Shaoyun Yi
University of South Carolina
Department of Mathematics
Columbia, SC 29208
E-mail: shaoyun@mailbox.sc.edu
Office: COL 1005D

I completed my Ph.D in May 2019 at the University of Oklahoma under the supervision of Ralf Schmidt. Currently, I am an Instructor in the Department of Mathematics at the University of South Carolina. Starting in Fall 2022, I will be a tenure-track Assistant Professor at Xiamen University. Here is my CV.

Research Interests

Number Theory, Representation Theory. Specifically, I am interested in classical modular forms, local and global representation theory, L-functions, the Langlands program and analytic number theory.

Publications and Preprints

  1. On distinguishing Siegel cusp forms of degree two (with Zhining Wei).
    Submitted, 2022.  [arXiv].

  2. Dimension formulas for Siegel modular forms of level 4 (with Manami Roy and Ralf Schmidt, and with an appendix by Cris Poor and David S. Yuen).
    Submitted, 2022.  [arXiv].

  3. Generalizations of the Erdős-Kac Theorem and the Prime Number Theorem (with Biao Wang, Zhining Wei and Pan Yan).
    Submitted, 2022.  [preprint available upon request].

  4. Classical and adelic Eisenstein series (with Manami Roy and Ralf Schmidt).
    Submitted, 2021.  [arXiv].

  5. Generalizations of Alladi's formula for arithmetical semigroups (with Lian Duan and Ning Ma).
    The Ramanujan Journal 58 (2022), no. 4, 1285-1319.  [arXiv, DOI].

  6. Congruences for dimensions of spaces of Siegel cusp forms and 4-core partitions (with Chiranjit Ray and Manami Roy).
    The Ramanujan Journal 58 (2022), no. 4, 1011-1023.  [SharedIt link, arXiv, DOI].

  7. Analogues of Alladi's formula over global function fields (with Lian Duan and Biao Wang).
    Finite Fields and Their Applications 74 (2021), 101874, 26 pp.  [arXiv, DOI].

  8. On counting cuspidal automorphic representations for GSp(4) (with Manami Roy and Ralf Schmidt).
    Forum Mathematicum 33 (2021), no. 3, 821-843.  [arXiv, DOI].

  9. Klingen p^2 vectors for GSp(4).
    The Ramanujan Journal 54 (2021), no. 3, 511-554.  [SharedIt link, DOI].

  10. Klingen vectors of level 2 for GSp(4).
    Ph.D. Thesis, University of Oklahoma, 2019.  [PDF].

Teaching

At University of South Carolina:

At University of Oklahoma:

Selected Talks

  1. Classical and adelic Eisenstein series,  International Conference on L-Functions and Related Themes, Minnan Normal University, Aug 7, 2022. (Invited talk, online)

  2. Some results on Eisenstein series,  AMS Special Session on Recent Advances on the Langlands Program, Spring Western Sectional Meeting, May 15, 2022. (Invited talk, online)

  3. Eisenstein series from an adelic point of view,  Algebra, Geometry, and Number Theory Seminar, University of South Carolina, Apr 15, 2022. (online)

  4. Classical and adelic Eisenstein series of weight 2,  34th Automorphic Forms Workshop, Provo, Utah, Mar 19, 2022. (online)

  5. On certain Siegel modular forms of level 4,  2022 Southern Regional Number Theory Conference, Louisiana State University, Mar 13, 2022. (online)

  6. Counting cuspidal automorphic representations of GSp(4) and dimensions of Siegel cusp forms,  Institute of Geometry and Physics, University of Science and Technology of China, Jan 11, 2022. (Invited talk, online)

  7. Counting cuspidal automorphic representations of GSp(4) and dimensions of Siegel cusp forms,  Sichuan Normal University, Dec 29, 2021. (Invited talk, online)

  8. On dimension formulas of Siegel modular forms of level 4,  WCNT 2021: Problems in Number Theory, Dec 17, 2021. (online)

  9. Classical modular forms and local-global representation theory,  Nankai University, Dec 10, 2021. (Invited talk, online)

