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Yaping Yang

I am currently a Lecturer at the University of Melbourne. I am a member of the Representation Theory Group .

I obtained my Ph.D degree in May 2014 from Northeastern University, under the supervision of Prof. Valerio Toledano Laredo. After my PhD, I spent a semester in 2014 as a postdoc at Mathematical Sciences Research Institute, Berkeley, and I worked as a visiting assistant professor at University of Massachusetts, Amherst (2014-2017).

My profile at the University of Melbourne https://ms.unimelb.edu.au/people/profile?id=2268

The Representation theory seminar at Melbourne: Representation Theory Seminar

Contact Information

Peter Hall building, Office 165

School of Mathematics and Statistics

The University of Melbourne

813 Swanston Street, Parkville VIC 3010.

Email:

yaping.yang1 (at) unimelb.edu.au

Phone: +61-0383443077

Research Interests

My research lies in the area of Lie algebras, geometric representation theory, quantum groups, and the related geometry and topology. More specifically:

  • 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 equations on the moduli space of elliptic curves.

  • I also 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 Mirković and Gufang Zhao about higher dimensional loop Grassmannians.

  • Recently, I work with Miroslav Rapčák, Yan Soibelman, and Gufang Zhao on vertex algebras associated to toric Calabi-Yau 3-folds. This is closely related to the moduli space of spiked instantons of Nekrasov.

Students:

  • Nicholas Macleod, PhD student , co-supervised (as a cosupervisor) with Omar Foda.

  • Michael Swaddle, PhD student, co-supervised (as a cosupervisor) with Paul Norbury.

  • Tyson Field, Master's student, co-supervised with David Ridout.

Tyson's research presentation slides: Wess-Zumino-Witten Models and the Knizhnik-Zamolodchikov Equations

  • Finley Mcglade, undergraduate student, co-supervised with Arun Ram. AMSI Vacation Research Scholarship: Nov. 6-Dec.1, 2017, and Jan. 23 to Feb. 8, 2018: Finn's Slides.

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 Mirković

Aug. 2014-Dec. 2014: The Mathematical Sciences Research Institute, Berkeley, CA. Postdoc Mentor: Edward Frenkel. https://www.msri.org/programs/276

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.

Visiting Positions:

Dec 23, 2019-Feb.29, 2020: Kavli Institute for the Physics and Mathematics of the Universe (IPMU), Japan.

Feb.9- Mar.3, 2019: Perimeter Institute for Theoretical Physics, Waterloo, Canada.

May 20-July.15, 2018: IST, Austria.

Jan.3- Feb.28, 2018: Perimeter Institute for Theoretical Physics, Waterloo, Canada.

Nov.1-Nov. 25, 2017: IST, Austria.

Oct. -Nov.1, 2017: Hausdorff Research Institute for Mathematics, Bonn, Germany.

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 Awards

2020-2022: Andrew Sisson Fellowship at the University of Melbourne.

May 2019-May 2022:DECRA 190101231 Integrable systems from gauge theories.

Jan.-Feb.,2018, 2019: 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.

Publications

Articles in preparation

Preprints

Peer-reviewed Journal articles:

Conference Proceedings :

Peer-reviewed

Without Peer-review

  • (with Gufang Zhao) How to sheafify an elliptic quantum group. 2017 MATRIX Annals, Editors: David R. Wood, Jan de Gier, Cheryl E. Praeger, Terence Tao. MATRIX Book Series, Volume 2, Springer, to appear. arXiv: 1803.06627

Talks I have given:

The year 2020:

June 23: Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds. GRT at Home. https://grt-home.org/event/grt_at_home_seminar-2/

Apr. 7: The Knizhnik–Zamolodchikov functor for rational Cherednik algebras

The year 2019:

Nov. 26, Elliptic weight functions for the cotangent bundle of Grassmanian. Seminar on elliptic Schubert classes.

Feb 4: Cohomological Hall algebras, vertex algebras and instantons, Kavli IPMU, the University of Tokyo

https://indico.ipmu.jp/indico/event/168/

The year 2018:

Dec 17-20: Factorization structures and quantization, University of Auckland. http://www.maths.adelaide.edu.au/pedram.hekmati/TQFT2018/

Sep. 19: How to give a 20-minute seminar, masters help classes, University of Melbourne.

June 26: Cohomological Hall algebras, vertex algebras and instantons, CIME School, Geometric Representation Theory and Gauge Theory​. June 25-29, Cetraro, Italy http://www.salafrancesco.altervista.org/cime-school.html

May 22: From geometry to quantum integrable systems, University of Birmingham.

May 1: Double current algebras and applications, Pure Mathematics Seminar, University of Queensland.

Apr. 30: From homotopy theory to representation theory, colloquium talk, University of Queensland.

