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 Lfunctions.
My CV is here
Research articles
(The versions below differ slightly from their published counterparts)

The quaternionic Maass Spezialschar on split SO(8) (with Jennifer JohnsonLeung, Finn McGlade, Isabella Negrini, and Manami Roy), preprint

Computation of Fourier coefficients of automorphic forms of type G_{2}, preprint, SAGE implementation

Exceptional theta functions and arithmeticity of modular forms on G_{2}, preprint

Exceptional SiegelWeil theorems for compact Spin_{8}, preprint

Modular forms of halfintegral weight on exceptional groups (with Spencer Leslie), Compositio Mathematica, accepted

The completed standard Lfunction of modular forms on G_{2} (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 SaitoKurokawa lift and cusp forms on G_{2}, Algebra and Number Theory, 15 (2021), no. 5, 12131244

On the residue method for period integrals (with Chen Wan and Michal Zydor), Duke Mathematics Journal, 170 (2021), no. 7, 14571515

The minimal modular form on quaternionic E_{8}, Journal of the Institute of Mathematics Jussieu, published online, Aug 2020

Modular forms on G_{2} and their standard Lfunction, Proceedings of the Simons Symposium "Relative Trace Formulas", Springer Nature 2021, 379427

A G_{2}period of a Fourier coefficient of an Eisenstein series on E_{6} (with Chen Wan and Michal Zydor), Israel Journal of Mathematics, (2019), 229279

The Fourier expansion of modular forms on quaternionic exceptional groups, Duke Mathematical Journal, Vol. 169, Number 7 (2020), 12091280

Multivariate RankinSelberg integrals on GL_{4} and GU(2,2) (with Shrenik Shah), Canadian Mathematical Bulletin, Vol. 61 (4), 2018, 822835

A multivariate integral representation on GL_{2} x GSp_{4} inspired by the pullback formula (with Shrenik Shah), Transactions of the American Mathematical Society, 371 (2019), 55915630

Lifting laws and arithmetic invariant theory, Cambridge Journal of Mathematics 6, No. 4 (2018), 347449

Unramified GodementJacquet theory for the spin similitude group, Journal of the Ramanujan Mathematical Society 33, No.3 (2018) 249282

The Spin Lfunction on GSp_{6} for Siegel modular forms, Compositio Mathematica 153
(2017), no. 7, 13911432

The Spin Lfunction on GSp_{6} via a nonunique model (with Shrenik Shah), American Journal of Mathematics 140 (2018), no. 3, 753788

On the RankinSelberg integral of Kohnen and Skoruppa (with Shrenik Shah), Mathematical Research Letters 24 (2017), no. 1, 173222
Other articles
Teaching at UCSD
Winter 2024: Math 103B (modern algebra II)
Fall 2023: Math 204A (number theory I)
Spring 2023: Math 100C (abstract algebra 3)
Winter 2023: Math 100B (abstract algebra 2)
Winter 2022: Math 105 (basic number theory)
Fall 2021: Math 204A (number theory I)
Spring 2021: Math 103B (modern algebra II)
Winter 2021: Math 205 (topics in number theory)
Fall 2020: Math 100A (abstract algebra)
Course notes
Summer 2022: The RankinSelberg method: A User's Guide
Spring 2022: Arizona Winter School 2022: Modular forms on exceptional groups
Winter 2021: UCSD, Math 205: Exceptional algebraic structures and applications
Fall 2019: Duke University, Math 305S (number theory)
Spring 2019: Duke University, Math 690 (topics in algebraic number theory)