# Home

## Yaping Yang

I am a Lecturer at the University of Melbourne.

I am co-organizing a workshop *"Cohomological Hall algebras in Mathematics and Physics"** *at Perimeter Institute, February 25-March 1, 2019

The Representation theory seminar at Melbourne: Representation Theory Seminar

## đź‘‰Contact đź‘‰Seminars đź‘‰Employment đź‘‰Publications đź‘‰Talks đź‘‰Teaching đź‘‰Personal đź‘‰Travel

# 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**: ďĽ‹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 Mirkovi
__Ä‡__and Gufang Zhao about higher dimensional loop Grassmannians. - Recently, I work with Miroslav RapÄŤĂˇk, 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.

# Seminars at Melbourne

### 2019

The Representation Theory Seminar 2019

### 2018

The Representation Theory Seminar 2018

### 2017

The Representation Theory Seminar 2017

# Students:

- Nicholas Macleod, PhD student, co-supervised with Omar Foda.
- Michael Swaddle, PhD student, co-supervised 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 Mirkovi__Ä‡__

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 Wongâ€™s undergraduate student Seminars.

# Visiting Positions:

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

May 2019-May 2012ďĽšDECRA 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

(with Ivan Mirkovi__Ä‡__ and Gufang Zhao) Higher dimensional loop Grassmannians, in preparation.

## Preprints

(with Miroslav RapÄŤĂˇk, Yan Soibelman, and Gufang Zhao) Cohomological Hall algebras, vertex algebras and instantons, https://arxiv.org/abs/1810.10402

(with Ivan Mirkovi__Ä‡__ and Gufang Zhao) Loop Grassmannians of quivers and affine quantum groups, https://arxiv.org/abs/1810.10095.

(with Valerio Toledano Laredo) The elliptic Casimir connection of a simple Lie algebra, https://arxiv.org/abs/1805.12261

(with Gufang Zhao) The PBW Theorem for the affine Yangians, https://arxiv.org/abs/1804.04375

(with Valerio Toledano Laredo) Universal KZB equations for arbitrary root systems, https://arxiv.org/abs/1801.10259

(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

## Peer-reviewed journal articles:

(with Gufang Zhao) On two cohomological Hall algebras, to appear in Proc. Roy. Soc. Edinburgh Sect. A. arXiv: 1604.01477.

(with Gufang Zhao) The cohomological Hall algebra for a preprojective algebra, Proc. Lond. Math. Soc. 116, 1029-1074 (46 pages) 01 May 2018. DOI: 10.1112/plms.12111 arXiv: 1407.7994.

(with Gufang Zhao), Cohomological Hall algebras and affine quantum groups, Selecta Mathematica, Vol. 24, Issue 2 (2018), pp. 1093-1119. arXiv:1604.01865

(with Nicolas Guay) On deformed double current algebras for simple Lie algebras, Mathematical Research Letters. Vol. 24, No. 5 (2017), pp. 1307-1384.

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), 101-153.

arXiv:1204.4873

(with Alex Suciu and Gufang Zhao) Intersections of translated algebraic subtori. J. Pure Appl. Algebra 217 (2013), no. 3, 481-494.

arXiv: 1109.1023

## Conference Proceedings:

(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 2019:

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 Theoryâ€‹. 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: Lusztigâ€™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".

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 Wongâ€™s homepage and undergraduate student Seminars.

# Travel Plans

### The Year 2019

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 Theoryâ€‹ 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 â€śGeometric Methods in Representation Theoryâ€ť, the College of Charleston in Charleston, SC