Tuesdays: 9:45-10:20, 1:30-2, 3-3:20
My research mainly concerns the following topics, with an eye towards collaborations with computer scientists and physicists:
Automorphic Forms, L-functions
Lattices and Sphere Packing
On the existence and temperedness of cusp forms for SL(3,Z) , Journal für die reine und angewandte Mathematik, 533 (2001), pp. 127-169.
Automorphic Distributions, L-functions, and Voronoi Summation for GL(3), with Wilfried Schmid,
Annals of Mathematics 164 (2006), pp. 423-488.
Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?, with David Jao and Ramarathnam Venkatesan, in Advances in Cryptology - ASIACRYPT 2005: 11th International Conference on the Theory and Application of Cryptology and Information Security, Springer Verlag Lecture Notes in Computer Science, 3788 (2005), pp. 21-40.
The Archimedean theory of the exterior square L-functions over Q, with Wilfried Schmid, Journal of the American Mathematical Society 25 (2012), 465-506.
Residual automorphic forms and spherical unitary representations of exceptional groups. Ann. of Math. (2) 177 (2013), no. 3, 1169–1179
Small representations, string instantons, and Fourier modes of Eisenstein series, with Michael Green and Pierre Vanhove. J. Number Theory 146 (2015), 187–309.
The sphere packing problem in dimension 24, with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska, Ann. of Math (2) 185 (2017), no. 3, 1017-1033.
Zhuohui Zhang (Ph.D. expected 2018)
Edmund Karasiewicz (Ph.D. 2017)
Tien Trinh (Ph.D. 2016)
Brandon Bate (Ph.D. 2013)
Zhi Qi (Hill Instructor, 2015-)
Noah Stephens-Davidowitz (DiMACS fellow, arriving 2018)
Maksym Radziwill (Hill Instructor, 2015)
Adi Akavia (DiMACS fellow, 2008-2009)
I am teaching section 3 of Math 300, which meets Tuesdays and Fridays in room ARC 108 from 12-1:20. General information about this course may be found here.
An additional course-wide workshop will be led by Abigail Raz on Tuesdays from 3:20-4:40 in Hill 005 (basement level), beginning on September 12.