Stacky Lie
groupoids and Lie n-groupoids Chenchang Zhu, submitted.
Work in progress
- Lie's II theorem for Lie algebroids (via stacky Lie groupoids).
- Morita equivalence of Poisson manifolds via stacks, with Henrique Bursztyn.
- 2-groupoids and 2-gerbes, with Bailing Wang.
Honors
- Gold Medal (Full score), in IMO: International Mathematical Olympiad, 1995 (Top 3% from 73 countries).
- Sonny Fellowship for Freshmen, 1996.
- Wu Si Award, the highest annual award at Peking University, 1997.
- Honorable Mention, in MCM: The Mathematical Contest in Modeling, 1998.
- UC Berkeley Regents Fellowship, Spring 2002.
- Liftoff Fellow of Clay Mathematics Institute, June 2004.
- Departmental Postdoctoral position in ETH, 2004-2005
Dissertation
Title: Integrating
Lie algebroids via stacks and their applications in Jacobi manifolds
Unlike a finite dimensional Lie algebra, a Lie algebroid does not
always come from a Lie groupoid. Non-integrability already shows up in
the case of infinite dimensional Lie algebras. I found that a Lie
algebroid can nevertheless always be integrated into an étale
stack with a groupoid structure, which I call a Weinstein groupoid.
The converse is true too; hence the Lie algebroid version of the 1-1
correspondence between Lie algebras and Lie groups is fully
established. Applying the above to Jacobi manifolds, I prove that the
integrating objects of Jacobi manifolds are contact groupoids. I also
have determined the integrability conditions.
Dissertation Committee: Alan Weinstein (Chair), Allen Knutson, Hitoshi
Murayama (outside member)
Date of graduation: 22nd of May 2004, University California at Berkeley,
U.S.A.
Teaching Experience
- ETH, Zürich
- Generalized complex geometry (undergraduate seminar), Spring 2006
-
- MMP(Undergraduate course) Mathematical method in physics, Fall
2005 and Spring 2006: Teaching Assistant and organizer of the exercise section
- Problem solving seminar, Fall 2004: Teaching assistant
- U.C. BERKELEY, Berkeley, CA
- Math53 (Undergraduate course) Multivariable Calculus, Fall 2003: Graduate
Student Instructor
- Math241 (Graduate course) Complex Manifolds, Spring 2003: Graduate Student
Instructor
- Math202B (Graduate course) Real Analysis, Spring 2002: Graduate Student
Instructor
- Math1B (Undergraduate course) Calculus II, Spring 2000: Graduate Student
Instructor
Activities
- Organization of Graduate
Colloquium in Zurich from October 2005 to June 2006 .
Talks
- Stacky Lie groupoids and Lie 2-groupoids, Geometry
seminar, EPFL, Switzerland, December 2006
- Intégration des algébroïdes de Lie par l'intermédiaire des champs , Algèbre et
Géométries, Institut Fourier, France, December 2006
- Symplectic stacky groupoids for poisson manifolds, Aspects géométriques et algébriques
des structures (ou algèbres) de Poisson, Université de Haute Alsace
Faculté des Sciences et Technique
Laboratoire de Mathématiques, Informatique et Applications, France, November 2006
- Gerbe de gamma et son cocycle, Week-end de rentrée de
l'Institut Fourier, France, September 2006
- A gerbe of the elliptic gamma function, Poisson 2006,
Tokyo, June 2006
- A gerbe of the elliptic gamma function, Symplectic geometry
seminar, University of California at Berkeley, March 2006
- A gerbe of the elliptic gamma function, Groupe de travail
``Systemes non holonomes'', Institut de Mathematiques
de Toulouse, France, March 2006
- Symplectic and contact groupoids, geometry seminar, Chinese Academy, Wuhan, China, September 2005
- Principal bundles of stacky groupoids and application in Poisson geometry,
GAP-3 (The Séminaire Itinérant Geometry and Physics), Dipartimento di Matematica e Informatica in Perugia, Italy, July 2005
- Prequantization and Reduction, Summer School and Conference on Poisson Geometry, Trieste, Italy, July 2005
- Integrating Lie algebroid via stacks, symplectic geometry seminar, Toronto University, February, 2005
- Weinstein groupoid is a 2-groupoid, symplectic geometry seminar, University
of California at Berkeley, February 14, 2005
- Integrating Poisson manifolds via stacks, geometry seminar, Arizona University,
Tucson, February 10, 2005
- Integrating Poisson manifolds via stacks, mini-conference Journées
de Physique Mathématique, Université Lyon 1, January 28, 2005
