Aaron Pollack

Associate Professor
Department of Mathematics
University of California San Diego

Email: apollack at ucsd dot edu

My primary research interest is algebraic number theory. I am especially interested in automorphic forms on exceptional groups and the questions surrounding the behavior at integers of certain automorphic L-functions.
My CV is here

Research articles

• The quaternionic Maass Spezialschar on split SO(8) (with Jennifer Johnson-Leung, Finn McGlade, Isabella Negrini, and Manami Roy), preprint
• Computation of Fourier coefficients of automorphic forms of type G₂, preprint, SAGE implementation
• Exceptional theta functions and arithmeticity of modular forms on G₂, preprint
• Exceptional Siegel-Weil theorems for compact Spin₈, preprint
• Modular forms of half-integral weight on exceptional groups (with Spencer Leslie), Compositio Mathematica, accepted
• The completed standard L-function of modular forms on G₂ (with Fatma Cicek, Giuliana Davidoff, Sarah Dijols, Trajan Hammonds, and Manami Roy), Mathematische Zeitschrift, accepted
• Modular forms on indefinite orthogonal groups of rank three, with an appendix "Next to minimal representation" by Gordan Savin, Journal of Number Theory, accepted
• A quaternionic Saito-Kurokawa lift and cusp forms on G₂, Algebra and Number Theory, 15 (2021), no. 5, 1213-1244
• On the residue method for period integrals (with Chen Wan and Michal Zydor), Duke Mathematics Journal, 170 (2021), no. 7, 1457-1515
• The minimal modular form on quaternionic E₈, Journal of the Institute of Mathematics Jussieu, published online, Aug 2020
• Modular forms on G₂ and their standard L-function, Proceedings of the Simons Symposium "Relative Trace Formulas", Springer Nature 2021, 379-427
• A G₂-period of a Fourier coefficient of an Eisenstein series on E₆ (with Chen Wan and Michal Zydor), Israel Journal of Mathematics, (2019), 229-279
• The Fourier expansion of modular forms on quaternionic exceptional groups, Duke Mathematical Journal, Vol. 169, Number 7 (2020), 1209-1280
• Multivariate Rankin-Selberg integrals on GL₄ and GU(2,2) (with Shrenik Shah), Canadian Mathematical Bulletin, Vol. 61 (4), 2018, 822-835
• A multivariate integral representation on GL₂ x GSp₄ inspired by the pullback formula (with Shrenik Shah), Transactions of the American Mathematical Society, 371 (2019), 5591-5630
• Lifting laws and arithmetic invariant theory, Cambridge Journal of Mathematics 6, No. 4 (2018), 347-449
• Unramified Godement-Jacquet theory for the spin similitude group, Journal of the Ramanujan Mathematical Society 33, No.3 (2018) 249-282
• The Spin L-function on GSp₆ for Siegel modular forms, Compositio Mathematica 153 (2017), no. 7, 1391–1432
• The Spin L-function on GSp₆ via a non-unique model (with Shrenik Shah), American Journal of Mathematics 140 (2018), no. 3, 753-788
• On the Rankin-Selberg integral of Kohnen and Skoruppa (with Shrenik Shah), Mathematical Research Letters 24 (2017), no. 1, 173-222

Other articles

• Exceptional groups and their modular forms, Notices of the American Mathematical Society (2021), Vol. 68, no. 2, 194-203; corrections

Teaching at UCSD

Course notes