Apr. 27: Double current algebras and applications, Algebra Seminar, University of Sydney

Apr. 13: Double current algebras and applications, University of Melbourne, Pure Mathematics Seminar. https://sites.google.com/site/jessegellredman/home/seminar

Mar. 1: How to sheafify an elliptic quantum group? Yale University. http://calendar.math.yale.edu/public_html/calendar/www/posters/2376.pdf

Jan. 15: Monodromy representations of elliptic braid groups, Perimeter Institute.

The year 2017:

Dec. 22: How to sheafify an elliptic quantum group? Geometric R-Matrices: From Geometry to Probability, Matrix program.https://www.matrix-inst.org.au/events/geometric-r-matrices/

Dec. 13: Algebraic elliptic cohomology and flops, AustMS meeting, Sydney.

Dec. 12: Towards a construction of higher dimensional loop Grassmannians, AustMS meeting, Sydney.

Dec. 4: A geometric construction of affine quantum groups, University of Sydney: https://sites.google.com/site/ausreptheory/conference2017

Dec. 1: From homotopy theory to representation theory, US-Mexico Conference, Mexico City. https://sites.google.com/view/usmexico-2017/home

Nov. 21: Lusztig’s character formula and Morava K-theory. IST, Austria.

Oct. 19: Macdonald polynomials and generalizations, Junior Hausdorff Trimester program.

Oct.18, A geometric construction of affine quantum groups, Junior Hausdorff Trimester program, "Symplectic Geometry and Representation theory".

http://www.him.uni-bonn.de/de/programs/current-trimester-program/representation-theory-2017/description/

Sep. 24-26, Towards a construction of higher dimensional loop Grassmannians, WIMSIG Conference 2017. http://www.austms.org.au/WIMSIG-conference-2017

Sep.11-15, Monodromy representations of elliptic braid groups, University of Adelaide. http://www.iga.adelaide.edu.au/workshops/WorkshopSep2017/

Aug. 10, An introduction to rational Cherednik algebras. Representation theory seminar at University of Melbourne https://sites.google.com/site/yapingyanghomepage/representation-theory-seminar

March 10-12, 2017: From homotopy theory to representation theory, AMS sectional meeting, Charleston, SC.

http://www.ams.org/meetings/sectional/2228_progfull.html

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

2018, Semester 2: The University of Melbourne.

Advanced Topics in Geometry and Topology (MAST90124)

https://handbook.unimelb.edu.au/2018/subjects/mast90124

Course webpage: https://sites.google.com/site/yapingyanghomepage/teaching/2018-semester-2

2015-2017: University of Massachusetts Amherst.

Spring 2017

1. Math412:Introduction to Abstract algebra II, room: LGRT 173,

Tu Th 8:30am-9:45AM,

Course webpage: https://sites.google.com/site/yapingyanghomepage/teaching/spring2017-math412

2. Math 235: Introduction to Linear Algebra, Tu Th 10:00am-11:15AM, Room: LGRT 121

Course webpage: https://sites.google.com/site/yapingyanghomepage/teaching/spring2017_math235

Course ID: yang81334 (you will receive a 50% penalty on late assignments).

Fall 2016:

1. Math 411-02 Introduction to abstract algebra I https://sites.google.com/site/yapingyanghomepage/teaching/fall2016_math411

2. Math 132.07, Calculus 2

Spring 2016:

1. Math 132.07, Calculus 2

2. Math 412, Introduction to Abstract algebra II

Fall 2015:

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 https://sites.google.com/site/yapingyanghomepage/teaching/fall-2015_math132h

Spring 2015:

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.A

Spring 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.

Personal

My husband Gufang Zhao is also a mathematician.

Prof. Shiu-Chun Wong’s homepage and undergraduate student Seminars.

Travel Plans

The Year 2021

May 17-21, 2021? New Perspective in Categorification and Quantization - Oaxaca, Mexico - Summer 2021

The Year 2020

Nov 16-Nov 27, FRONTIERS IN REPRESENTATION THEORY. Matrix.

https://www.matrix-inst.org.au/events/frontiers-in-representation-theory/

Sep 6-11, 2020: Geometry and Physics of Quantum Toroidal Algebra

http://www.birs.ca/events/2020/5-day-workshops/20w5024

Mar 1-Mar 6, 2020: Hong Kong University of Science and Technology, HK. (cancelled)

Dec23, 2019-Feb.29, 2020, IPMU, Japan

The Year 2019

Dec 16-20: Geometric Representation Theory and Quantum Field Theories, Tsinghua Sanya Internationl Mathematics Forum: http://www.tsimf.cn/meeting/show?id=200#MMM2

Feb. 25-March 1, Cohomological Hall Algebras in Mathematics and Physics

https://www.perimeterinstitute.ca/conferences/cohomological-hall-algebras-mathematics-and-physics

