Homepage

Gufang Zhao
Postdoc

Institute of Science and Technology Austria
Am Campus, 1
Klosterneuburg 3400
Österreich

E-mail (don't copy-paste): Vorname.Familienname@ist.ac.at



Research Interest:

My research lies at the interface between algebraic geometry and representation theory. More specifically, I've been working on projects concerning derived category of coherent sheaves, oriented cohomology theories of algebraic varieties, and their applications in representation theory. I am also fond of varieties of local systems and instantons, quantum integrable systems, and related aspects in mathematical physics.

Erdos Number = 4

Research Statement.

CV.

Teaching Statement.

Here is a video of me talking about my joint work with Yaping Yang, recorded in the Mathematical Physics Seminar in the Perimeter Institute, Waterloo, Mar. 2016.

Yaping's talk on this project, recorded at the Hausdorff Research Institute for Mathematics in Bonn, Oct. 2017.


My papers and preprints

Talks I have given 

Teaching

External links

Personal


My Papers and Preprints

Peer-Reviewed Journal Articles

1. (with Y. Yang) The cohomological Hall algebra of a preprojective algebra. 44 pages, to appear in Proc. Lond. Math. Soc.. arXiv: 1407.7994.
An earlier ArXiv version of this paper was entitled "Formal cohomological Hall algebra of a quiver".

2. (with Y. Yang) Cohomological Hall algebras and affine quantum groups. 22 pages, to appear in Selecta Math.. arXiv: 1604.01865.

3. (with M. Levine and Y. Yang) Algebraic elliptic cohomology theory and flops 1, with an appendix by Joel Riou. 29 pages, to appear in Math. Ann..  arXiv:1311.2159.
See here for an unpublished earlier version (with more background introductory materials for my own reference).

4. (with C. Zhong) Geometric representations of the formal affine Hecke algebrasAdv. Math. 317 (2017), 50--90arXiv: 1406.1283.

5. (with A. Suciu and Y. Yang) Homological finiteness of abelian covers. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XIV (2015), 101--153. ArXiv:1204.4873.

6. (with A. Suciu and Y. Yang) Intersections of translated algebraic subtoriJ. Pure Appl. Algebra 217 (2013), no. 3, 481--494. 

Submitted
7. (with V. Nandakumar) Categorification via blocks of modular representations of sl_n. 21 pages, (2016). arxiv: 1612.06941.

8. (with Y. Yang) On two cohomological Hall algebras. 26 pages, (2016). arXiv: 1604.01477
revised version is available hereSignificant expositional changes. Revised on Jul. 28, 2017.

9. (with C. Zhong) Elliptic affine Hecke algebras and their representations. 40 pages, (2015). arXiv: 1507.01245.
revised version is available here. It contains a duality conjecture. Revised on Aug. 2, 2017.

10. (with C. Su and C. Zhong) On the K-theory stable bases of the Springer resolution. 43 pages, (2017). arxiv: 1708.08013

Preprints

11. (with Y. Yang) Quiver varieties and elliptic quantum groups, 43 pages, (2017). arxiv: 1708.01418

12. (with M. Levine and Y. Yang) Algebraic elliptic cohomology theory and flops 2: $SL$-cobordism. 18 pages, (2016). arxiv: 1610.00396

13. Stability conditions for noncommutative symplectic resolutions. 37 pages, (2014). arXiv: 1405.1898. 
 
14. (with J. Weyman) Noncommutative desingularization of orbit closures for some representations of $GL_n$. 44 pages, (2012). arXiv: 1204.0488. 

Work in Progress 
15. (with I. Mirković and Y. Yang) Higher dimensional loop Grassmannians via fusion.

16. (with Z. Lin) Dense orbit ind-constructible abelian categories.

Theses

17. Derived category and cohomology of resolution of singularities: examples from representation theory. Ph.D. Thesis, Northeastern University, (2014).
This is a cumulative thesis.  e-version available here. See the slides I used in my defense.

18. Remarks on some classical theorems about characteristic classes. B.Sc. Thesis, Zhejiang University, (2009). 


Expository talks with Notes 

Arithmetic Fourier transform and proof of the first Kac conjecture
Spring school on Kac conjectures and quiver varieties, Wuppertal, Mar. 2015
.

Procesi bundles and symplective McKay equivalence. 
Joint M.I.T.-Northeastern Student Seminar on Quantum cohomology and Representation theory, Boston, Mar. 2014.

Derived Beilinson-Bernstein localization in positive characteristic and affne braid group action. 
Joint M.I.T.-Northeastern Student Seminar on Quantum cohomology and Representation theory, Boston, Oct. 2013. Notes for Part 1Part 2

BLvdB's characteristic free tilting bundles on Grassmannians and noncommutative desingularizations. Quiver and Invariant Theory Seminar, Spring 2012. 

