Jayce Robert Getz
Assistant Professor in the Department of Mathematics
Automorphic representations and arithmetic geometry.
Current Appointments & Affiliations
- Assistant Professor in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2012
Contact Information
- 225 Physics, Duke Mathematics Department, Durham, NC 27708-0320
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jaycegetz@gmail.com
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http://www.math.duke.edu/~jgetz
- Background
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Education, Training, & Certifications
- Ph.D., University of Wisconsin at Madison 2007
- M.A., University of Wisconsin at Madison 2006
- B.A., Harvard University 2004
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Academic Positions Outside Duke
- Tenure Track Assistant Professor, McGill University. 2010 - 2012
- Veblen Research Instructor , Princeton University and IAS. 2007 - 2010
- Recognition
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Awards & Honors
- Member of the Institute for Advanced Study (IAS). C. Simonyi Endowment, in part. 2018
- Ferran Sunyer i Balaguer Prize. Institut d'Estudis Catalans. April 2011
- School of Mathematics/ Members. Institute for Advanced Study. 2009
- School of Mathematics/ Members. Institute for Advanced Study. 2008
- School of Mathematics/ Members. Institute for Advanced Study. September 2007
- Excellence in Mathematical Research Award. University of Wisconsin at Madison. April 2007
- Detur Book Prize. Harvard University. 2002
- 1st Place in Mathematics. International Science and Engineering Fair. 2000
- 2nd place overall. International Science and Engineering Fair. 2000
- Intel Science Talent Search (2nd Place). Intel. 2000
- Karl Meger Memorial Award. International Science and Engineering Fair. 2000
- Expertise
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Subject Headings
- Research
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Selected Grants
- Langlands Functoriality in Nonsolvable and Relative Settings awarded by National Science Foundation 2014 - 2018
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Fellowships, Supported Research, & Other Grants
- Algebraic cycles on Shimura varieties and distinguished representations awarded by Natural Sciences and Engineering Research Council (NSERC) Discovery Grant 2010 - 2012
- NSF Postdoctoral Research Fellowship awarded by National Science Foundation (NSF) 2007 - 2010
- NDSEG Graduate Fellowship awarded by American Society for Engineering Education (ASEE) 2004 - 2007
- Publications & Artistic Works
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Selected Publications
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Books
- Getz, J, and Goresky, M. Hilbert modular forms with coefficients in intersection homology and quadratic base change. January 1, 2012. Full Text
- Getz, J, and Goresky, M. Introduction. January 1, 2012. Full Text
- Getz, JR, and Hahn, H. An introduction to automorphic representations with a view towards trace formulae. . (Textbook) Link to Item
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Book Sections
- Getz, J, and Goresky, M. "Eisenstein series with coefficients in intersection homology." In Progress in Mathematics, 179-182. January 1, 2012. Full Text
- Getz, J, and Goresky, M. "Generalities on Hilbert modular forms and varieties." In Progress in Mathematics, 57-89. January 1, 2012. Full Text
- Getz, J, and Goresky, M. "The full version of theorem 1.3." In Progress in Mathematics, 167-177. January 1, 2012. Full Text
- Getz, J, and Goresky, M. "Automorphic vector bundles and local systems." In Progress in Mathematics, 91-110. January 1, 2012. Full Text
- Getz, J, and Goresky, M. "Review of chains and cochains." In Progress in Mathematics, 21-28. January 1, 2012. Full Text
- Getz, J, and Goresky, M. "The automorphic description of intersection cohomology." In Progress in Mathematics, 111-134. January 1, 2012. Full Text
- Getz, J, and Goresky, M. "Explicit construction of cycles." In Progress in Mathematics, 151-166. January 1, 2012. Full Text
- Getz, J, and Goresky, M. "Review of intersection homology and cohomology." In Progress in Mathematics, 29-39. January 1, 2012. Full Text
- Getz, J, and Goresky, M. "Review of arithmetic quotients." In Progress in Mathematics, 41-55. January 1, 2012. Full Text
- Getz, J, and Goresky, M. "Hilbert modular forms with coefficients in a Hecke module." In Progress in Mathematics, 135-150. January 1, 2012. Full Text
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Journal Articles
- Getz, JR. "Nonabelian fourier transforms for spherical representations." Pacific Journal of Mathematics 294, no. 2 (January 1, 2018): 351-373. Full Text
- Getz, JR. "A four-variable automorphic kernel function." Research in the Mathematical Sciences 3, no. 1 (December 2016). Full Text
- Getz, JR, and Herman, PE. "A nonabelian trace formula." Research in the Mathematical Sciences 2, no. 1 (December 2015). Full Text
- Getz, JR, and Klassen, J. "Isolating Rankin-Selberg lifts." Proceedings of the American Mathematical Society 143, no. 8 (April 6, 2015): 3319-3329. Full Text
- Getz, JR, and Hahn, H. "A general simple relative trace formula." Pacific Journal of Mathematics 277, no. 1 (2015): 99-118. Full Text
- Getz, JR, and Hahn, H. "Algebraic cycles and tate classes on hilbert modular varieties." International Journal of Number Theory 10, no. 1 (February 1, 2014): 161-176. Full Text
- Getz, JR, Wambach, E, Getz, JR, and Wambach, E. "Twisted relative trace formulae with a view towards unitary groupsTwisted relative trace formulae with a view towards unitary groups (PublishedAccepted)." American Journal of Mathematics 136 (January 3, 2014): 1-57.
