About Me
I am a CLE Moore Instructor and NSF Postdoctoral Fellow at MIT. I am interested in representation theory, number theory, and algebraic geometry.
In 2018/2019, I was an NSF Postdoctoral Fellow at Princeton University.
Before that, I was a graduate student at the University of Michigan under the advisement of Kartik Prasanna.
Here is a photo of me in front of the statue at Oberwolfach in April 2016.
Contact Info
Email:  charchan [at] mit [dot] edu 
Office:  2231B; (617) 2531798 
Mail: 
Massachusetts Institute of Technology Department of Mathematics Headquarters Office Simons Building (Building 2), Room 106 77 Massachusetts Avenue 
Publications/Preprints
(Published or arXiv versions may differ from the local versions.)

The Drinfeld stratification for GLn (joint with A. Ivanov)
(pdf, 40 pages)We define a stratification of DeligneLusztig varieties and their parahoric analogues which we call the Drinfeld stratification. In the setting of inner forms of GLn, we study the cohomology of these strata and give a complete description of the unique closed stratum. We state precise conjectures on the representationtheoretic behavior of the stratification.

On loop DeligneLusztig varieties of Coxeter type for inner forms of GLn (joint with A. Ivanov)
(pdf, 35 pages)For a reductive group G over a nonarchimedean local field, one can mimic the construction from classical DeligneLusztig theory by using the loop space functor. We study this construction in the special case that G is an inner form of GLn and the loop DeligneLusztig variety is Coxeter type. We prove an irreducibility result by calculating the formal degree, and use this to prove that the cohomology realizes almost all supercuspidals representations whose Lparameter factors through an elliptic unramified maximal torus.
The formal degree calculation relies on a careful study of the individual cohomology groups H^i and the action of Frobenius, which will appear in a forthcoming paper "The Drinfeld stratification for loop GLn" (again joint with A. Ivanov).

Cohomological representations of parahoric subgroups (joint with A. Ivanov)
(pdf, 24 pages)We generalize a cohomological construction of representations due to Lusztig from the hyperspecial case to arbitrary parahoric subgroups of a reductive group over a local field which splits over an unramified extension. We compute the character of these representations on certain very regular elements.

Affine DeligneLusztig varieties at infinite level (joint with A. Ivanov)
(pdf, 67 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 calculate its cohomology and make a comparison with automorphic induction.

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.

The cohomology of semiinfinite DeligneLusztig varieties
(pdf, 46 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.
To appear in J. Reine Angew. Math.

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.
Selecta Math., 24 (2018), no. 4, 31753216

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!