  10. Dimension formulas for spaces of Siegel modular forms of Klingen level 4,  Sun Yat-sen University (Zhuhai), Dec 6, 2021. (Invited talk, online)

  11. Siegel modular forms of degree 2 and Klingen level 4,  Morningside Seminar on Number Theory, Morningside Center of Mathematics, Nov 17, 2021. (Invited talk, online)

  12. Siegel modular forms of degree 2 and Klingen level 4,  University of Science and Technology of China, Nov 2, 2021. (Invited talk, online)

  13. On dimensions of the spaces of Siegel modular forms,  Algebra, Geometry, and Number Theory Seminar, University of South Carolina, Oct 29, 2021. (hybrid)

  14. Siegel modular forms of level 4,  PAlmetto Joint Arithmetic, Modularity, and Analysis Series III, Sept 26, 2021. (online)

  15. Dimension formulas of Siegel cusp forms for certain congruence subgroups,  Women in automorphic forms, Bielefeld University, Sept 21, 2021. (online)

  16. On counting cuspidal automorphic representations of GSp(4),  New Developments in Number Theory, Jun 1, 2021. (online)

  17. On counting cuspidal automorphic representations of GSp(4),  Mid-Atlantic Seminar On Numbers V, Mar 28, 2021. (online)

  18. An equidistribution theorem for cuspidal automorphic representations of GSp(4),  Sichuan University, Jan 29, 2021. (Invited talk, online)

  19. Analogues of Alladi's formula over global function fields,  PAlmetto Joint Arithmetic, Modularity, and Analysis Series II, Dec 6, 2020. (online)

  20. The equidistribution theorem for a certain family of cuspidal automorphic representations for GSp(4),  Capital Normal University, Nov 14, 2020. (Invited talk, online)

  21. An equidistribution theorem for GSp(4) by counting cuspidal automorphic representations,  University of Science and Technology of China, Nov 12, 2020. (Invited talk, online)

  22. On counting cuspidal automorphic representations and an equidistribution theorem for GSp(4),  Algebra, Geometry, and Number Theory Seminar, University of South Carolina, Oct 30, 2020. (online)

  23. On counting automorphic representations and its connection to an equidistribution theorem for GSp(4),  Algebra Seminar, University of North Texas, Oct 23, 2020. (Invited talk, online)

  24. An equidistribution theorem for cuspidal automorphic representations for GSp(4),  Shandong University, Oct 22, 2020. (Invited talk, online)

  25. Klingen vectors of level 2 for GSp(4),  Number Theory Seminar, University of South Carolina, Oct 31, 2019.

  26. Klingen p^2 vectors for GSp(4),  Ninth Annual Upstate Number Theory Conference, Cornell University, Apr 28, 2019.

  27. A bridge between modular forms theory and representation theory,  Cameron University Math Seminar Series, Cameron University, Apr 16, 2019. (Invited talk)

  28. Klingen p^2 vectors for GSp(4),  33rd Automorphic Forms Workshop, Duquesne University, Mar 10, 2019.

  29. Klingen p^2 vectors for GSp(4),  Algebraic Geometry and Number Theory Seminar, Clemson University, Feb 26, 2019. (Invited talk)

  30. Klingen p^2 vectors for GSp(4),  Lie Groups Seminar, Oklahoma State University, Feb 13, 2019. (Invited talk)

  31. Klingen p^2 vectors for GSp(4, F),  PANTS XXXI, University of South Carolina, Dec 8, 2018.

  32. Klingen p^2 vectors for GSp(4),  Algebra and Representation Theory Seminar, University of Oklahoma, Nov 30, 2018.

  33. Dimensions of Kl(p^2)-invariant vectors for GSp(4, F),  31st Automorphic Forms Workshop, East Tennessee State University, Mar 8, 2017.

  34. Dimensions of spaces of Parahori-invariant vectors for Iwahori-spherical representations of GSp(4),  TORAS I, University of Oklahoma, Mar 28, 2015.

Math Links