- Getz, JR. "Invariant four variable automorphic kernel functions." arXiv (2014). Link to Item
- Getz, JR. "An approach to nonsolvable base change and descent." Journal of the Ramanujan Mathematical Society 27, no. 2 (2012): 143-211. (Academic Article) Link to Item
- Getz, J. "Intersection numbers of Hecke cycles on Hilbert modular varieties." American Journal of Mathematics 129, no. 6 (2007): 1623-1658. Full Text
- Basha, S, Getz, J, Nover, H, and Smith, E. "Systems of orthogonal polynomials arising from the modular j-function." Journal of Mathematical Analysis and Applications 289, no. 1 (2004): 336-354. Full Text
- Getz, J. "A generalization of a theorem of Rankin and Swinnerton-Dyer on zeros of modular forms." Proceedings of the American Mathematical Society 132, no. 8 (2004): 2221-2231. Full Text
- Getz, J, and Mahlburg, K. "Partition identities and a theorem of Zagier." Journal of Combinatorial Theory. Series A 100, no. 1 (2002): 27-43. Full Text
- Getz, J. "Extension of a theorem of Kiming and Olsson for the partition function." Ramanujan Journal 5, no. 1 (2001): 47-51. Full Text
- Getz, JR, and Liu, B. "A refined Poisson summation formula for certain Braverman-Kazhdan spaces (Submitted)." Link to Item
- Getz, JR, and Liu, B. "A summation formula for triples of quadratic spaces (Submitted)." Link to Item
- Getz, JR. "A summation formula for the Rankin-Selberg monoid and a nonabelian trace formula (Submitted)." Link to Item
- Getz, JR. "Secondary terms in asymptotics for the number of zeros of quadratic forms over number fields(Published online)." Journal of the London Mathematical Society . Full Text
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- Teaching & Mentoring
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Recent Courses
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Advising & Mentoring
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Postdocs Mentored
Michael Lipnowski (now at McGill), 2013--2016
Fritz Hoermann (now at Albert-Ludwigs-Universitat Freiburg), 2010--2011
Graduate Students Supervised
Chung-Ru Lee, PhD Candidate, Duke University, Fall 2016-present
Huong Tran, PhD Candidate, Duke University, Fall 2015-present
Jason Pol\'{a}k, PhD in 2016, McGill University (Post-doc at the University of Melbourne)
Maxime Turgeon, Master in 2013, McGill University (PhD candidate in Statistics)
Undergraduate Students Supervised
Trung Can, Ben Nativi, Gary Zhou, Duke University, Summer 2017
Josh Izzard, Duke University, May 2013--Apr 2014
Jamie Klassen, McGill University, Summer 2012
Highschool Students Supervised
Nolan Miranda, May 2016-Aug 2016
Angela Deng, May 2014--Dec 2015
Erik Anderson, 2010--2011
Available to mentor:
- PhD
- Post-Doc
- Undergraduate
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Postdocs Mentored
- Scholarly, Clinical, & Service Activities
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Presentations & Appearances
- A summation formula for triples of quadratic spaces. Algebra and Number Theory Seminar. Yale University. November 2017 2017
- A summation formula for triples of quadratic spaces. Group, Lie and Number Theory Seminar. University of Michigan. November 2017 2017
- A summation formula for triples of quadratic spaces. Automorphic Forms and Related Topics. Vietnam Institute Advanced Study in Math (VIASM). August 2017 2017
- Summation formula for the Rankin-Selberg monoid via the circle method. Automorphic Forms and Related Topics. AMS special session. May 2017 2017
- Summation formula for the Rankin-Selberg monoid via the circle method. Harmonic analysis and the trace formula. MFO. May 2017 2017
- Summation formula for the Rankin-Selberg monoid via the circle method. Automorphic Forms and Representation Seminar Seminar. Purdue University. February 2017 2017
- Langlands functoriality conjecture. Department Colloquium. Sookmyung Women's University. August 2016 2016
- Triple product L-functions and limiting forms of trace formulae. Number Theory Seminar. Korea Institute for Advanced study (KIAS). August 2016 2016
- Triple product L-functions and limiting forms of trace formulae. Number Theory Seminar. Yonsei University. August 2016 2016
- Triple product L-functions and limiting forms of trace formulae. Automorphic Forms Workshop. Wake Forest University. March 2016 2016
- Triple product L-functions and limiting forms of trace formulae. Langlands Program Seminar. CUNY Graduate Center. March 2016 2016
