Zhongyipan Lin

Hi! I am a Boas Assistant Professor at Northwestern University. I am teaching differential calculus and elementary differential equations in Fall Quarter 2022. I am interested in number theory and related topics. I just graduated from Johns Hopkins University. My PhD advisor is David Savitt.

Submitted

  1. A Deligne-Lusztig type correspondence for tame p-adic groups (49 pages, updated on 10/10/2023, arXiv:2306.02093)
    We formulate a generalization of the explicit Serre weight conjectures for quasi-split tame groups.
  2. Heisenberg varieties and the existence of de Rham lifts (33 pages, pdf)
    We show the existence of de Rham lifts for mod p L-parameters for unitary groups.
  3. The Emerton-Gee stacks for tame groups (66 pages, pdf)
    We construct the Emerton-Gee stack for tamely ramified groups.
  4. Lyndon-Demushkin method and crystalline lifts of G2-valued Galois representations (updated on 12/26/2023, arXiv:2011.08773)
    We develop the obstruction theory for lifting characteristic p Galois representations valued in reductive groups of type Bl, Cl, Dl and G2.
    As an application, we show when all p > 3, all G2-valued characteristic p Galois representations admit a crystalline lift.

Drafts (to be expanded)

  1. The Emerton-Gee stacks for tame groups, II (37 pages, pdf)
    We construct the moduli of potentially semistable Galois representations valued in tame p-adic groups and classify the irreducible components of the reduced Emerton-Gee stacks for classical groups, subject to numerical conditions which we have verified for unitary groups in the "Heisenberg variety" paper.
  2. Extension of Crystalline representations valued in general reductive groups. (pdf)
    We show extensions of crystalline representations valued in general reductive groups are crystalline, assuming some Hodge-Tate weights of a certain adjoint representation is slightly less than 0.

Publications

  1. Crystalline lifts and a variant of the Steinberg-Winter theorem (Doc. Math. 2022, arXiv:2011.08766)
    We propose a necessary and sufficient condition for an automorphism of a reductive group to have a fixed maximal torus. We prove it in the Borel-de Siebenthal case over arbitrary fields.
    As an application, all semi-simple (local) Galois representations valued in general reductive groups admit crystalline lifts.

Some code for symbolic computation

  • Explicit presentation for G2, code

My boy (1yr)