Zhiwei Yun's Research Page

Research Interest--Representation Theory; Number Theory; Algebraic Geometry; the Langlands Program

Publications and Preprints

(with K.Jakob) A Deligne-Simpson problem for irregular G-connections over P1. arXiv:2301.10967. Submitted.

(with A.Ionov) Tilting sheaves for real groups and Koszul duality. arXiv:2301.05409. Submitted.

(with D.Nadler and P.Li) Functions on the commuting stack via Langlands duality. arXiv:2301.02618. Submitted.

(with R.Bezrukavnikov, P. Boixeda Alvarez, M. McBreen) Non-abelian Hodge moduli spaces and homogeneous affine Springer fibers. arXiv:2209.14695. To appear in Pure Appl. Math. Q. (Special volume for G.Lusztig)

(with T. Feng, W.Zhang) Higher theta series for unitary groups over function fields. arXiv:2110.07001. Submitted.

(with D.Nadler) Automorphic gluing functor in Betti Geometric Langlands. arXiv:2105.12318.

(with T. Feng, W.Zhang) Higher Siegel--Weil formula for unitary groups: the non-singular terms. arXiv:2103.11514. Submitted.

Rigidity method for automorphic forms over function fields. PDF, to appear in Proceedings of Arizona Winter School 2022.

Special cycles for Shtukas are closed. PDF, Pure Appl. Math. Q. 18 (2022), no. 5, 2203--2220. (Special volume for B.Gross)

Minimal reduction types and the Kazhdan-Lusztig map. arXiv link, Indag. Math. (N.S.) 32 (2021), no. 6, 1240--1274. (Special volume for T.A.Springer)

(with K.Jakob) Euphotic representations and rigid automorphic data. PDF, Selecta Math. (N.S.) 28 (2022), no. 4.

(with G.Lusztig) From conjugacy classes in the Weyl group to representations. arXiv:1912.01754. To appear in Proceedings of the Southeastern Lie Theory Workshop 2019.

Higher signs for Coxeter groups. PDF, Peking Math. J. 4 (2021), no. 2, 285--303.

(with G.Lusztig) Z/m-graded Lie algebras and perverse sheaves, IV. PDF, Represent. Theory 24 (2020), 360--396.

(with G.Lusztig) Endoscopy for Hecke categories, character sheaves and representations. PDF, Forum of Mathematics, Pi, 8 (2020), E12. Corrigendum, Forum Math. Pi 9 (2021), Paper No. e11, 3 pp.

(with J.Yang) Semilinear automorphisms of classical groups and quivers. PDF, Sci. China Math. 62 (2019), no. 11, 2355--2370.

(with W.Zhang) Shtukas and the Taylor expansion of L-functions (II). PDF, Ann. of Math. (2) 189 (2019), no. 2, 393--526.

(with D.Nadler) Spectral action in Betti Geometric Langlands. PDF, Israel J. Math. 232 (2019), no. 1, 299--349.

(with D.Nadler) Geometric Langlands correspondence for SL(2), PGL(2) over the pair of pants. PDF, Compos. Math. 155(2019), no. 2, 324--371.

Hitchin type moduli stacks in automorphic representation theory. PDF, Proceedings of ICM 2018.

(with A.Oblomkov) The cohomology ring of certain compactified Jacobians. arXiv:1710.05391.

(with G.Lusztig) Z/m-graded Lie algebras and perverse sheaves, III: graded double affine Hecke algebra. PDF, Representation Theory 22(2018), 87--118.

(with G.Lusztig) Z/m-graded Lie algebras and perverse sheaves, II. PDF, Representation Theory 21(2017), 322--353.

(with G.Lusztig) Z/m-graded Lie algebras and perverse sheaves, I. PDF, Representation Theory 21(2017), 277--321.

Lectures on Springer theories and orbital integrals. PDF, in The IAS/Park City Mathematical Series 2015.

(with W.Zhang) Shtukas and the Taylor expansion of L-functions. PDF, Annals of Math. 186 (2017), no. 3, 767--911.

(with A.Oblomkov) Geometric representations of graded and rational Cherednik algebras. PDF, Advances in Math. 292 (2016), 601-706.

Epipelagic representations and rigid local systems, PDF, Selecta Math. (N.S.), 22 (2016), no. 3, 1195-1243.

Galois representations attached to moments of Kloosterman sums and conjectures of Evans. With an appendix by C.Vincent. PDF, Compositio Math. 151 (2015), no. 1, 68-120.

Rigidity in automorphic representations and local systems. PDF, Current Developments in Mathematics 2013, International Press, 2014.

Rigidity in the Langlands correspondence and applications (survey article), PDF, Proceedings of ICCM (International Congress of Chinese Mathematicians) 2013

The spherical part of local and global Springer actions. PDF, Math Annalen, 359 (2014), no. 3-4, 557-594.

(with D.Maulik) Macdonald formula for curves with planar singularities, PDF, J.Reine Angew. Math., 694 (2014), 27-48.

