Zhiwei Yun 恽之玮
Fall 2010--Spring 2012: C.L.E. Moore instructor at MIT
Fall 2009--Spring 2010: Member at the Institute for Advanced Study (IAS)
June 2009: Ph.D. at Princeton University. My advisor was Robert MacPherson
Email: First initial last name at math dot mit dot edu
Office: 77 Massachusetts Av, Room 2-173, Cambridge, MA 02139
Research Area--Geometric Representation Theory
Springer representations and Hitchin fibrations
Langlands correspondence for function fields
Rigid local systems, motives with exceptional Galois groups
Trace formulae, orbital integrals and Fundamental Lemmas
Perverse sheaves, equivariant geometry and Koszul duality
Broader interest: Algebraic Geometry, Representation Theory, Number Theory
[Curriculum Vitae] [Publications] [Teaching]
Publications and Preprints
Warning: all links to the arXiv are not the final version.
Algebraic Geometry
(with Davesh Maulik) Macdonald formula for curves with planar singularities, to appear in J.Reine Angew. Math., posted as arXiv:1107.2175
Rigid local systems and construction of motives
Motives with exceptional Galois groups and the inverse Galois problem, submitted, posted as arXiv:1112.2434
(with Jochen Heinloth and Bao-Chau Ngô) Kloosterman sheaves for reductive groups, to appear in Annals of Math., posted as arXiv:1005.2765
Global Springer Theory and Hitchin fibrations
The spherical part of local and global Springer actions, submitted, posted as arXiv:1106.2259
Langlands duality and global Springer theory, PDF, to appear in Compositio. Math. (This is the revised version of the second half of "Towards a global Springer theory III")
Global Springer Theory, PDF Advances in Math. 228 (2011), 266-328. (This is the combined and revised version of "Towards a global Springer theory I, II")
Fundamental lemmas in relative trace formulae
The fundamental lemma of Jacquet-Rallis, Duke Math. J. 156 (2011), No.2, 167-228. Posted as arXiv:0901.0900 (With an appendix by Julia Gordon: Transfer to characteristic zero. arXiv:1005.0610)
Affine Grassmannian and affine flag varieties
(with G.Lusztig) A (-q)-analogue of weight multiplicities, posted as arXiv:1203.0521
(with R.Bezrukavnikov) On Koszul duality for Kac-Moody groups (with appendices by Zhiwei Yun), to appear in Represent. Theory, posted as arXiv:1101.1253
(with Xinwen Zhu) Integral homology of loop groups via Langlands dual groups, Represent. Theory 15 (2011), 347-369, posted as arXiv:0909.5487
Weights of mixed tilting sheaves and geometric Ringel duality. Selecta Math. (N.S.) 14 (2009), no. 2, 299-320. Posted as arXiv:0805.1495
Goresky-MacPherson calculus for the affine flag varieties. Canad. J. Math. 62 (2010), no. 2, 473-480. A more detailed version is available at arXiv:0712.4395
Ph.D. Thesis
Towards a global Springer theory III: Endoscopy and Langlands duality, posted as arXiv:0904.3372
Towards a global Springer theory II: the double affine action, posted as arXiv:0904.3371
Towards a global Springer theory I: the affine Weyl group action, posted as arXiv:0810.2146
Papers in preparation
Generalized Kloosterman sheaves and Lusztig's correspondence
Arithmetic Fundamental Lemma for function fields
Endoscopic transfer of Green functions via global Springer theory
Other writings
Math Review for the paper "Formule des traces et fonctorialité: le début d'un programme." by Frenkel, Langlands and Ngô (as if I understood it)
Notes on D-modules (for Talbot 2008), PDF
Notes on equivariant derived categories, PDF
Teaching
18.03 Differential Equations Recitations, Fall 2011, MIT
18.04 Complex Analysis Recitations, Spring 2011, MIT
18.01 Calculus Recitations, Fall 2010, MIT
MAT 103 Calculus, Fall 2007, Princeton University
Conferences I have been to or will go to
(Co-organizer)Workshop on Algebraic Geometry, Number Theory and Representation Theory, Beijing International Center for Math Research, 7/30-8/3/2012
Fibration de Hitchin et Integrales orbitales, Universite de Caen, France, 5/21-5/23/2012
Automorphic forms and related geometry--Assessing the legacy of I.I.Piatetski-Shapiro, Yale University, New Haven, 4/23-4/27/2012
(Co-organizer)Geometric Representation Theory, AMS Central Sectional Meeting, Lawrence, Kansas, 3/30-4/1/2012
Enveloping Algebras and Geometric Representation Theory, Oberwolfach, Germany, 3/4-3/10/2012
FRG Conference: Periods of automorphic forms and applications to L-functions, Columbia University, New York, 9/16-9/18/2011
(Co-organizer) Workshop on arithmetic and algebraic geometry, Beijing International Center for Math Research, 8/2-8/4/2011
(Co-organizer) Summer School on arithmetic geometry, Beijing International Center for Math Research, 7/11-7/29/2011
Workshop on the arithmetic geometry of Shimura varieties and Rapoport-Zink spaces, Kyoto University, Japan, 7/4-7/8/2011
Physics-Mathematics Summer Institute (PhyMSI), the CIRM session on DAHA and Langlands program, Luminy, France, 6/20-7/1/2011
AGNES 2011 (Algebraic Geometry Northeastern Series), MIT, 4/1--4/3/2011
CMS Winter Meeting, Vancouver, Canada, 12/4-12/6/2010
The second Pan Asian Number Theory Conference (PANT), RIMS, Kyoto, Japan 9/13-9/17/2010
Workshop on Arithmetic Geometry and Related Topics, TIMS, Taipei, Taiwan, 7/12-7/16/2010
AIM Workshop: Relative trace formula and periods of automorphic forms, Palo Alto, CA, 8/24-8/28/2009
Workshop on Topological Field Theories, Northwestern University, 5/18-5/22/2009
Talbot Workshop: Fukaya categories, 3/23-3/27/2009, Nags Head, NC
Gauge Theory and Langlands Duality, Kavli Institute for Theoretical Physics, UC Santa Barbara, 7/21-8/8/2008
Talbot Workshop: Affine Lie Algebras and Chiral Structures, Plymouth, MA, 3/30-4/5/2008
Conference on Algebro-Geometric Derived Categories and Applications, IAS, 3/10-3/14/2008
Workshop on Gauge Theory and Representation Theory, IAS, 11/26-11/30/2007
Trends in Non-commutative Geometry, Northwestern University, 5/18-5/25/2007
Workshop on Homological Mirror Symmetry and Applications I & II, IAS, 1/22-1/26/2007 & 3/26-3/30/2007
Clay Summer School on Arithmetic Geometry, Göttingen University, Germany, 7/17-8/11/2006
Summer Institute in Algebraic Geometry, University of Washington, 8/1-8/12/2005
Summer school on Shimura varieties, Center of Mathematical Sciences, Zhejiang University, China, 7/3-7/15/2005
Arizona Winter School: Arithmetic Fundamental Groups, University of New Mexico, 3/12-3/16/2005
Generals exam---A list of questions I was asked