# Research

### Research Interests

Automorphic Forms, Representation Theory, Trace Formula, L-Functions. My research is partially supported by NSF Award DMS-2000192 (later transfered to DMS-2103720). My CV is here (last update: 2021/11).

### Publications

1.

A local relative trace formula for the Ginzburg-Rallis model: the geometric side.Memoirs of the American Mathematical SocietyVolume 261, Number 1263.doi:10.1090/memo/12632.

Multiplicity one theorem for the Ginzburg-Rallis Model: the tempered case.Trans. Amer. Math. Soc.371 (2019), 7949-7994.doi:10.1090/tran/76903.

The local Ginzburg-Rallis model over complex field.Pacific Journal of Mathematics291-1 (2017), 241-256.doi:10.2140/pjm.2017.291.2414.

A local trace formula and the multiplicity one theorem for the Ginzburg-Rallis model.Ph.D. thesis, 2017.5.

A local trace formula for the generalized Shalika model,with Raphael Beuzart-Pleassis.Duke Mathematical JournalVolume 168, Number 7 (2019), 1303-1385.doi:10.1215/00127094-2018-00646.

The local Ginzburg-Rallis model for generic representations.J. Number Theory198 (2019), 74-123.doi:10.1016/j.jnt.2018.10.0047.

A G_2-period of a Fourier coefficient of an Eisenstein series on E_6,with Aaron Pollack and Michal Zydor.Israel Journal of Mathematics 234(2019), 229-279.doi:10.1007/s11856-019-1919-x8.

The multiplicity problems for the unitary Ginzburg-Rallis models,with Lei Zhang, accepted byIsrael Journal of Mathematics, 50 pages.9.

On the residue method for period integrals,with Aaron Pollack and Michal Zydor.Duke Mathematical JournalVolume 170, Number 7 (2021), 1457-1515. doi: 10.1215/00127094-2020-007810.

On multiplicity formula for spherical varieties,accepted byJournal of the European Mathematical Society, 51 pages.11. Periods of automorphic forms associated to strongly tempered spherical varieties, with Lei Zhang, submitted, 76 pages.

12. A multiplicity formula of K-types, submitted, 41 pages.

13. Multiplicities for strongly tempered spherical varieties, with Lei Zhang, submitted, 74 pages.

### Invited Talks

- Joint Berkeley-Caltech-Stanford Number Theory (online), April 18, 2022.
- The 7th KTGU Mathematics Workshop for Young Researchers (online), Kyoto, Japan, February 15, 2022.
- Periods, functoriality and L-functions, CIRM (online), Luminy, France, January 10–14, 2022.
- Number theory seminar at Rutgers-New Brunswick (online), November 23, 2021.
- Lecture series at Academy of Mathematics and Systems Science (online), Beijing, November 19–23, 2021.
- Basic Functions, Orbital Integrals, and Beyond Endoscopy, BIRS workshop (online), Banff, Canada, November 15-19, 2021.
- Relative Aspects of the Langlands Program, L-Functions and Beyond Endoscopy, CIRM (online), Luminy, France, May 24–28, 2021.
*Special Session on Recent Developments in Automorphic Representations,*- Representation Theory and Number Theory seminar (online) at National University of

Singapore, Singapore, September 17, 2020. - Mathematics Colloquium at Rutgers-Newark, Rutgers University-Newark, January 28, 2020.
*Number Theory Seminar*, Cornell University, Ithaca, November 1, 2019.*Duke Number Theory Seminar*, Duke University, Durham, October 11, 2019.*New Developments in Representation Theory of p-adic Groups*, MFO, Oberwolfach, Germany, September 29–October 4, 2019.*Special Session on Automorphic Forms and L-Functions*, AMS Section Meeting, University of Wisconsin-Madison, September 14–15, 2019.*Automorphic representations and Langlands program*, July 22–26, 2019, Soochow University, Suzhou, China.*Summer School on Automorphic Representations and the Langlands Program*, July 8–19, 2019, Soochow University, Suzhou, China.*The 8th International Congress of Chinese Mathematicians*, June 9–14, 2019, Beijing, China.*On the Langlands Program: Endoscopy and Beyond*, December 17, 2018–January 18, 2019, Institute for Math. Sciences, National University of Singapore, Singapore.*BC Number Theory/Algebraic Geometry Seminar*, Boston College, Boston, November 29, 2018.*Number Theory / Representation Theory Seminar*, University of Wisconsin-Madison, Madison, October 11, 2018.- Number Theorey Seminar at Nanjing Univeristy, Nanjing, June 19 and 21, 2018.
*Workshop on Automorphic Forms, Geometry and Representation Theory*, Zhejiang University, Hangzhou, June 4–8, 2018.*Lie Theory Seminar*, University of Minnesota, Minneapolis, May 4, 2018.*Harvard Number Theory Seminar*, Harvard University, Boston, January 31, 2018.*The 2017 Paul J. Sally, Jr. Midwest Representation Theory Conference*, in honor of Freydoon Shahidi on the occasion of his 70th birthday. Purdue University, West Lafayette, Oct. 20–22, 2017.*University of Chicago Number Theory Seminar*, University of Chicago, Chicago, October 17, 2017.*Northwestern Number Theory Seminar*, Northwestern University, Evanston, October 16, 2017.*Shanghai Center for Mathematical Science*, Fudan University, Shanghai, August 10, 2017.*Harmonic Analysis and the Trace Formula*, MFO, Oberwolfach, Germany, May 21–27, 2017.*MIT Lie Groups Seminar*, Boston, March 8, 2017.*Number Theory Seminar at Ohio State University*, Columbus, February 20, 2017.*Duke Number Theory Seminar*, Duke University, Durham, February 15, 2017.*Rutgers-Newark Junior Number Theory Days 2016*, Rutgers University-Newark, Newark, November 18–19, 2016.*Automorphic Forms and Arithmetic Seminar*, Columbia University, New York, November 4, 2016.*Special Session on Representation Theory, Automorphic Forms and Related Topics*, AMS Section Meeting, University of St. Thomas, Minneapolis, October 28–30, 2016.*Relative Trace Formula, Periods, L-functions and Harmonic Analysis*, CIRM, Luminy, France, May 23–27, 2016.*30th Automorphic Forms Workshop*, Wake Forest University, Winston-Salem, March 7–10, 2016.*Workshops on Automorphic Kernel Functions*, American Institution of Mathematics, San Jose, November 30–December 4, 2015.