## Jayce Robert Getz## Assistant ProfessorDepartment of MathematicsDuke University Durham, NC 27708-0320 E-mail: jgetz(at)jmath(dot)jduke(dot)jedu (with the last three j's deleted) Research interest: Number theory Recommended reading for everyone: On The Usefulness of Useless Knowledge |

- Comparisons of trace formulae, both globally and locally
- Variants of the Hitchin fibration following Ngo
- Cycles on Shimura varieties
- Analytic number theory arising out of limits of trace formulae
- Algebraic envelopes of Galois representations
- Representation theory of reductive groups over local fields

** PhD Mathematics, University of Wisconsin at Madison, 2007**

** AB Mathematics, Harvard University, 2004**

- Chung-Ru Lee, Duke University, Fall 2016-present.
- Huong Tran, Duke University, Fall 2015-present
- Jason Polak, McGill Univesity, Fall 2011-Spring 2016: Currently postdoc with Vilonen and Xue at the University of Melbourne.

Heekyoung Hahn and I are writing a book on automorphic representations.

The chapters that are in reasonable shape will be posted here. The old course notes are here.

These may differ slightly from the published versions. If you have any comments or corrections, please email me at the address above.

*A summation formula for triples of quadratic spaces*, (with B. Liu), submitted.*A refined Poisson summation formula for certain Braverman-Kazhdan spaces*, (with B. Liu), submitted.*Secondary terms in asymptotics for the number of zeros of quadratic forms over number fields*, J. London Math. Soc., to appear.*Nonabelian Fourier transforms for spherical representations*, Pacific J. Math, to appear.*A summation formula for the Rankin-Selberg monoid and a nonabelian trace formula*submitted.*A four variable automorphic kernel function*, Research in the Mathematical Sciences (2016), 3:20*A general simple relative trace formula*(with H. Hahn), Pacific J. Math., Vol. 277, No. 1 (2015) 99-118.*A nonabelian trace formula*(with P. E. Herman), Research in the Mathematical Sciences (2015) 2:14.-
*Isolating Rankin-Selberg lifts*(with J. Klassen), Proc. Amer. Math. Soc., Vol. 143 (2015) 3319-3329. *Algebraic cycles and Tate classes on Hilbert modular varieties*(with H. Hahn), Int. J. Number Theory, Vol. 10, No. 1 (2014) 161--176.*An approach to nonsolvable base change and descent*, J. Ramanujan Math. Soc., Vol. 27, No. 2 (2012) 143-211.*Twisted relative trace formulae with a view towards unitary groups*(with E. Wambach), American J. Math., Vol. 136 (2014) 1-57.

Note: in section 10.4 of the published version the Jacobson density theorem was erroneously invoked where the Dixmier-Malliavin lemma should have been invoked.-
**Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change**(with M. Goresky), winner of the 2011 Ferran Sunyer i Balaguer Prize, Progress in Math. -
*Intersection numbers of Hecke cycles on Hilbert modular varieties*, American J. Math., Vol. 129, No. 6 (2007), 1623-1658. *Systems of orthogonal polynomials arising from the modular j-function*(with S. Basha, H. Nover, E. Smith), J. Math. Anal. and Appl., Vol. 289, No. 1 (2004), 336-354. Corrigendum.*A generalization of a theorem of Rankin and Swinnerton-Dyer on zeros of modular forms*, Proc. Amer. Math. Soc., 132 (2004), 2221-2231. Corrigendum.*Partition identities and a theorem of Zagier*(with K. Mahlburg), J. Comb. Theory (A), 100, (2002), 27-43.-
*Extension of a theorem of Kiming and Olsson for the partition function*, Ramanujan J., Vol. 5, No. 1 (2001), 47-51. -
*On congruence properties of the partition function*, Int. J. Math. and Math. Sci., Vol. 23, No. 7 (2000), 493-496.

**Upcoming trips**

- Einstein Institute of Mathematics, Jerusalem, August 14-24, 2018.
- Porquerolles Conference, France, September 2-8, 2018.
- Sixth Abel Conference: Celebrating the Mathematical Impact of Robert Langlands, November 14-16, 2018.
- On the Langlands Program: Endoscopy and Beyond, IMS-NUS, Singapore, December 17, 2018-Jan 18, 2019.
- AMS Special Session on Counting Methods in Number Theory, AMS-MAA Joint Meeting, Janurary 2019.
- Recent Developments in Automorphic Forms, AMS meeting, University of Hawaii Manoa, March 22-24, 2019.
- Relative Aspects of the Langlands Program, L-Functions and Beyond Endoscopy, CIRM, France, May 25-29, 2020.