Huai-Liang CHANG
张怀良
PhD in Mathematics
Stanford University, 2007

Professor
Department of Mathematics



(852) 2358 7454
mahlchang@ust.hk
Room 3490
Personal Web

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ORCID
0000-0001-9922-9224

Scopus ID
55272657900




Research Interest Publications Projects Teaching Assignment RPG Supervision Space used




Research Interest

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Algebraic geometry
String theory



Publications

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All Years 40 2022 0 2021 2 2020 2 2019 2 2018 1 2017 3 2016 30

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Expand All Collapse All


2021 2

Polynomial structure of Gromov-Witten potential of quintic 3-folds
Annals Of Mathematics, v. 194, (3), November 2021, p. 585-645
Chang, Huai-liang; Guo, Shuai; Li, Jun Article
The theory of n –mixed-spin-p fields
Geometry and Topology, v. 25, (2), April 2021, p. 775-811
Chang, Huai-liang; Guo, Shuai; Li, Jun; Li, Weiping Article

2020 2

A Vanishing Associated with Irregular MSP Fields
International Mathematics Research Notices, v. 2020, (20), October 2020, p. 7347-7396
Chang, Huai-liang; Li, Jun Article
Invariants of stable quasimaps with fields
Transactions of The American Mathematical Society, v. 373, (5), May2020, p. 3669-3691
Chang, Huai-Liang; Li, Mun Lin Article

2019 2

Mixed-Spin-P fields of Fermat polynomials
Cambridge Journal of Mathematics, v. 7, (3), September 2019, p. 319-364
Chang, Huai-liang; Li, Jun; Li, Weiping; LiU, Melissa Chiu-Chu Article
Virtual Residue and an Integral Formalism
Journal of Geometric Analysis, v. 29, (1), January 2019, p. 83-104
Chang, Huailiang; Li, Mulin Article

2018 1

Genus-One Gromov–Witten Invariants of Quintic Three-folds via MSP Localization
International Mathematics Research Notices, v. 2020, (19), 2020, article number rny201, p. 6347-6390
Chang, Huai-Liang; Guo, Shuai; Li, Wei Ping; Zhou, Jie Article

2017 3

A Survey on Mixed Spin P-fields
Chinese Annals of Mathematics. Series B, v. 38, (4), 2017, p. 869-882
Chang, Huai-Liang; Li, Jun; Li, Wei-Ping; Liu, Chiu Chu Melissa Article
Torus Localization and Wall Crossing for Cosection Localized Virtual Cycles
Advances in Mathematics, v. 308, February 2017, p. 964-986
Chang, Huai-Liang; Kiem, Young Hoon; Li, Jun Article
On the Mathematics and Physics of Mixed Spin P-fields
Proceedings of Symposia in Pure Mathematics, v. 96, 2017, p. 47-73
Chang, Huai-Liang; Li, Jun; Li, Wei-Ping; Liu, Chiu-Chu Melissa Conference paper

2015 3

An algebraic proof of the hyperplane property of the genus one GW-invariants of quintics
Journal of Differential Geometry, v. 100, (2), June 2015, p. 251-299
Chang, Huai-Liang; Li, Jun Article
Witten’s top Chern class via cosection localization
Inventiones Mathematicae, v. 200, (3), June 2015, p. 1015-1063
Chang, Huai-Liang; Li, Jun; Li, Wei Ping Article
MSP fields and Gromov Witten invariants of Quintic Calabi Yau threefold
MSP fields and Gromov Witten invariants of Quintic Calabi Yau threefold, Institute of Mathematics Academia Sinica, Taiwan, January 2015
Chang, Huai-liang Conference paper

