# Home

## Yaping Yang

I am currently a Lecturer at the University of Melbourne. I am a member of the **R****epresentation 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

(with Ivan Mirković and Gufang Zhao) Higher dimensional loop Grassmannians, in preparation.

## Preprints

(with Miroslav Rapčák, Yan Soibelman, and Gufang Zhao) Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds. https://arxiv.org/abs/2007.13365

(with Gufang Zhao) The cohomological Hall algebras of a preprojective algebra with symmetrizer, https://arxiv.org/abs/1911.02689

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

(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 Miroslav Rapčák, Yan Soibelman, and Gufang Zhao) Cohomological Hall algebras, vertex algebras and instantons. Commun. Math. Phys.. 376, pages1803--1873(2020).

(with Gufang Zhao) The PBW Theorem for the affine Yangians, to appear in Transform. Groups. DOI: 10.1007/s00031-020-09572-6 https://arxiv.org/abs/1804.04375

(with Gufang Zhao) On two cohomological Hall algebras, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 150,

(with Gufang Zhao) The cohomological Hall algebra for a preprojective algebra, Proc. Lond. Math. Soc. 116, 1029-1074 (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 https://doi.org/10.1007/s00029-017-0366-y

(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 https://dx.doi.org/10.4310/MRL.2017.v24.n5.a4

(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,

*Mathematische Annalen***volume 375**, pages1823–1855(2019). arXiv:1311.2159.**DOI:**10.1007/s00208-019-01880-x(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 DOI:10.2422/2036-2145.201205_008

(with Alex Suciu and Gufang Zhao) Intersections of translated algebraic subtori. J. Pure Appl. Algebra 217 (2013), no. 3, 481-494. arXiv: 1109.1023 DOI:10.1016/j.jpaa.2012.06.025

## Conference Proceedings :

### Peer-reviewed

(with Ivan Mirković and Gufang Zhao) Loop Grassmannians of quivers and affine quantum groups, to appear at Proceedings of the Conference "Interactions between Representation Theory and Algebraic Geometry" held at the University of Chicago, https://arxiv.org/abs/1810.10095.

(with Finn McGlade, and Arun Ram) Positive level, negative level and level zero, https://arxiv.org/abs/1907.11796. Proceedings to the International Conference in Schubert Calculus.

### 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".

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.