- Triple product L-functions and limiting forms of trace formulae. Number Theory Seminar. Boston College. March 2016 2016
- Four-variable automorphic kernel functions. Illinois Number Theory Conference. UIUC. August 2015 2015
- Remarks on a paper of Frenkel, Langlands, and Ngo. Workshop on L-functions and trace formula. Purdue University. May 2015 2015
- Descent and base change with a view towards the Artin conjecture. Colloquium. Emory University. January 2015 2015
- A nonabelian trace formula. ELEFANT workshop. Hausdorff Center. July 2014 2014
- A nonabelian trace formula. Special Seminar. University of Chicago. December 2013 2013
- An approach to nonsolvable base change for GL(2). Lie theory seminar. University of Minnesota. April 2013 2013
- An approach to nonsolvable base change for GL(2). Grad/Fac seminar. Duke University. February 2013 2013
- An approach to nonsolvable base change for GL(2). Number theory seminar. University of South Carolina. December 2012 2012
- An approach to nonsolvable base change for GL(2). Athens/Atlanta Number Theory Day. Emory University. October 2012 2012
- An approach to nonsolvable base change for GL(2). Midwest Number Theory Day. UIUC. October 2012 2012
- An approach to nonsolvable base change for GL(2). Number theory seminar. Harvard University. April 2012 2012
- Hilbert modular forms with coefficients in intersection homology. Séminaire d'Algèbre et de Géométrie Gradué. Laval University. March 2012 2012
- An approach to nonsolvable base change for GL(2). Colloquium. Duke University. February 2012 2012
- An approach to nonsolvable base change for GL(2). Colloquium. Johns Hopkins University. January 2012 2012
- An approach to nonsolvable base change for GL(2). Colloquium. University of Maryland. January 2012 2012
- An approach to nonsolvable base change for GL(2). Colloquium. Cornell University. November 2011 2011
- Distinction, special cycles, and twisted relative trace fomulae. Number theory seminar. University of Chicago. May 2011 2011
- Intersection numbers of Hecke cycles on Hilbert modular varieties. Montreal-Toronto Meeting on Hilbert modular varieties. Fields Institute. April 2011 2011
- Twisted relative endoscopy. Number theory/algebraic geometry seminar. Yale University. March 2011 2011
- Relative endoscopy and arithmetic geometry of Shimura varieties. Special values of L-functions and arithmetic geometry. October 2010 2010
- Relative endoscopy and arithmetic of Shimura varieties. Number theory seminar. Kyoto University. October 2010 2010
- Relative endoscopy and arithmetic of Shimura varieties. Montreal-Toronto Meeting on Arithmetic of Shimura varieties. CRM, Montreal. September 2010 2010
- Elliptic descent of global orbital integrals. Canadian Number Theory Association XI. Acadia University. July 2010 2010
- Twisted relative trace formulae. Lie theory seminar. Cornell University. October 2009 2009
- Twisted relative trace formulae with applications to unitary groups. Algebraic Geometry/Number Theory Seminar. Johns Hopkins University. February 2009 2009
- Trace formulae and locally symmetric spaces. Colloquium. Boston College. January 2009 2009
- Trace formulae and locally symmetric spaces. Colloquium. McGill University. December 2008 2008
- Trace formulae and locally symmetric spaces. Members' Seminar. IAS. December 2008 2008
- Twisted relative trace formulae with applications to unitary groups. Quebec-Vermont number theory seminar. McGill University. December 2008 2008
- Twisted relative trace formulae with applications to unitary groups. Number theory seminar. McMaster University. November 2008 2008
- Twisted relative trace formulae with applications to unitary groups. Number theory/representation theory seminar. University of Toronto. November 2008 2008
- Twisted relative trace formulae with applications to unitary groups. Shimura varieties and trace formula seminar. IAS. November 2008 2008
- Twisted relative trace formulae with applications to unitary groups. Automorphic forms/number theory seminar. University of Minnesota. September 2008 2008
- Twisted relative trace formulae with applications to unitary groups. Number theory seminar. University of Maryland. September 2008 2008
- Twisted relative trace formulae. Colloquium. University of Minnesota. September 2008 2008
- Twisted relative trace formulae with a view towards unitary groups. Workshop on locally symmetric spaces. Banff International Research Station. May 2008 2008
