series (postscript file), with Ben Brubaker.
Here's the same paper as a
Unraveling the (miniature) Rubik's cube through it's Cayley
Graph with Dan Auerbach.
On derivatives of modular forms of negative weight, with
YoungJu Choie. To appear in the Pure and Applied Mathematics
Quarterly, dedicated to John Coates.
On the Averages of Characteristic Polynomials from Classical Groups,
with Alex Gamburd. To appear in Communications in Mathematical
A Summation Formula for Divisor Functions Associated to Lattices
with Jennifer Beineke. (To appear in Forum Math.) Here's the
Appendix which will become obsolete when Professor Sato's
Lifting Automorphic Representations on Double Covers of Orthogonal
Groups with Friedberg and Ginzburg. (To appear in Duke Math. J.)
The Rankin Selberg Method: An Introduction and Survey. (To
appear in the volume dedicated to Steve Rallis.)
Generalized Frobenius Schur Numbers with David Ginzburg
(In Journal of Algebra 278).
Small representations for Odd Orthogonal Groups
with Friedberg and Ginzburg (In IMRN 25).
Moments of the Riemann Zeta Function and Eisenstein Series I
with Jennifer Beineke (in Journal of Number Theory).
Moments of the Riemann Zeta Function and Eisenstein Series II
with Jennifer Beineke (in Journal of Number Theory).
- The last two papers supercede ``Moments of L-functions of Maass forms
and the Riemann zeta function'' with Jennifer Beineke.
periods on GL(3) with Jennifer Beineke. In the
Canadian Journal of Mathematics.
Theory and the Trace Formula. Here's the (preliminary)
Sums of twisted GL(3) automorphic L-functions
joint with Friedberg and Hoffstein. To appear in a
volume dedicated to Joseph Shalika.
On the dimension of the space of theta functions
joint with Alex Pekker. Based on Alex' senior thesis.
To appear in Proceedings of the AMS.
L-function of degree 27 for Spin(9), joint with Ginzburg.
A short version will appear in the Ramanujan Journal.
A Rankin-Selberg Integral using
The Automorphic Minimal Representation of SO(7)
by Bump, Friedberg and Ginzburg. This has appeared
in the Journal of the Ramanujan Math. Society.
- On the cubic
Shimura lift for PGL(3), with Friedberg and Ginzburg. This
appeared in the Israel Journal of Mathematics.
Hidden symmetries for a renormalized integral of Eisenstein
series, with Jennifer Beineke. This appeared in Forum Math.
Whittaker-Fourier Coefficients of Metaplectic Eisenstein Series
with William Banks and Daniel Lieman. To appear in
Toeplitz minors, with Persi Diaconis. This appeared in
the Journal of Combinatorial Theory A.
- Correction to Toeplitz minors as a
postscript file and a
Unitary Correlations and the Fejer kernel, with
Persi Diaconis and Joseph B. Keller. This appeared in
Mathematical Physics, Analysis and Geometry.
Lectures and Course Materials
- TeXmacs is a better way
of writing mathematics.
- Sage, the computer algebra system,
is excellent and rapidly developing.
- GNU Go in case
you need it.
- Keith Matthews'
Number Theory Web (North American Mirror).
Back to Stanford Math Department.
email:bump at math dot stanford dot edu