• Yiqin He (何益钦)

    Research interest: Number theory and representation theory

Morningside Center of Mathematics, No.55, Zhongguancun East Road, 
Beijing, 100190, China
Personal information:
I am currently a postdoc at the Morningside Center of Mathematics, Beijing, China.
My research interest mainly rests in Number theory and representation theory, especially the p-adic Langlands programme and its arithmetic applications. My research on p-adic Langlands program begins with the study of L-invariants. While the trianguline p-adic Galois representations are studied widely, there are fewer examples of results for the non-trianguline p-adic Galois representations. 
In my PhD thesis, we extend the theory of simple L-invariants to non-trianguline case. We define parabolic Fontaine-Mazur and Breuil's simple L-invariants for certain potentially semi-stable non-crystalline (not necessarily trianguline) Galois representation. Moreover, the correspondence between these two simple L-invariants can be realized in the p-adic completed cohomology of some Shimura varieties (especially, in the space of p-adic automorphic forms on certain definite unitary group).
In early years, I am also interested in Combinatorics, especially the constructions of Directed strongly regular graphs and the classification of the Directed strongly regular Cayley graphs on dihedral groups (based on the applications of representation theory).

Education & Career :
2018/09-2023/06  Ph.D     Peking University, Beijing, China (Supervisor: Yiwen Ding)
2014/09-2018/06  B.S       Xiangtan University, Xiangtan, China
Publications & Preprints:
1. Y. He, Extensions of locally analytic generalized parabolic Steinberg representations. arXiv: 2211.00476, preprint, 70 pages. 
2. Y. He, Parabolic Simple L-Invariants. arXiv: 2211.10847, preprint, 59 pages. 
3. Y. He, B. Zhang, The application of representation theory in directed strongly regular graphs. (English summary) J. Combin. Theory Ser. A 161 (2019), 508–536. 
4. Y. He, B. Zhang, R. Feng, Directed strongly regular Cayley graphs on dihedral groups. (English summary) Appl. Math. Comput. 391 (2021), Paper No. 125651, 13 pp.

New World Mathematics Awards (now the "ICCM Best Thesis Award"), Bachelor Thesis Award-Silver Prize, Yau Mathematical Sciences Center, 2019.