Research

Research Interests

Automorphic Forms, Representation Theory, Trace Formula, L-Functions. My research is partially supported by NSF Award DMS-2349836. My CV is here (last update: 2024/07).

 

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), Volume 258, pages 185–248. 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, 112 pages.

12. A multiplicity formula of K-types, accepted by International Mathematics Research Notices, 46 pages.

13. Multiplicities for some strongly tempered spherical varieties, with Lei Zhang, submitted, 117 pages.

14. A Conjecture on Multiplicities for Strongly Tempered Spherical Varieties, with Lei Zhang. Pacific Journal of Mathematics 337-2 (2025), 339-363.

15. Relative Langlands duality for some strongly tempered spherical varieties, with Zhengyu Mao and Lei Zhang, submitted, 35 pages.

16. A local twisted trace formula for Whittaker induction of coregular symmetric pairs: the geometric side, with Raphael Beuzart-Pleassis, submitted, 137 pages.

17. Strongly tempered hyperspherical Hamiltonian spaces, with Zhengyu Mao and Lei Zhang, submitted, 48 pages.

 

Invited Talks

• Workshop on Real reductive groups and Theta correspondence, Tianyuan Mathematics Research Center, Kunming, China, July 21–27, 2024.
• Simons Symposium on Periods and L-values of Motives, Schloss Elmau, Germany, June 9–15, 2024.
• Summer School and Workshop on Relative Langlands Duality, University of Minnesota, June 3–8, 2024.
• Special Session on Automorphic Forms and Trace Formulae, 2024 Spring Eastern Sectional Meeting, Howard University, April 6–7, 2024.
• Duke Number Theory Seminar, Duke University, Durham, February 21, 2024.
• 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.
• Math Colloquia at University of Minnesota, Minneapolis, November 17, 2022.
• 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.