- Weinstein groupoid is a 2-groupoid, geometry seminar, Geneva University,
Switzerland, January 7, 2005
- Integrating Poisson manifolds via stacks, Symplectic geometry seminar, ETH
Zürich, Switzerland, November 22, 2004
- Why stacks are useful in Lie theory, Graduate Colloquium, ETH Zürich,
October 25, 2004
- Poisson sigma model and differentiable stacks, Mathematical and Physical Aspects of String Theory, Ascona, Switzerland, July 18-23, 2004
- Integrating Lie algebroids via stacks, Groupoids and Stacks in Physics and Geometry, CIRM-Luminy, France, June 28 - July 2, 2004
- Interating Poisson manifolds via stacks, Poisson 2004, University
of Luxembourg, in the poster section, June 7-11, 2004
- Integrating Lie algebroids via stacks, department seminar, Northwestern University, May 2004
- Integrating Lie algebroids via stacks II, symplectic geometry seminar, University of California at Berkeley, May 2004
- Integrating Lie algebroids via stacks I, North California symplectic
geometry seminar, University of California at Berkeley, May 2004
- Prequantization of coadjoint orbits and contact (groupoid) reductions,geometric quantization seminar, University of California at Berkeley, October 2003
- Contact reduction via groupoids, symplectic geometry seminar, University
of California at Berkeley, May 2003
- Jacobi manifolds, contact groupoids and prequantizations, symplectic
geometry seminar, University of California at Berkeley, November 2002
- Jacobi manifolds and their contact groupoids, research seminar, Women's
program, IAS, May 2002
Conferences Invited/Participated
- Lyon, France, Journées Clermont-Ferrand--Lyon, December 2006
- Mulhouse, France, Aspects géométriques et algébriques
des structures (ou algèbres) de Poisson, November 2006
- Tokyo, Japan, Poisson 2006, June 2006
- Diablerets, Switzerland, Winter school of mathematical physics, March 2006
- MSRI, Berkeley, U.S., Generalized McKay
correspondence, March 2006
- Perugia, Italy, The Séminaire Itinérant Geometry and Physics III, July 2005
- Trieste, Italy, Summer School and Conference on Poisson Geometry, July 2005
- Lyon, France, Journés de Physique Mathématique,
January 28, 2005
- Ascona, Switzerland, Mathematical and Physical
Aspects of String Theory, July 18-23, 2004
- CIRM-Luminy, France, Groupoids and Stacks in Physics and Geometry,June
28- July 2, 2004
- University of Luxembourg, Luxembourg city, Poisson 2004---4th Conference
on Poisson Geometry, June 7-11, 2004
- ESI, Vienna , AlanFest---Moment Maps and Poisson Geometry, August 4-8,
2003
- Lisieux, Normandy,The Séminaire Itinérant Geometry and Physics I---Groupoids and Quantization Workshop, July
13-20, 2003
- ULB, Brussels, PQR 2003---Poisson Geometry, Deformation Quantization
and Group Representation, June 13-22, 2003
- IPAM, UCLA, Symplectic Geometry and Physics Workshop, March 24-28,
2003
- Beijing, ICM 2002---International Conference of Mathematicians, August
20-28, 2002
- IAS, Princeton, Program for Women in Mathematics---Symplectic Geometry,
May 2002
- IAS, Park City, String Theory and Stacks, July 2002
- IAS, Princeton, Program for Women in Mathematics---Mathematical Physics,
May 2001
Biographical
Born: May 21st, 1977 in Wuhan, HuBei, China
Citizenship: P. R. China
Language
- English (very good, 5 years teaching and research experience in the States)
- French (pas mal, pas de problèmes dans la vie)
- Chinese (native)
References
- Prof. Alan Weinstein (advisor), Mathematics Department, U.C. Berkeley, Berkeley, CA 94720, U.S.A.
Tel: +1 (510) 642-3518, Fax: +1 (510) 642-8204, alanw@math.berkeley.edu
- Prof. Giovanni Felder, Department Mathematik, ETH, Rämistrasse 101 8092 Zürich, Switzerland
Tel: +41 (44) 632-3409 Fax: +41 (44) 632-1085, felder@math.ethz.ch
- Prof. Allen Knutson, Mathematics Department, U.C. San Diego, 9500 Gilman Drive Dept 0112 La Jolla, CA 92093 U.S.A.,
Tel: +1 (858) 534-3590, Fax: +1 (858) 534-5273, allenk@math.berkeley.edu
- Prof. Nicolai Reshetikhin, Mathematics Department, U.C. Berkeley, Berkeley, CA 94720, U.S.A.
Tel: +1 (510) 643-6234, Fax: +1 (510) 642-8204, reshetik@math.berkeley.edu
- Prof. Marius Crainic, Mathematical institute, Utrecht University, P.O Box 80.010, 3508
TA Utrecht, The Netherlands.
Tel: +31 30 2531429, Fax: +31 30 2518394, crainic@math.uu.nl