I am an NSF Postdoctoral Fellow at Princeton University. I am interested in representation theory, number theory, and algebraic geometry.
Beginning Fall 2019, I will move to MIT as a CLE Moore Instructor and NSF Postdoctoral Fellow.
Here is a photo of me in front of the statue at Oberwolfach in April 2016.
|Email:||charchan [at] princeton [dot] edu|
|Office:||Fine Hall 310|
Fine Hall, Washington Road
Princeton, NJ 08544-1000
(Published or arXiv versions may differ from the local versions.)
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, 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.
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!