Here is a photo of me in front of the statue at Oberwolfach in April 2016.
I am interested in representation theory, algebraic geometry, and number theory.
I will be at Princeton University during Spring 2015.
|Email:||charchan [at] umich [dot] edu|
Department of Mathematics
University of Michigan, Ann Arbor
2074 East Hall
530 Church Street
Ann Arbor, MI 48109
|Office:||East Hall 4836|
The cohomology of semi-infinite Deligne-Lusztig varieties
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.
Deligne-Lusztig constructions for division algebras and the local Langlands correspondence, II
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.
Deligne-Lusztig constructions for division algebras and the local Langlands correspondence
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!