Derived Category of Coherent Sheaves and Non-commutative Resolutions
Tapas SeminarSummer 2011.
Selected talks I have given

From configuration of points on the punctured plane to Higgs bundles on an elliptic 
curve, Colloquium, SUNY at Buffalo, NY, Sep. 2017.

Quiver varieties and elliptic quantum groups, Representation Theory Seminar, The University of North Carolina at Chapel Hill, NC, Sep. 2017.

Representations of the elliptic affine Hecke algebra and Hitchin systems on an elliptic curve. Representation Theory Seminar, Amherst, MA, Feb. 2017.

Equivarient elliptic cohomology of symplectic resolutions, Algebra Seminar, University of Melbourne, Australia, Dec. 2016.

From points on the punctured plane to Higgs bundles on an elliptic curve, Seminar in Combinatorics, Geometry, and Representation Theory, Smith College, Northampton, MA, Oct. 2016

Cohomological Hall algebras and affine quantum groups, Algebra Seminar, SUNY at Buffalo, NY, Oct. 2016

Elliptic quantum groups and affine Grassmannians on an elliptic curve, Mathematics Seminar, Zhejiang University, Hangzhou, China, Aug. 2016

What elliptic cohomology might have to do with other generalized  Schubert calculi, Workshop on equivariant generalized Schubert calculus and its applications, Ottowa, Apr. 2016.


Quiver varieties and elliptic quantum groups
, Mathematical Physics Seminar, Perimeter Institute, Waterloo, ON, Canada. Mar. 2016.


Quiver varieties and elliptic quantum groups, Algebra and Topology Seminar, State University of New York, Albany, NY. Mar. 2016.


Elliptic affine Hecke algebras and their representations
, Algebra Seminar, University of Ottawa, Canada. Nov. 2015.


Preprojective cohomological Hall algebra, Yangian, and Donaldson-Thomas invariants
. Algebra Seminar, University of Connecticut, Storrs, CT. Oct. 2015


Preprojective cohomological Hall algebra, Yangian, and Donaldson-Thomas invariants
. Valley Geometry Seminar, Amherst, MA. Oct. 2015.


Elliptic affine Hecke algebras and their representations. 
Park City Institute
, Midway, UT, Jul. 2015.


Cohomological Hall algbera of a preprojective algebra
. International Conference on Representation Theory and Commutative Algebra, Storrs, CT, Apr. 2015.


Formal group laws and cohomology of quiver varieties
Seminaire Caen Cergy Clermont Paris - Theorie des Representations
, Paris, Nov. 2014.


Stability conditions for noncommutative symplectic resolutions
Conference on Geometric Methods in Representation Theory 2, University of Missouri in Columbia, Nov. 2013.


Grassmannian parameterizations of representations (after Huisgen-Zimmermann).
 Representation Theory Seminar, Northeastern, Oct. 2013.


Noncommutative desingularization of orbit closures for some GLn representations.
 
Graduate Student Representation Theory Conference, Manhattan, KS, Apr. 2013. (Most polished-up slides in all my talks with the same title.)


Noncommutative desingularization of orbit closures for some GLn representations
Conference on Geometric Methods in Representation Theory, University of Missouri in Columbia, Nov. 2012.


stringy moduli space for noncommutative symplectic resolutions (after Anno-Bezrukavnikov-Mirkovic)Graduate Student Research Seminar, Northeastern, Oct. 2012.


Lefschetz decompositions, wonderful resolutions, and categorical crepant resolution of singularities
 (after kuznetsov and Abuaf)Quiver and Invariant Theory Seminar, Fall 2012.

Noncommutative desingularization of orbit closures for some GLn-representations. Maurice Auslander International Conference, April 2012.


My teaching experiences

2015 to 2017, I was a Visiting Assistant Professor at UMass Amherst. 

Go to my teaching page to find the course materials.


2009 to 2014: Teaching Assistant, Northeastern University, Boston, U.S.A

Spring 2014 Recitation for  Calculus 3 for science and Engineering
Fall 2013 Calculus 1

Fall 2011-Spring 2013:

Teaching Assistant for Real Analysis
Fall 2010:  Calculus 3 for Science and Engineering
Spring 2010:     Discrete Mathematics

Fall 2009:

Recitation for Calculus 3 for science and Engineering
 
Collaborators, advisors, and mentors

Roman Bezrukavnikov

Tamás Hausel

Marc Levine

Ivan Mirković

Vinoth Nandakumar

Changjian Su

Alexandru I. Suciu

Valerio Toledano Laredo

Éric Vasserot

Jerzy Weyman

Yaping Yang

Changlong Zhong


(C) 2012 Gufang Zhao. Webpage design: Yaping Yang.
Last edited: May 29, 2017
Subpages (2): Personal Teaching