- Jacquet-Langlands transfer and distinction. Number theory seminar. Caltech. February 2008 2008
- Jacquet-Langlands transfer and distinction. Number theory seminar. UCLA. February 1, 2008 2008
- Relative trace formulae with a view towards Shimura varieties. Number theory/representation theory seminar. University of Michigan. February 2008 2008
- Hilbert modular forms with coefficients in intersection homology. Algebra/Number Theory Seminar. Penn State University. November 2007 2007
- Hilbert modular forms with coefficients in intersection homology. Algebraic Geomerty Seminar. Duke University. October 2007 2007
- Hilbert modular forms with coefficients in intersection homology. Joint Number Theroy Seminar. Princeton University and IAS. September 2007 2007
- Hilbert modular forms with coefficients in intersection homology. Algebraic Geomerty Seminar. University of Chicago. May 2007 2007
- Hilbert modular forms with coefficients in intersection homology. Automorphic Forms Seminar. University of Minnesota. March 2007 2007
- Hilbert modular forms with coefficients in intersection homology. Number theory/representation theory seminar. University of Toronto. March 2007 2007
- Hilbert modular forms with coefficients in intersection homology. Number theory seminar. Boston College. February 2007 2007
- Intersection homology theory of Hilbert modualr varieties. Mathematics Seminar. Johns Hopkins University. January 2007 2007
- Hilbert modular forms with coefficients in intersection homology. Automorphic forms/Representation theory seminar. Purdue University. November 2006 2006
- Hilbert modular forms with coefficients in intersection homology. Midwest Number Theory Conference IV. UIUC. October 2006 2006
- Hilbert modular forms with coefficients in intersection homology. Number theory seminar. Ohio State University. October 2006 2006
- Hilbert modular forms with coefficients in intersection homology. Arithmetic Geometry Semina. Humboldt University. July 2006 2006
- Hilbert modular forms with coefficients in intersection homology. Recent Developments in the Arithmetic of Shimura Varieties and Arakelov. CRM, Bellaterra, Spain. July 2006 2006
- Hilbert modular forms with coefficients in intersection homology. AMS Special Session on Computational Arithmetic Geometry. AMS. April 2006 2006
- Hilbert modular forms with coefficients in intersection homology. Combinatorics/Algebra/Number Theory Seminar. Iowa State University. April 2006 2006
- Hilbert modular forms with coefficients in intersection homology. AMS Special Session on Arithmetic Geometry/Modular Forms. AMS. January 2006 2006
- Hilbert modular forms with coefficients in intersection homology. Automorphic representations, L-functions, and Periods. RIMS Kyoto. January 2006 2006
- Introduction to intersection homology. Mathmatics Seminar. Osaka University. January 2006 2006
- Hilbert modular forms with coefficients in intersection homology. Intersection of Arithmetic Cycles and Automorphic Forms. CRM. December 2005 2005
- Hilbert modular forms with coefficients in intersection homology. Number theory seminar. Brown University. November 2005 2005
- Hilbert modular forms with coefficients in intersection homology. Number theory seminar. Johns Hopkins University. November 2005 2005
- Intersection numbers of Hecke cycles on Hilbert modular varieties. Midwest Number Theory Conference III. University of Wisconsin. November 2005 2005
- Hilbert modular forms with coefficients in intersection homology. Number theory seminar. UCLA. October 2005 2005
- Intersection numbers of Hecke cycles on Hilbert modular varieties. NSF Focused Research Group workshop. University of Maryland. October 2005 2005
- Intersection numbers of Hecke cycles on Hilbert modular varieties. ArithmeTexas. Texas A&M. April 2005 2005
- Intersection numbers of Hecke cycles on Hilbert modular varieties. Number theory seminar. University of Rochester. March 2005 2005
- Intersection numbers of Hecke cycles on Hilbert modular varieties. The 19th Annual Automorphic Forms Workshop. UTexas at Denton. March 2005 2005
- Intersection numbers of Hecke cycles on Hilbert modular varieties. Midwest Number Theory Conference II. UIUC. February 2005 2005
- Intersection numbers of Hecke cycles on Hilbert modular varieties. Number theory seminar. University of Wisconsin. February 2005 2005
