Department of Mathematics
The University of Chicago
5734 S. University Ave
Chicago, IL, 60637, USA
E-mail:chi [at] math [dot] uchicago [dot] edu Office: TAAC (5607 S. Drexel) Room 30
I am a graduate student in Department of Mathematics at The University of Chicago.
My advisor is Professor Ngô Bảo Châu.
Broadly speaking, my research interest lies in the junction of Algebraic Geometry, Number Theory and Representation Theory.
More specifically, in current research I apply techniques in geometric representation theory to solve problems in p-adic harmonic analysis.
The geometry of some generalized affine Springer fibers
I study basic geometric properties of some group analogue of affine Springer fibers (as opposed to more classical Lie algebra affine Springer fibers).
Roughly speaking, these are certain algebraic varieties which encode orbital integrals of spherical Hecke functions on a p-adic reductive group. My emphasis is on the essential differences from the classical Lie algebra situation.
The main purpose is to formulate a conjecture that relates the number of irreducible components of such varieties
to certain weight multiplicities defined by the Langlands dual group. I prove the conjecture in the case of unramified conjugacy class. My main motivation for this work
is an ongoing/future project to establish an explicit endoscopic transfer for functions in the center of the Iwahori-Hecke algebra.
Erratum to "Dimension des fibres de Springer affines pour les groupes" (with Alexis Bouthier), preliminary version
We establish a dimension formula for the group version affine Springer fibers studied in the previous paper. From results in the previous paper we know
that the method for proving dimension formula in Lie algebra case does not generalize to our situation. Instead we took a new approach which combines
global methods ("Hitchin-Frenkel-Ngô fibration") and some specialization trick. The paper is densely written to fit its role as an erratum.
Math 151-153 Calculus I, II, III: Autumn 2014, Winter 2015, Spring 2015, Autumn 2017 (ongoing)
Math 195 Math Methods in Social Sciences (multi-variable calculus and linear programming): Spring 2016, Winter 2017, Spring 2017
Math 196 Linear Algebra: Autumn 2015, Autumn 2016
As Teaching Assistant:
Math 161-163 Honors Calculus (IBL style) I, II, III: Autumn 2013, Winter 2014, Spring 2014