About

I am an Assistant Professor at the University of Michigan. I am a member of the Number Theory group. I like representation theory, number theory, and algebraic geometry.

Before moving to Michigan, I was a CLE Moore Instructor and NSF Postdoctoral Fellow at MIT under Zhiwei Yun.

Before moving to MIT, I was an NSF Postdoctoral Fellow at Princeton under Christopher Skinner.

Before moving to Princeton, I was a graduate student at the Michigan under Kartik Prasanna.

Before graduate school, I was an undergraduate at Stanford. I spent a term at Budapest Semesters in Mathematics and a term at Oxford. I spent my summers as a counselor at PROMYS.

Before that, I spent my childhood in beautiful, sunny, cactus-y Tucson, Arizona.

Stripes! Oberwolfach 2016, 2019; Zoom teaching 2020.

My research is partially supported by NSF grant DMS-2101837, DMS-2401114, and a Sloan Research Fellowship. Thank you to the University of Michigan for this article on the latter!

Contact

Email:	charchan [at] umich [dot] edu
Office:	East Hall 4844
Mail:	Department of Mathematics 2074 East Hall 530 Church Street Ann Arbor, MI 48109-1043

Some activities

• Together with Thomas Lam and Geordie Williamson, we organized the special semester Modern perspectives in representation theory, held May 5, 2025 through June 13, 2025 at the Sydney Mathematical Research Institute. Thank you to SMRI for hosting the following interview by Masoud Kamgarpour!

  • Interview on perspectives on research in mathematics

• The deadline to apply for Arizona Winter School 2025: Representation theory of p-adic groups is November 21, 2024. You can find the following resources on the Arizona Winter School page:

  • Lecture notes
  • Lecture video recordings

  Thank you to my project assistant Masao Oi and my study group leader Calder Morton-Ferguson!

• The deadline to apply for Women+ and Mathematics 2024: Symmetry and Arithmetic is February 16, 2024. The intended audience is undergraduate students, graduate students, and researchers from a broad spectrum of institutions. Please see the website for course descriptions. My four lectures on "Deligne--Lusztig theory: examples and applications", intended to be accessible to advanced undergraduate mathematics majors, can be found here:

  • Lecture 1: Deligne--Lusztig varieties
  • Lecture 2: Character table
  • Lecture 3: Semisimple elements
  • Lecture 4: Character sheaves

  Thank you to Si Ying Lee for being my course assistant!

• The deadline to apply for Arizona Winter School 2021: Virtual School in Number Theory is December 7, 2020. The intended audience is undergraduates, but we welcome all interested participants. Accompanying lecture notes on my course on quadratic forms can be found here: Quadratic forms and the local-global principle. Thank you to my course assistants Elisa Bellah, Sheela Devadas, Aleksander Horawa, and Maryam Khaqan for their work crafting problem sets, holding discussion sessions, and correcting my errors!

Papers

(Briefly annotated list available here.)

(Published or arXiv versions may differ from the local versions.)

1. Green functions for positive-depth Deligne--Lusztig induction (joint with M. Oi)
   [arXiv:2506.04449]

2. The scalar product formula for parahoric Deligne--Lusztig induction
   [arXiv:2405.00671]

3. Generic character sheaves on parahoric subgroups (joint with R. Bezrukavnikov)
   [arXiv:2401.07189]

4. Characterization of supercuspidal representations and very regular elements (joint with M. Oi)
   [pdf, 75 pages] [arXiv:2301.09812]

5. Geometric L-packets of Howe-unramified toral supercuspidal representations (joint with M. Oi)
   [pdf, 55 pages] [arXiv:2105.06341]
   To appear in J. Eur. Math. Soc. (JEMS)

6. The Drinfeld stratification for GLn (joint with A. Ivanov)
   [pdf, 40 pages] [arXiv:2001.06600]
   Selecta Math. (N.S.) 27 (2021), no. 3, Paper No. 50, 54 pp

7. On loop Deligne--Lusztig varieties of Coxeter type for inner forms of GLn (joint with A. Ivanov)
   [pdf, 35 pages] [arXiv:1911.03412]
   Camb. J. Math. 11 (2023), no. 2, 441-505

8. Cohomological representations of parahoric subgroups (joint with A. Ivanov)
   [pdf, 24 pages] [arXiv:1903.06153] [journal]
   Represent. Theory, 25 (2021), 1-26

9. Affine Deligne--Lusztig varieties at infinite level (joint with A. Ivanov)
   [pdf, 67 pages] [arXiv:1811.11204] [journal]
   Math. Ann., 380 (2021), no. 3-4, 1801-1890

10. Period identities of CM forms on quaternion algebras
    [pdf, 48 pages] [arXiv:1807.09435] [journal]
    Forum Math. Sigma 8 (2020), Paper No. e25, 75 pages

11. The cohomology of semi-infinite Deligne-Lusztig varieties
    [pdf, 46 pages] [arXiv:1606.01795] [journal]
    J. Reine Angew. Math., 768 (2020), 93-147

12. Deligne-Lusztig constructions for division algebras and the local Langlands correspondence, II
    [pdf, 31 pages] [arXiv:1505.07185] [journal]
    Selecta Math., 24 (2018), no. 4, 3175--3216

13. Deligne-Lusztig constructions for division algebras and the local Langlands correspondence
    [pdf, 61 pages] [arXiv:1406.6122] [journal]
    Please note that the preprint includes a lengthy example which does not appear in the published version.
    Adv. Math., 294 (2016), 332--383

This webpage is largely based off of my friend Zev Chonoles's webpage. A huge thank you to him for allowing me to use his html and css code!