Professor and Chair of
|Department of Mathematics
Hill Center-Busch Campus
Rutgers, The State
of New Jersey
110 Frelinghuysen Rd
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Generating cryptographically-strong random
lattice bases and
recognizing rotations of Zn,
joint with Tamar
Lichter Blanks, in PQCrypto 2021.
Tamar's Video presentation.
Lecture notes on lattices from the automorphic point of view,
from a Spring 2020 course. So far the notes cover
a proof of Siegel's
integration formula using Eisenstein series. Future updates will center
on Borel and Harish-Chandra's reduction theory.
A template method for Fourier coefficients of Langlands Eisenstein series,
Dorian Goldfeld and Michael Woodbury, to appear
Rivista di Matematica della Universita di Parma,
Proceedings of the "Second Symposium on Analytic Number Theory".
On the convergence of Kac-Moody Eisenstein series,
Lisa Carbone, Howard Garland, Kyu-Hwan Lee, and Dongwen Liu,
On Arthur's unitarity conjecture for split real groups,
to appear in the American Journal of Mathematics.
Stopping time signatures for some algorithms in cryptography,
Percy Deift and Thomas Trogdon,
Universal optimality of the E8 and Leech lattices and
Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska,
On the nonexistence of automorphic
eigenfunctions of exponential growth on
Tien D. Trinh, preprint.
Kissing numbers and transference theorems from generalized tail bounds, with
Noah Stephens-Davidowitz, preprint.
Coppersmith's lattices and ``focus groups'': an attack on small-exponent RSA, with
Bhargav Narayanan and Ramarathnam Venkatesan, Journal of Number
Theory (to appear).
A Spectral reciprocity formula and non-vanishing for L-functions on
GL(4)xGL(2) , with
Valentin Blomer and Xiaoqing Li, preprint.
Weights, raising and lowering operators, and K-types for automorphic
forms on SL(3,R), with
Jack Buttcane, preprint.
The balanced Voronoi formulas for GL(n), with
Fan Zhou, preprint.
Estimates on Eisenstein
distributions for reciprocals of p-adic L-functions: the case of
irregular primes, with
Stephen Gelbart, Ralph
Greenberg, and Freydoon Shahidi, preprint.
The sphere packing problem in
with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska, preprint.
Video of IAS
Some properties of
optimal functions for sphere packing
in dimensions 8 and 24,
with Henry Cohn, preprint.
Cryptanalysis of the NFL schedule (expository piece).
Non-abelian analogs of lattice rounding,
Evgeni Begelfor and
Venkatesan, to appear in Groups Complexity Cryptology.
SL(2,Z)-invariance and D-instanton contributions to the D^6R^4
Vanhove, Communications in Number Theory and
Physics 9 (2015), pp.307-344.
Entirety of cuspidal Eisenstein series on loop groups,
with Howard Garland and Manish Patnaik, to appear in the American
Journal of Mathematics.
What mathematics is really behind the distributional Γ-factors?
(for the Schmid
A p-adic integral for
the reciprocal of L-functions, with Stephen Gelbart, Alexei
Pantchichkine, and Freydoon Shahidi, to appear in a Contemporary Mathematics
volume in memory of Ilya Piatetski-Shapiro.
forms and spherical unitary representations
of exceptional groups , to appear in Annals of
Click here for the programs and
representations, string instantons, and Fourier modes of Eisenstein
series, with Michael Green and
Pierre Vanhove; includes appendix "Special Unipotent Representations"
Dan Ciubotaru and Peter E. Trapa.
coefficients of automorphic forms, character variety orbits, and small
representations, with Siddhartha Sahi,
to appear in Journal of Number Theory.
The archimedean theory
of the Exterior Square L-functions over Q,
with Wilfried Schmid,Journal
of the American Mathematical Society,
25 (2012), pp. 465-506.
of automorphic distributions and mirabolic Eisenstein series,
with Wilfried Schmid, to appear in Contemporary
in honor of Gregg Zuckerman's 60th birthday.
automorphic distributions, with Wilfried Schmid, to appear in
On the rapid
decay of cuspidal automorphic forms, with Wilfried Schmid, to
appear in Advances in Mathematics.
Eisenstein series for
higher-rank groups and string theory amplitudes,
with Michael B.
Green, Jorge Russo, and Pierre
Vanhove, Communcations in Number
Theory and Physics 4 (2010), 551-596.
Non-degeneracy of Pollard Rho
Collisions, with Ramarathnam Venkatesan, International
Mathematics Research Notices.
A method for computing general
automorphic forms on general groups, Forum
Conference on Analytic
Number Theory and Higher Rank Groups, NYU, May 19-23, 2008.
Power point for lectures
1 and 3,
scanned notes for lecture
for older powerpoint format.)
Slides from the Technion conference talk (12/20/2005) on
of automorphic distributions to analytic number theory": powerpoint or
presentations (can be
viewed with a browser, e.g. Internet Explorer):
from a general talk (click
here for the