Peter Hall building(#160), Office 175 School of Mathematics and Statistics The university of Melbourne 813 Swanston Street, Parkville VIC 3010.
yaping.yang1 (at) unimelb.edu.au
## Research InterestMy research lies in the area of integrable systems, Lie algebras, geometric representation theory, motivic homotopy theory and the related geometry and topology. I have an on-going project joint with Valerio Toledano Laredo studying the monodromy representation of elliptic braid groups, which comes from the Knizhnik-Zamolodchikov-Bernard (KZB) equations on the moduli space of elliptic curves. I have an on-going project joint with Gufang Zhao. We apply the tool of cohomology theories to study quantum groups and Nakajima quiver varieties. I am working with Marc Levine and Gufang Zhao about the elliptic cohomology theory in the motivic setting. I am also working with Ivan Mirkovic and Gufang Zhao about higher dimensional loop Grassmannians. ## Seminar## The representation theory seminarTyson Field, Master student, co-supervised with David Ridout. ## Employment:Aug. 2017- Present: Lecturer, The University of Melbourne, Australia. Jan. 2015-Aug. 2017: Visiting Assistant Professor, University of Massachusetts, Amherst, MA. Postdoc Mentor: Ivan Mirkovic Aug. 2014-Dec. 2014: The Mathematical Sciences Research Institute, Berkeley, CA. Postdoc Mentor: Edward Frenkel. ## Education:2009-2014: Ph.D., Northeastern University, Boston, MA. Advisor: Valerio Toledano Laredo 2005-2009: B. S. Zhejiang University, Hangzhou, China. Shiu-Chun Wong’s undergraduate student Seminars. ## As a visitor:June -July 31, 2017: Max Planck Institute for Mathematics, Bonn, Germany. May 17-Aug. 3, 2016: Universitat Duisburg-Essen, Fakultat fur Mathematik, Essen, Germany. Mar 14-Mar 19, 2016: Perimeter Institute for Theoretical Physics, Waterloo, Canada. Feb 7-Feb 12, 2016: The Banff International Research Station: Vertex Algebras and Quantum Groups, Alberta, Canada. Jan3-Jan 9, 2016: Simons center for Geometry and Physics, Stony Brook. June -Aug. 2015: Max Planck Institute for Mathematics, Bonn, Germany. June-July. 2015: Park City Mathematics Institute, Utah. May-Aug., 2012: Universitat Duisburg-Essen, Fakultat fur Mathematik, Essen, Germany. May-July, 2013: Universitat Duisburg-Essen, Fakultat fur Mathematik, Essen, Germany. ## Fellowships and AwardsJan.-Feb.,2018: Emmy Noether Fellowship - Perimeter Institute Jul.2016-Jul.2018: AMS Simons Travel Grant. Aug.-Dec., 2014: Cha-Chern Scholarship, the Mathematical Sciences Research Institute. May-June, 2013: Ling-Ma Fellowship, Northeastern University. 2009-May, 2014: Teaching Assistantship, Northeastern University ## Publications## Articles in preparation(with Ivan Mirkovic and Gufang Zhao) Higher dimensional loop Grassmannians, in preparation. (with Valerio Toledano Laredo) Universal KZB equations for arbitrary root systems, preliminary version available. (with Valerio Toledano Laredo) The elliptic Casimir connection, preliminary version available. ## Preprints(with Gufang Zhao) Quiver varieties and elliptic quantum groups, https://arxiv.org/abs/1708.01418 (with Marc Levine and Gufang Zhao) Algebraic Elliptic cohomology theory and flops II, SL-cobordism, arXiv:1610.00396 (with Gufang Zhao), Cohomological Hall algebras and affine quantum groups, 17 pages, preprint, arXiv: 1604.01865 (with Gufang Zhao) On two cohomological Hall algebras, 26 pages, preprint, arXiv: 1604.01477 (with Gufang Zhao) The cohomological Hall algebras for a preprojective algebra, 44 pages, Here is an updated version, which contains discussions about Lusztig's 2015 reformulation of his 1979 conjecture on characters of modular representations. ## Peer-reviewed journal articles:(with Nicolas Guay) On deformed double current algebras for simple Lie algebras, to appear in Mathematical Research Letters. ArXiv: 1608.02900 (with Marc Levine and Gufang Zhao) Algebraic Elliptic cohomology theory and flops I, with an appendix by Jo\"el Riou on dualizability in the motivic stable homotopy category, to appear in Math. Annalen. arXiv:1311.2159. (with Alex Suciu and Gufang Zhao) Homological finiteness of abelian covers. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XIV (2015), 1-53. (with Alex Suciu and Gufang Zhao) Intersections of translated algebraic subtori. J. Pure Appl. Algebra 217 (2013), no. 3, 481-494. ## Talks I have given:## The year 2017:Aug. 10, An introduction to rational Cherednik algebras. https://sites.google.com/site/yapingyanghomepage/representation-theory-seminar March 10-12, 2017: From homotopy theory to representation theory, AMS sectional meeting, Charleston, SC. ## The year 2016:December: Monodromy representations of elliptic braid groups, University at Albany. November: Cohomology theories and affine quantum groups, University of Melbourne, Australia. November: Cohomology theories and affine quantum groups, Australia National University, Canberra, Australia. August: Quantum groups and cohomology theories, Zhejiang