2014 5

A Vanishing Result for Donaldson Thomas Invariants of P-1 Scroll
Acta Mathematica Sinica, English Series, v. 30, (12), December 2014, p. 2079-2084
Chang, Huai-Liang Article
Algebro-geometric approach toward higher genus GW invariants of Quintics
Calabi-Yau Geometry and Mirror Symmetry conference, National Taiwan University, Taipei, Taiwan, 6-10 January 2014
Chang, Huai-Liang Conference paper
Landau Ginzburg type theories from algebraic geometry
The Hong Kong Mathematical Society Annual General Meeting 2014, Hong Kong Polytechnic University, 6 June 2014
Chang, Huai-Liang Conference paper
Landau Ginzburg Type Theories from Algebraic Geometry
The International Mathematical Meeting and the Annual Meeting of the Taiwanese Mathematical Society (2014 AMMS), National Cheng Kung University, Taiwan, 6-7 December 2014
Chang, Huai-Liang Conference paper
Physics motivation and a fast Introduction to theories of P fields and Spin-curves
The Third Advanced Seminar on Symplectic Geometry and Topological Field Theory, Beijing International Center for Mathematical Research, 1-5 December 2014
Chang, Huai-Liang Conference paper

2013 4

Poincaré invariants are Seiberg–Witten invariants
Geometry & Topology, v. 17, (2), 2013, p. 1149-1163
Chang, Huai-Liang; Kiem, Young-Hoon Article
On A twisted Landau-Ginzburg Type Theory
Scuola Internazionale Superiore di Studi Avanzati(SISSA), Trieste, Italy, August 2013
Chang, Huai-Liang; Li, Jun; Li, Wei Ping Conference paper
On Algebraic Geometric Construction of Enumerative Invariants
University of Michigan, US, Feb 2013
Chang, Huai-Liang Conference paper
Witten's Top Chern Class Revisited
International Workshop on Complex Geometry, Chinese University of Hong Kong, 18-19 April 2013
Chang, Huai-Liang Conference paper

2012 5

Gromov-Witten Invariants of Stable Maps with Fields
International Mathematics Research Notices, v. 2012, (18), January 2012, p. 4163-4217
Chang, Huai-Liang; Li, Jun Article
Algebraic geometric construction of Gun-Sharpe-Witten model and Fan-Jarvis-Ruan Witten theory

Chang, Huai-Liang Conference paper
Introduction to Gromov Witten and Fan Jarvis Ruan Witten Theory (I,II)
Mini-course in differential geometry, National Center for Theoretical Science, Hsinchu, Taiwan, July, 2012
Chang, Huai-Liang Conference paper
Introduction to Gromov Witten and Fan-Jarvis-Ruan-Witten theory
Kavli Institute for the Physics and Mathematics of the Universe, Tokyo University, Tokyo, Japan, June 2012
Chang, Huai-Liang Conference paper
The conference of Mirror Symmetry and Related Topics (MSRT)

Chang, Huai-Liang Conference paper

2011 8

Semi-perfect obstruction theory and Donaldson–Thomas invariants of derived objects
Communications in Analysis and Geometry, v. 19, (4), 2011, p. 807-830
Chang, Huai-Liang; Li, Jun Article
Algebraic geometry of A-twsited Landau Ginzburg theory
National Seoul University, January 2011
Chang, Huai-Liang Conference paper
Algebraic geometry of A-twsited topological string theory of Landau Ginzburg type
Peking University, 27 May 2011
Chang, Huai-Liang; Li, Jun Conference paper
Introduction to Fan-Jarvis-Ruan-Witten theory
Taida Institue for Mathematical Sciences, Taiwan, January 2011
Chang, Huai-Liang Conference paper
Moduli of stable maps with elds and its applications
Workshop on Moduli and Birational Geometry, Pohang, Korea, July 2011
Chang, Huai-Liang Conference paper
On Algebra-geometric proof of Li-Zinger Conjecture for g=1 Gromov-Witten invariant of Quintic Calabi-Yau threefold

