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 2017-2018 academic year, I will be supported by a Rackham Predoctoral Fellowship.
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 5080|
(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 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.
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 then calculate its cohomology and make a comparison with automorphic induction.
Preliminary version. November 2017.
The cohomology of semi-infinite Deligne-Lusztig varieties
(pdf, 42 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.
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.
To appear in Selecta Math.
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!