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.
Here is a photo of me in front of the statue at Oberwolfach in April 2016.
|Email:||charchan [at] mit [dot] edu|
|Office:||2-231B; (617) 253-1798|
Massachusetts Institute of Technology
Department of Mathematics
Simons Building (Building 2), Room 106
77 Massachusetts Avenue
(Published or arXiv versions may differ from the local versions.)
We define a stratification of Deligne--Lusztig 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 representation-theoretic behavior of the stratification.
For a reductive group G over a non-archimedean local field, one can mimic the construction from classical Deligne--Lusztig 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 Deligne--Lusztig 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 L-parameter 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).
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.
We construct an inverse limit of covers of affine Deligne--Lusztig varieties for GLn (and its inner forms) and prove that it is isomorphic to the semi-infinite Deligne--Lusztig 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 L-functions agree, (the norms of) these periods---which occur on different quaternion algebras---are closely related by Waldspurger's formula. We give a direct proof of an explicit identity between the torus periods themselves.
The cohomology of semi-infinite Deligne-Lusztig varieties
(pdf, 46 pages)
We prove a 1979 conjecture of Lusztig on the cohomology of semi-infinite Deligne--Lusztig 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.
We extend the results of arXiv:1406.6122 to arbitrary division algebras over an arbitrary non-Archimedean local field. We show that Lusztig's proposed p-adic analogue of Deligne-Lusztig varieties gives a geometric realization of the local Langlands and Jacquet-Langlands correspondences.
Selecta Math., 24 (2018), no. 4, 3175--3216
Deligne-Lusztig 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 Jacquet-Langlands correspondences.
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!