- Systems of orthogonal polynomials arising from the modular j-function. Additive Number Theory Conference. University of Florida. November 2004 2004
- Systems of orthogonal polynomials arising from the modular j-function. Additive Number Theory Conference. University of Florida. November 2004 2004
- Classical and p-adic modular forms arising from the Borcherds exponents of other modular forms. Joint Trivial Notions and Modular Seminar. Harvard University. April 2004 2004
- Systems of orthogonal polynomials arising from the modular j-function. AMS special session on continued fractions. AMS. January 2004 2004
- Systems of orthogonal polynomials arising from the modular j-function. Big Sky Conference on Discrete Math. University of Montana. September 2003 2003
- Systems of orthogonal polynomials arising from the modular j-function. Modular Curves Seminar. Harvard University. September 2003 2003
- Systems of orthogonal polynomials arising from the modular j-function. Number theory seminar. University of Wisconsin. July 2003 2003
- A generalization of a theorem of Rankin and Swinnerton-Dyer on zeros of modular forms. Number theory seminar. University of Wisconsin. July 2002 2002
- Partition identities and a theorem of Zagier. Math Table Seminar. Harvard University. November 2001 2001
- Partition identities and a theorem of Zagier. Modular Forms seminar. Harvard University. November 2001 2001
- Partition identities and a theorem of Zagier. Number theory seminar. University of Wisconsin. July 2001 2001
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Outreach & Engaged Scholarship
- Judge. Greater Metropolitan New York Math Fair. Brooklyn Technical High School. March 2009 2009
- Invited Panelist. NSF Give a Day, Make a Difference Outreach. NSF. May 2004 2004
- Invited Speaker. International Mathematics Olympiad Awards Ceremony. July 2001 2001
- Invited Panelist. NSF 50 Scientists and Engineers in the Schools Outreach. NSF. May 2001 2001
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Service to the Profession
- Participant. Worskop on Functoriality and the trace formula. AIM. December 2017 2017
- Participant. Workshop on Mod p/p-adic Langlands programs. Korean Institute for Advanced Study (KIAS). August 2016 2016
- Co-Organizer. Workshop on Automorphic Kernel Functions. American Institute of Mathematics (AIM). December 2015 2015
- Participant. Conference on Analysis, Spectra and Number Theory. Princeton University and IAS. December 2014 2014
- Co-Organizer. Automorphic Forms and Related Topics. AMS Special Session. November 2014 2014
- Co-Founder and Co-Organizer. Number Theory Seminar. Duke University. September 2012 2012
- Co-Organizer. Algebraic Geometry Seminar. Duke University. September 2012 2012
- Co-Organizer. Bellairs Workshop in Number Theory. Barbado. May 2011 2011
- Co-Organizer. CRM-ISM Colloquium. McGill University. September 2010 2010
- Co-Organizer. Quebec-Vermont Number Theory Seminar. McGill University. September 2010 2010
- Participant. Workshop on the stable trace formula, automorphic forms, and Galois representations. Banff International Research Station. August 2008 2008
- Participant. FRG workshop on recent Developments in Number Theory: Selmer Groups, L-functions, and Galois Deformation. UCLA. March 2008 2008
- Co-Organizer. Joint Number Theory Seminar. Princeton University and IAS. September 2007 2007
- Participant. Workshop on the Tate conjecture'. AIM. July 2007 2007
- Participant. FRG workshop on Automorphic Galois Representations, L-functions and Arithmetic. Columbia University. June 2006 2006
- Participant. Advanced Course on Arakelov Geometry and Shimura Varieties. Centre de Recerca Matematica. February 2006 2006
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Service to Duke
- Faculty Leader. Duke Oopertunities in Math (DOmath2017). Duke University. May 2017 2017
- Duke University. Graduate Admission. January 2017 2017
- Duke University. Thesis defense committee, Humberto Diaz. May 2016 2016
- Duke University. Graduate Admission . January 2016 2016
- Duke University. Pure ARP Search. January 2015 2015
- Speaker. Grad/Faculty Seminar. February 2013 2013
- Duke University. Pure ARP Search. January 2013 2013
- Co-Organizer. Algebaric Geometry Seminar. Duke University. September 2012 2012
- Co-Founder and Co-Organizer. Number Theory Seminar. Duke University. 2012 2012
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