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.

In preparation


  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. 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.
  5. Lyndon-Demushkin method and crystalline lifts of G2-valued Galois representations (arXiv:2011.08773, submitted)
    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.
  6. 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.


  1. Crystalline lifts and a variant of the Steinberg-Winter theorem (to appear in Doc. Math. 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.

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