**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