Chang, Huai-Liang; Li, Jun Conference paper
On Algebro-geometric proof of Li-Zinger Conjecture for g=1 Gromov-Witten invariant of Quintic
National Cheng Kung University, December 2011
Chang, Huai-Liang; Li, Jun Conference paper
Toward Algebraic geometry of Gauged Linear Sigma model in A side
Taida Institue for Mathematical Sciences, Taiwan, January 2011
Chang, Huai-Liang Conference paper

2010 3

On Donaldson-Thomas invariants of P1 scroll
Yat-Sen University School of Mathematics and Computational Science, Guangzhou, July 2010
Chang, Huai-Liang Conference paper
On genus one Gromov Witten invariant of Quintic threefold
Hong Kong Math Society Annual General Meeting, March 2010
Chang, Huai-Liang Conference paper
Toward algebraic geometry behind Gauged Linear Sigma model in all genus
InternationalCongress of Chinese Mathematicans, Peking, December 2010
Chang, Huai-Liang Conference paper

2009 1

Donaldson Thomas invariants
Hong Kong Geometry Colloquium, CUHK, September 2009
Chang, Huai-Liang Conference paper

2002 1

Characterization of maps having the KKM property
SOOCHOW JOURNAL OF MATHEMATICS, v. 28, (3), July 2002, p. 329-338
Jeng, Jyh-Chung; Huang, Young-Ye; Chang, Huai-Liang Article


Expand All Collapse All


Article 2

Polynomial structure of Gromov-Witten potential of quintic 3-folds
Annals Of Mathematics, v. 194, (3), November 2021, p. 585-645
Chang, Huai-liang; Guo, Shuai; Li, Jun
The theory of n –mixed-spin-p fields
Geometry and Topology, v. 25, (2), April 2021, p. 775-811
Chang, Huai-liang; Guo, Shuai; Li, Jun; Li, Weiping


Expand All Collapse All


Article 2

A Vanishing Associated with Irregular MSP Fields
International Mathematics Research Notices, v. 2020, (20), October 2020, p. 7347-7396
Chang, Huai-liang; Li, Jun
Invariants of stable quasimaps with fields
Transactions of The American Mathematical Society, v. 373, (5), May2020, p. 3669-3691
Chang, Huai-Liang; Li, Mun Lin


Expand All Collapse All


Article 2

Mixed-Spin-P fields of Fermat polynomials
Cambridge Journal of Mathematics, v. 7, (3), September 2019, p. 319-364
Chang, Huai-liang; Li, Jun; Li, Weiping; LiU, Melissa Chiu-Chu
Virtual Residue and an Integral Formalism
Journal of Geometric Analysis, v. 29, (1), January 2019, p. 83-104
Chang, Huailiang; Li, Mulin


Expand All Collapse All


Article 1

Genus-One Gromov–Witten Invariants of Quintic Three-folds via MSP Localization
International Mathematics Research Notices, v. 2020, (19), 2020, article number rny201, p. 6347-6390
Chang, Huai-Liang; Guo, Shuai; Li, Wei Ping; Zhou, Jie


Expand All Collapse All


Article 2

A Survey on Mixed Spin P-fields
Chinese Annals of Mathematics. Series B, v. 38, (4), 2017, p. 869-882
Chang, Huai-Liang; Li, Jun; Li, Wei-Ping; Liu, Chiu Chu Melissa
Torus Localization and Wall Crossing for Cosection Localized Virtual Cycles
Advances in Mathematics, v. 308, February 2017, p. 964-986
Chang, Huai-Liang; Kiem, Young Hoon; Li, Jun

Conference paper 1

On the Mathematics and Physics of Mixed Spin P-fields
Proceedings of Symposia in Pure Mathematics, v. 96, 2017, p. 47-73
Chang, Huai-Liang; Li, Jun; Li, Wei-Ping; Liu, Chiu-Chu Melissa


Expand All Collapse All


Article 2

An algebraic proof of the hyperplane property of the genus one GW-invariants of quintics
Journal of Differential Geometry, v. 100, (2), June 2015, p. 251-299
Chang, Huai-Liang; Li, Jun
Witten’s top Chern class via cosection localization
Inventiones Mathematicae, v. 200, (3), June 2015, p. 1015-1063
Chang, Huai-Liang; Li, Jun; Li, Wei Ping