Orbital integrals and Dedekind zeta functions, PDF, The Legacy of Srinivasa Ramanujan, RMS-Lecture Notes Series No. 20, 2013, 399--420.

Motives with exceptional Galois groups and the inverse Galois problem, PDF, Invent. Math., 196 (2014), Issue 2, 267-337.

(with G.Lusztig) A (-q)-analogue of weight multiplicities, PDF, J. Ramanujan Math. Soc. 28A (Special Issue-2013) 311--340.

(with J.Heinloth and B.C. Ngô) Kloosterman sheaves for reductive groups, PDF, Annals of Math., 177 (2013), no.1 , 241--310.

(with R.Bezrukavnikov) On Koszul duality for Kac-Moody groups (with appendices by Zhiwei Yun), PDF, Represent. Theory 17 (2013), 1--98.

Langlands duality and global Springer theory, PDF, Compositio. Math. 148 (2012), 835--867. (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")

The fundamental lemma of Jacquet-Rallis, PDF, Duke Math. J. 156 (2011), No.2, 167-228. With an appendix by J.Gordon: Transfer to characteristic zero.

(with X.Zhu) Integral homology of loop groups via Langlands dual groups, PDF, Represent. Theory 15 (2011), 347-369.

Weights of mixed tilting sheaves and geometric Ringel duality, PDF, Selecta Math. (N.S.) 14 (2009), no. 2, 299-320.

Goresky-MacPherson calculus for the affine flag varieties, PDF, Canad. J. Math. 62 (2010), no. 2, 473-480.

Ph.D. Thesis

Towards a global Springer theory III: Endoscopy and Langlands duality, arXiv:0904.3372

Towards a global Springer theory II: the double affine action, arXiv:0904.3371

Towards a global Springer theory I: the affine Weyl group action, arXiv:0810.2146

Other writings

Math Review for the paper "A categorical approach to the stable center conjecture." by Bezrukavnikov, Kazhdan and Varshavsky, PDF

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), PDF

Math Review for the paper "Geometrization of trace formulas." by Frenkel and Ngô, PDF

Notes on D-modules (for Talbot 2008), PDF

Notes on equivariant derived categories, PDF

Conferences I have been to or will go to

ICM 2018, Brazil, 8/2018

Duke Math Journal conference, 4/2017

Functoriality and the trace formula, AIM, 12/4-12/8/2017

AMS meeting special session on Rational Cherednik algebras and Categorification UC Riverside, 11/4-11/5/2017

p-adic Hodge Theory and Automorphic Forms, BICMR, Beijing, 6/5-6/9/2017

(Co-organizer)Oberwolfach Arbeitsgemeinschaft: Higher Gross-Zagier formulas, Germany, 4/2-4/8/2017

Joint Mathematics Meetings, Atlanta, 1/4-1/7/2017

Global Langlands correspondence AIM, 12/5-12/9/2016

The Seventh International Congress of Chinese Mathematicians (ICCM), Beijing, 8/6-8/11/2016

The Langlands correspondence in arithmetic and geometry, Korea Institute for Advanced Study (Seoul), 8/1-8/5/2016

Algebraic Lie Theory and Symplectic Geometry, Sanya, 3/21-3/25/2016

Meeting of AMS Western Section, Fullerton, 10/24-10/25/2015

Workshop on Springer Theory and Related Topics, UMass Amherst, 10/9-10/11/2015

AMS Summer Institute in Algebraic Geometry, Salt Lake City, 7/13-7/31/2015

(Co-organizer)PCMI Summer Session, Geometry of moduli spaces and representation theory, Park City, 6/28-7/18/2015

(Co-organizer)Sanya Math Forum: Algebraic Groups and their representations, Sanya, 12/15-12/19/2014

MSRI Program Geometric Representation Theory, Berkeley, 8/18-12/19/2014

Representation Theory, Integrable Systems and Quantum Fields, Northwestern University, 5/19-5/23/2014

(Co-organizer)Langlands Correspondence and Constructive Galois Theory, Oberwolfach, 2/2-2/8/2014

(Co-organizer)Sanya Math Forum: Langlands program, Sanya, 12/20-12/22/2013

Current Development in Mathematics , Harvard-MIT, 11/22-11/23/2013

The Sixth International Congress of Chinese Mathematicians (ICCM), Taipei, 7/14-7/19/2013

Sino-French Conference on Arithmetic Geometry , Chern Institute of Mathematics, Tianjin, 6/24-6/28/2013

Young Mathematicians Forum, Peking University, 6/18-20/2013

WAGS (Western Algebraic Geometry Symposium), Harvey Mudd College, 2/16-2/17/2013

Springer Memorial Conference, Hong Kong, 1/4-1/9/2013

The Legacy of Srinivasa Ramanujan-An International Conference, University of Delhi, India, 12/17-12/22/2012

(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 (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

AMS 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