University, Hangzhou, China. February: Cohomological Hall algebras and affine quantum groups, the Banff International Research Station, Banff. January: Cohomological Hall algebras and affine quantum groups, Simons center for Geometry and Physics, Stony Brook. ## The year 2015:August: Yangians and Cohomological Hall algebras for a preprojective algebra. Oberseminar, Max Planck Institute for Mathematics, Bonn. April: Conformal blocks and the Knizhnik-Zamolodchikov equations. Representation Theory Seminar, UMass, Amherst. February: Algebraic elliptic cohomology theory and flops. Valley Geometry Seminar, UMass, Amherst. January: The vertex representations of quantum toroidal algebras. Seminaire Math Jeunes, Ecole Normale Superieure, Paris, France. ## The year 2014:November: Conformal blocks and KZ connections. Representation Theory Mini-Workshop, Kansas State University, Manhattan, KS. October: Monodromy representations of braid groups. Geometric Representation Theory Pizza Seminar, MSRI, Berkeley, CA. October: Loop Grassmannians and the Zastava spaces of reductive groups. The GRASP (Geometry, Representations, and Some Physics) seminar, UC Berkeley, CA. May: Functor between finite-dimensional representation categories. Workshop on Yangians and Quantum Loop Algebras, Austin, TX. January: $\mathbb{A}^1$-homotopy theory and the slice spectral sequence. Graduate Student Research Seminar, Northeastern. ## The year 2013:October: Universal KZB equations for arbitrary root systems and the elliptic Casimir connection. Non-commutative algebra seminar, M.I.T., Boston, MA. September: Differential equations on hyperplane complements II. Graduate seminar on Quantum cohomology and Representation theory, Northeastern, Boston, MA. September: Differential equations on hyperplane complements I}. Graduate seminar on Quantum cohomology and Representation theory, M.I.T., Boston, MA. ## The year 2012:November: Algebraic Elliptic cohomology theory and flops II. Graduate Student Seminar, Harvard University. November: Algebraic Elliptic cohomology theory and flops I. Graduate Student Seminar, Harvard University. October: Universal KZB equations for arbitrary root systems. Graduate Student Research Seminar, Northeastern. ## The year 2011:May: Representations of Lie Algebras and D-modules, Tapas Seminar, Northeastern. April: Homological finiteness of abelian covers. AMS Sectional Meeting, Worcester, MA. ## Teaching## 2015-2017: University of Massachusetts Amherst.## Spring 20171. Math412:Introduction to Abstract algebra II, room: LGRT 173, Tu Th 8:30am-9:45AM, Course webpage: 2. Math 235: Introduction to Linear Algebra, Tu Th 10:00am-11:15AM, Room: LGRT 121 Course webpage: Course ID: yang81334 (you will receive a 50% penalty on late assignments).
1. Math 411-02 Introduction to abstract algebra I 2. Math 132.07, Calculus 2
2. Math 412, Introduction to Abstract algebra II
1. Instructor, Math 132H.01, honors Calculus 2, University of Massachusetts Amherst. 2. Instructor, Math 132H.02, honors Calculus 2, University of Massachusetts Amherst. The course webpage
1. Instructor, Math 132.12 Calculus 2, University of Massachusetts Amherst. 2. Instructor, Math 132.13 Calculus 2, University of Massachusetts Amherst. ## 2009-2014: Teaching Assistant, Northeastern University, Boston, U.S.ASpring 2014: Teaching Assistant, Math 2331 Linear Algebra. Fall 2013: Instructor, Math 1215 Mathematical thinking. Spring 2013: Instructor, Math 1231 Calculus for Business and Economics. Fall 2012: Instructor, Math 1215 Mathematical thinking. Spring 2012:Teaching Assistant, Math 2280 and 2285 Statistics and Software. Fall 2011: Recitation Leader, Math 1241 Calculus 1. Spring 2011: Instructor, Math 2321 Calculus 3 for Science and Engineering. Fall 2010: Recitation Leader, Math 2321 Calculus 3 for Science and Engineering. Spring 2010: Instructor, Math 2280 Statistical thinking. Fall 2009: Recitation Leader, Math 2321 Calculus 3 for Science and Engineering. ## PersonalMy husband Gufang Zhao is also a mathematician. Prof. Shiu-Chun Wong’s homepage and undergraduate student Seminars. ## Travel PlansMarch 10-12 (Friday-Sunday), 2017: AMS Spring Southeastern Sectional Meeting “Geometric Methods in Representation Theory”, the College of Charleston in Charleston, SC March 12-20, 2017: University of Connecticut. June 1-Aug 1, 2017: Max Planck institute, Bonn, Germany. July 3-7, 2017: Summer school at Dijon: http://school-tlag2017.math.cnrs.fr/index.html 11-15 September 2017: http://www.iga.adelaide.edu.au/workshops/WorkshopSep2017/ [55mins + 5mins for questions.] 24-26 September 2017, Oct. 16-18, at the HIM, Bonn. November 27th - December 1st, 2017: US-Mexico Conference in Mexico City in the Mathematics Institute of of UNAM. December 4-8, 2017: University of Sydney. December 12-15: AustMS meeting, Sydney. [One talk in Representation theory, and one talk in K-theory!! 25mins/each] December 18-22: MATRIX program, Geometric R-Matrices: From Geometry to Probability, |