Conference paper 1

MSP fields and Gromov Witten invariants of Quintic Calabi Yau threefold
MSP fields and Gromov Witten invariants of Quintic Calabi Yau threefold, Institute of Mathematics Academia Sinica, Taiwan, January 2015
Chang, Huai-liang


Expand All Collapse All


Article 1

A Vanishing Result for Donaldson Thomas Invariants of P-1 Scroll
Acta Mathematica Sinica, English Series, v. 30, (12), December 2014, p. 2079-2084
Chang, Huai-Liang

Conference paper 4

Algebro-geometric approach toward higher genus GW invariants of Quintics
Calabi-Yau Geometry and Mirror Symmetry conference, National Taiwan University, Taipei, Taiwan, 6-10 January 2014
Chang, Huai-Liang
Landau Ginzburg type theories from algebraic geometry
The Hong Kong Mathematical Society Annual General Meeting 2014, Hong Kong Polytechnic University, 6 June 2014
Chang, Huai-Liang
Landau Ginzburg Type Theories from Algebraic Geometry
The International Mathematical Meeting and the Annual Meeting of the Taiwanese Mathematical Society (2014 AMMS), National Cheng Kung University, Taiwan, 6-7 December 2014
Chang, Huai-Liang
Physics motivation and a fast Introduction to theories of P fields and Spin-curves
The Third Advanced Seminar on Symplectic Geometry and Topological Field Theory, Beijing International Center for Mathematical Research, 1-5 December 2014
Chang, Huai-Liang


Expand All Collapse All


Article 1

Poincaré invariants are Seiberg–Witten invariants
Geometry & Topology, v. 17, (2), 2013, p. 1149-1163
Chang, Huai-Liang; Kiem, Young-Hoon

Conference paper 3

On A twisted Landau-Ginzburg Type Theory
Scuola Internazionale Superiore di Studi Avanzati(SISSA), Trieste, Italy, August 2013
Chang, Huai-Liang; Li, Jun; Li, Wei Ping
On Algebraic Geometric Construction of Enumerative Invariants
University of Michigan, US, Feb 2013
Chang, Huai-Liang
Witten's Top Chern Class Revisited
International Workshop on Complex Geometry, Chinese University of Hong Kong, 18-19 April 2013
Chang, Huai-Liang


Expand All Collapse All


Article 1

Gromov-Witten Invariants of Stable Maps with Fields
International Mathematics Research Notices, v. 2012, (18), January 2012, p. 4163-4217
Chang, Huai-Liang; Li, Jun

Conference paper 4

Algebraic geometric construction of Gun-Sharpe-Witten model and Fan-Jarvis-Ruan Witten theory

Chang, Huai-Liang
Introduction to Gromov Witten and Fan Jarvis Ruan Witten Theory (I,II)
Mini-course in differential geometry, National Center for Theoretical Science, Hsinchu, Taiwan, July, 2012
Chang, Huai-Liang
Introduction to Gromov Witten and Fan-Jarvis-Ruan-Witten theory
Kavli Institute for the Physics and Mathematics of the Universe, Tokyo University, Tokyo, Japan, June 2012
Chang, Huai-Liang
The conference of Mirror Symmetry and Related Topics (MSRT)

Chang, Huai-Liang


Expand All Collapse All


Article 1

Semi-perfect obstruction theory and Donaldson–Thomas invariants of derived objects
Communications in Analysis and Geometry, v. 19, (4), 2011, p. 807-830
Chang, Huai-Liang; Li, Jun