Feb. 4-8: Representation theory, gauge theory and integrable systems at Kavli IPMU, the University of Tokyo

https://indico.ipmu.jp/indico/event/168/

The Year 2018

Dec. 17-21, 2018: A conference on character varieties and quantisation, the University of Auckland.

http://www.maths.adelaide.edu.au/pedram.hekmati/TQFT2018/

Dec 10-16: https://www.matrix-inst.org.au/events/geometric-and-categorical-representation-theory/

Dec. 4-7, 2018: Co-organiser of the session on the topic of Representation Theory, Australian Mathematical Society Annual Meeting, the University of Adelaide. http://maths.adelaide.edu.au/austms2018/

June 25-29:CIME School, Geometric Representation Theory and Gauge Theory​ http://www.salafrancesco.altervista.org/cime-school.html

June 3-7, 2018: Helvetic Algebraic Geometry Seminar https://people.math.ethz.ch/~rahul/ChAGS18.html

May 20-July 15: IST, Austria.

Apr. 29-May 5, 2018: University of Queensland, https://smp.uq.edu.au/event/1391/maths-colloquium

Apr 27-Apr. 29, 2018: University of Sydney Algebra Seminar, http://www.maths.usyd.edu.au/u/AlgebraSeminar/

Mar.2-Mar. 9, 2018: UMass, Amherst. http://people.math.umass.edu/~mirkovic/

Feb. 28-Mar.2, 2018: Yale university. Hosts: Sasha Tsymbaliuk and Philsang Yoo.

http://calendar.math.yale.edu/public_html/calendar/www/posters/2376.pdf

Feb.19-Feb.23: University of Alberta, https://sites.ualberta.ca/~nguay/

Jan.1-Feb.28, 2018: Perimeter Institute for Theoretical Physics, Waterloo, CA. https://www.perimeterinstitute.ca/

The Year 2017

Dec.18-22, 2017: MATRIX program, Geometric R-Matrices: From Geometry to Probability, Creswick Campus of The University of Melbourne

https://www.matrix-inst.org.au/events/geometric-r-matrices/

Dec.12-15, 2017: AustMS meeting, Sydney. [One talk in Representation theory, and one talk in K-theory!! 25mins/each] https://www.mq.edu.au/about/about-the-university/faculties-and-departments/faculty-of-science-and-engineering/departments-and-centres/department-of-mathematics/news-and-events/austms-annual-meeting-2017

Dec.4-8, 2017: University of Sydney: https://sites.google.com/site/ausreptheory/conference2017

Nov.27-Dec.1, 2017: US-Mexico Conference in Mexico City in the Mathematics Institute of of UNAM. https://sites.google.com/view/usmexico-2017/home

Nov.1-Nov. 25, 2017: IST, Austria Tamas Hausel's group. https://portal.app.ist.ac.at/#/home

Oct.1-Oct.31, 2017: HIM, Bonn/ Talk on Oct. 16-18. http://www.him.uni-bonn.de/de/programs/current-trimester-program/representation-theory-2017/description/

Sep.24-26, 2017, University of South Australia in Adelaide, http://www.austms.org.au/WIMSIG-conference-2017, [25-minute talk (including time for questions)]

Sep.11-15, 2017: http://www.iga.adelaide.edu.au/workshops/WorkshopSep2017/ [55mins + 5mins for questions.]

July 3-7, 2017: Summer school at Dijon: http://school-tlag2017.math.cnrs.fr/index.html

Jun.1-Aug. 1, 2017: Max Planck institute, Bonn, Germany.

Mar. 12-20, 2017: University of Connecticut.

Mar. 10-12, 2017: AMS Spring Southeastern Sectional Meeting “Geometric Methods in Representation Theory”, the College of Charleston in Charleston, SC

Professional service

The Year 2019

Co-organizer of the workshop on "Geometric Representation Theory and Quantum Field Theory" December 16-20 2019, TSIMF, Sanya, China. https://ymsc-strings.github.io/events/GeoRepSanya/index.html

Co-organizer of the workshop "Cohomological Hall algebras in Mathematics and Physics" at Perimeter Institute, February 25-March 1, 2019 https://www.perimeterinstitute.ca/conferences/cohomological-hall-algebras-mathematics-and-physics

The Year 2018

Co-organiser of the session on the topic of Representation Theory, Australian Mathematical Society Annual Meeting, the University of Adelaide. http://maths.adelaide.edu.au/austms2018/

Co-organizer of the Representation Theory Seminar at the University of Melbourne, Australia.

The Year 2017

A panel member for the job hiring at the University of Melbourne, Australia.

Co-organizer of the Representation Theory Seminar at the University of Melbourne, Australia.

The Year 2012-2014

Co-organizer of the Graduate Student Research Seminar at Northeastern University.