Gufang Zhao
Postdoc
Institute of Science and Technology Austria
Am Campus, 1
Klosterneuburg 3400
Österreich
Email (don't copypaste): 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 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. 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 See here for an unpublished earlier version (with more background introductory materials for my own reference). 4.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 algebras. Adv. Math. 317 (2017), 5090. arXiv: 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), 101153. ArXiv:1204.4873.6. (with A. Suciu and Y. Yang) Intersections of translated algebraic subtori. J. Pure Appl. Algebra 217 (2013), no. 3, 481494.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. 9. (with C. Zhong) Elliptic affine Hecke algebras and their representations. 40 pages, (2015). arXiv: 1507.01245. A revised version is available here. It contains a duality conjecture. Revised on Aug. 2, 2017. 10. (with C. Su and C. Zhong) On the Ktheory 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.
Theses17. Derived category and cohomology of resolution of singularities: examples from representation theory. Ph.D. Thesis, Northeastern University, (2014).This is a cumulative thesis. eversion 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 BeilinsonBernstein 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 1, Part 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 Noncommutative Resolutions. Tapas Seminar, Summer 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.
Noncommutative desingularization of orbit closures for some GLnrepresentations. Maurice Auslander International Conference, April 2012. 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
Collaborators, advisors, and mentors (C) 2012 Gufang Zhao. Webpage design: Yaping Yang.