Conference paper 7

Algebraic geometry of A-twsited Landau Ginzburg theory
National Seoul University, January 2011
Chang, Huai-Liang
Algebraic geometry of A-twsited topological string theory of Landau Ginzburg type
Peking University, 27 May 2011
Chang, Huai-Liang; Li, Jun
Introduction to Fan-Jarvis-Ruan-Witten theory
Taida Institue for Mathematical Sciences, Taiwan, January 2011
Chang, Huai-Liang
Moduli of stable maps with elds and its applications
Workshop on Moduli and Birational Geometry, Pohang, Korea, July 2011
Chang, Huai-Liang
On Algebra-geometric proof of Li-Zinger Conjecture for g=1 Gromov-Witten invariant of Quintic Calabi-Yau threefold

Chang, Huai-Liang; Li, Jun
On Algebro-geometric proof of Li-Zinger Conjecture for g=1 Gromov-Witten invariant of Quintic
National Cheng Kung University, December 2011
Chang, Huai-Liang; Li, Jun
Toward Algebraic geometry of Gauged Linear Sigma model in A side
Taida Institue for Mathematical Sciences, Taiwan, January 2011
Chang, Huai-Liang


Expand All Collapse All


Conference paper 3

On Donaldson-Thomas invariants of P1 scroll
Yat-Sen University School of Mathematics and Computational Science, Guangzhou, July 2010
Chang, Huai-Liang
On genus one Gromov Witten invariant of Quintic threefold
Hong Kong Math Society Annual General Meeting, March 2010
Chang, Huai-Liang
Toward algebraic geometry behind Gauged Linear Sigma model in all genus
InternationalCongress of Chinese Mathematicans, Peking, December 2010
Chang, Huai-Liang


Expand All Collapse All


Conference paper 1

Donaldson Thomas invariants
Hong Kong Geometry Colloquium, CUHK, September 2009
Chang, Huai-Liang


Expand All Collapse All


Article 1

Characterization of maps having the KKM property
SOOCHOW JOURNAL OF MATHEMATICS, v. 28, (3), July 2002, p. 329-338
Jeng, Jyh-Chung; Huang, Young-Ye; Chang, Huai-Liang


Expand All Collapse All


2015 3

An algebraic proof of the hyperplane property of the genus one GW-invariants of quintics
Journal of Differential Geometry, v. 100, (2), June 2015, p. 251-299
Chang, Huai-Liang; Li, Jun Article
Witten’s top Chern class via cosection localization
Inventiones Mathematicae, v. 200, (3), June 2015, p. 1015-1063
Chang, Huai-Liang; Li, Jun; Li, Wei Ping Article
MSP fields and Gromov Witten invariants of Quintic Calabi Yau threefold
MSP fields and Gromov Witten invariants of Quintic Calabi Yau threefold, Institute of Mathematics Academia Sinica, Taiwan, January 2015
Chang, Huai-liang Conference paper

2014 5

A Vanishing Result for Donaldson Thomas Invariants of P-1 Scroll
Acta Mathematica Sinica, English Series, v. 30, (12), December 2014, p. 2079-2084
Chang, Huai-Liang Article
Algebro-geometric approach toward higher genus GW invariants of Quintics
Calabi-Yau Geometry and Mirror Symmetry conference, National Taiwan University, Taipei, Taiwan, 6-10 January 2014
Chang, Huai-Liang Conference paper
Landau Ginzburg type theories from algebraic geometry
The Hong Kong Mathematical Society Annual General Meeting 2014, Hong Kong Polytechnic University, 6 June 2014
Chang, Huai-Liang Conference paper
Landau Ginzburg Type Theories from Algebraic Geometry
The International Mathematical Meeting and the Annual Meeting of the Taiwanese Mathematical Society (2014 AMMS), National Cheng Kung University, Taiwan, 6-7 December 2014
Chang, Huai-Liang Conference paper
Physics motivation and a fast Introduction to theories of P fields and Spin-curves
The Third Advanced Seminar on Symplectic Geometry and Topological Field Theory, Beijing International Center for Mathematical Research, 1-5 December 2014
Chang, Huai-Liang Conference paper

