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 Society Volume 261, Number 1263. doi:10.1090/memo/1263

2. Multiplicity one theorem for the Ginzburg-Rallis Model: the tempered case. Trans. Amer. Math. Soc. 371 (2019), 7949-7994. doi:10.1090/tran/7690

3. The local Ginzburg-Rallis model over complex field. Pacific Journal of Mathematics 291-1 (2017), 241-256. doi:10.2140/pjm.2017.291.241

4. 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 Journal Volume 168, Number 7 (2019), 1303-1385. doi:10.1215/00127094-2018-0064

6. The local Ginzburg-Rallis model for generic representations. J. Number Theory 198 (2019), 74-123. doi:10.1016/j.jnt.2018.10.004

7. 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-x

8. The multiplicity problems for the unitary Ginzburg-Rallis models, with Lei Zhang. Israel Journal of Mathematics 2023, 50 pages. https://doi.org/10.1007/s11856-023-2471-2

9. On the residue method for period integrals, with Aaron Pollack and Michal Zydor. Duke Mathematical Journal Volume 170, Number 7 (2021), 1457-1515. doi: 10.1215/00127094-2020-0078

10. On a multiplicity formula for spherical varieties, Journal of the European Mathematical Society 24 (2022), no. 10, 3629–3678. DOI 10.4171/JEMS/1172

11. Periods of automorphic forms associated to strongly tempered spherical varieties, with Lei Zhang, accepted by Memoirs of the American Mathematical Society, 109 pages.

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

13. Multiplicities for strongly tempered spherical varieties, with Lei Zhang, submitted, 116 pages.

14. A Conjecture for Multiplicities of Strongly Tempered Spherical Varieties, with Lei Zhang, submitted, 17 pages.

15. BZSV duality for some strongly tempered spherical varieties, with Zhengyu Mao and Lei Zhang, preprint, 30 pages.

16. A local twisted trace formula for Whittaker induction of coregular symmetric pairs: the geometric side, with Raphael Beuzart-Pleassis, preprint, 127 pages.

 

Invited Talks

• RIMS conference “Research on automorphic forms”, Kyoto, Japan, January 22-26, 2024.
• Princeton/IAS Number Theory Seminar, Princeton, November 16, 2023.
• Number Theory and Representation Theory seminar, Zhejiang University, Hangzhou, June 28, 2023.
• Lecture series in Nanjing University, Nanjing, China, May 22-23, 2023.
• University of Arizona Algebra and Number Theory Seminar, Tucson, January 12, 2023.
• AMS Special Session on Automorphic Forms and Representation Theory, 2023 Joint Mathematics Meetings, Boston, January 6-7, 2023.
• Séminaire Représentations des Groupes Réductifs, Institut de Mathématiques de Marseille, Luminy, France, October 6, 2022.
• Johns Hopkins Number Theory Seminar, Baltimore, September 21, 2022.
• Number Theory and Representation Theory seminar at University of Melbourne, Melbourne, August 4, 2022.
• 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, AMS Section Meeting (online), March 20–21, 2021.
• 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.
• Séminaire Représentations des Groupes Réductifs, Institut de Mathématiques de Marseille, Luminy, France, January 10, 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.