About Me
I am a graduate student in the math department at the University of Michigan in Ann Arbor. My advisor is Kartik Prasanna.
Here is a photo of me in front of the statue at Oberwolfach in April 2016.
I am interested in representation theory, number theory, and algebraic geometry.
In the 20172018 academic year, I will be supported by a Rackham Predoctoral Fellowship.
Past Updates
I am organizing a learning seminar on Borcherds products with Brandon Carter in Winter 2016.
I will be at Princeton University during Spring 2015.
Contact Info
Email:  charchan [at] umich [dot] edu 
Mail: 
Department of Mathematics University of Michigan, Ann Arbor 2074 East Hall 530 Church Street Ann Arbor, MI 48109 
Office:  East Hall 5080 
Publications/Preprints
(Published or arXiv versions may differ from the local versions.)

Period identities of CM forms on quaternion algebras
(pdf, 48 pages)For any two Hecke characters of a fixed quadratic extension, one can consider the two torus periods coming from integrating one character against the automorphic induction of the other. Because the corresponding Lfunctions agree, (the norms of) these periodswhich occur on different quaternion algebrasare closely related by Waldspurger's formula. We give a direct proof of an explicit identity between the torus periods themselves.
Submitted.

Affine DeligneLusztig varieties at infinite level (joint with A. Ivanov)
(pdf, 44 pages)We construct an inverse limit of covers of affine DeligneLusztig varieties for GLn (and its inner forms), and prove that it is isomorphic to the semiinfinite DeligneLusztig variety. We then calculate its cohomology and make a comparison with automorphic induction.
Preliminary version. November 2017.

The cohomology of semiinfinite DeligneLusztig varieties
(pdf, 42 pages)We prove a 1979 conjecture of Lusztig on the cohomology of semiinfinite DeligneLusztig varieties attached to division algebras over local fields. We also prove the two conjectures of Boyarchenko on these varieties.
Submitted.

DeligneLusztig constructions for division algebras and the local Langlands correspondence, II
(pdf, 31 pages) (published, 42 pages)We extend the results of arXiv:1406.6122 to arbitrary division algebras over an arbitrary nonArchimedean local field. We show that Lusztig's proposed padic analogue of DeligneLusztig varieties gives a geometric realization of the local Langlands and JacquetLanglands correspondences.
To appear in Selecta Math.

DeligneLusztig constructions for division algebras and the local Langlands correspondence
(pdf, 61 pages)We compute a cohomological correspondence between representations proposed by Lusztig in 1979 and show that for quaternion algebras over a local field of positive characteristic, this correspondence agrees with that given by the local Langlands and JacquetLanglands correspondences.
Adv. Math., 294 (2016), 332383.
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!