Zhiwei
Yun 惲之瑋Zhiwei
Yun 惲之瑋
Fall 2009--Spring 2010: Member at the Institute for Advanced Study (IAS)
Fall 2010--Spring 2012: C.L.E. Moore instructor at MIT
Email: my first initial followed by last name at math dot ias dot edu
Office: Fuld Hall 402, Einstein Drive, Princeton, NJ 08540
Research Interest--Geometric Representation Theory
Generalizations of Springer representations; Geometry of Hitchin fibrations
Local and global Langlands correspondences for function fields
Orbital integral identities
Perverse sheaves (and their weights) on algerbaic varieties; Equivariant cohomology
Publications and Preprints
(with Xinwen Zhu) Integral homology of loop groups via Langlands dual groups, posted as arXiv:0909.5487
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
The fundamental lemma of Jacquet-Rallis in positive characteristics (Revised: Group Version of FL added), posted as arXiv:0901.0900
(joint with R.Bezrukavnikov) On the Koszul duality for affine Kac-Moody groups (Draft), PDF
Towards a global Springer Theory I: the affine Weyl group action, posted as arXiv:0810.2146
Weights of mixed tilting sheaves and geometric Ringel duality. To appear in Selecta Mathematica, Vol. 14, No. 2(2009).Available at arXiv:0805.1495
Goresky-MacPherson calculus for the affine flag varieties. To appear in Canad. J. Math. A more detailed version is available at arXiv:0712.4395
Papers in preparation
Subregular affine Springer fibers and subregular Hitchin fibers
Notes
Notes on D-modules (for Talbot 2008), PDF
Notes on equivariant derived categories, PDF
Seminar talks I gave or will be giving
TBD
---Princeton University, Geometry, Representation theory and Moduli Seminar, 11/16/2009
TBD
---SUNY at Stony Brook, Algebra, Geometry and Physics Seminar, 11/11/2009
Koszul duality for sheaves
---University of Maryland, 11/2/2009
Koszul duality for sheaves
---University of Toronto, Geometric Representation Theory Seminar, 10/20/2009
Homology of loop groups via Langlands dual groups
---IAS, Postdoc member talks, 10/2/2009
Global Springer representations and Langlands duality
---IAS, Seminar on Shimura varieties and trace formula, 11/14/2008
Global analogue of Springer representations
---MIT, Lie groups seminar, 11/12/2008
Global analogue of Springer representations
---Univeristy of Chicago, Representation Theory Seminar, 11/05/2008
Global analogue of Springer representations
---Northwestern University, Geometry/Physics Seminar, 11/04/2008
Teaching
MAT 103 Calculus, Fall 2007, Princeton University
Conferences I have been to or will go to
The second Pan Asian Number Theory Conference (PANT), Kyoto, Japan 9/13-9/17/2010
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