2013 4

Poincaré invariants are Seiberg–Witten invariants
Geometry & Topology, v. 17, (2), 2013, p. 1149-1163
Chang, Huai-Liang; Kiem, Young-Hoon Article
On A twisted Landau-Ginzburg Type Theory
Scuola Internazionale Superiore di Studi Avanzati(SISSA), Trieste, Italy, August 2013
Chang, Huai-Liang; Li, Jun; Li, Wei Ping Conference paper
On Algebraic Geometric Construction of Enumerative Invariants
University of Michigan, US, Feb 2013
Chang, Huai-Liang Conference paper
Witten's Top Chern Class Revisited
International Workshop on Complex Geometry, Chinese University of Hong Kong, 18-19 April 2013
Chang, Huai-Liang Conference paper

2012 5

Gromov-Witten Invariants of Stable Maps with Fields
International Mathematics Research Notices, v. 2012, (18), January 2012, p. 4163-4217
Chang, Huai-Liang; Li, Jun Article
Algebraic geometric construction of Gun-Sharpe-Witten model and Fan-Jarvis-Ruan Witten theory

Chang, Huai-Liang Conference paper
Introduction to Gromov Witten and Fan Jarvis Ruan Witten Theory (I,II)
Mini-course in differential geometry, National Center for Theoretical Science, Hsinchu, Taiwan, July, 2012
Chang, Huai-Liang Conference paper
Introduction to Gromov Witten and Fan-Jarvis-Ruan-Witten theory
Kavli Institute for the Physics and Mathematics of the Universe, Tokyo University, Tokyo, Japan, June 2012
Chang, Huai-Liang Conference paper
The conference of Mirror Symmetry and Related Topics (MSRT)

Chang, Huai-Liang Conference paper

2011 8

Semi-perfect obstruction theory and Donaldson–Thomas invariants of derived objects
Communications in Analysis and Geometry, v. 19, (4), 2011, p. 807-830
Chang, Huai-Liang; Li, Jun Article
Algebraic geometry of A-twsited Landau Ginzburg theory
National Seoul University, January 2011
Chang, Huai-Liang Conference paper
Algebraic geometry of A-twsited topological string theory of Landau Ginzburg type
Peking University, 27 May 2011
Chang, Huai-Liang; Li, Jun Conference paper
Introduction to Fan-Jarvis-Ruan-Witten theory
Taida Institue for Mathematical Sciences, Taiwan, January 2011
Chang, Huai-Liang Conference paper
Moduli of stable maps with elds and its applications
Workshop on Moduli and Birational Geometry, Pohang, Korea, July 2011
Chang, Huai-Liang Conference paper
On Algebra-geometric proof of Li-Zinger Conjecture for g=1 Gromov-Witten invariant of Quintic Calabi-Yau threefold

Chang, Huai-Liang; Li, Jun Conference paper
On Algebro-geometric proof of Li-Zinger Conjecture for g=1 Gromov-Witten invariant of Quintic
National Cheng Kung University, December 2011
Chang, Huai-Liang; Li, Jun Conference paper
Toward Algebraic geometry of Gauged Linear Sigma model in A side
Taida Institue for Mathematical Sciences, Taiwan, January 2011
Chang, Huai-Liang Conference paper

2010 3

On Donaldson-Thomas invariants of P1 scroll
Yat-Sen University School of Mathematics and Computational Science, Guangzhou, July 2010
Chang, Huai-Liang Conference paper
On genus one Gromov Witten invariant of Quintic threefold
Hong Kong Math Society Annual General Meeting, March 2010
Chang, Huai-Liang Conference paper
Toward algebraic geometry behind Gauged Linear Sigma model in all genus
InternationalCongress of Chinese Mathematicans, Peking, December 2010
Chang, Huai-Liang Conference paper

2009 1

Donaldson Thomas invariants
Hong Kong Geometry Colloquium, CUHK, September 2009
Chang, Huai-Liang Conference paper

2002 1

Characterization of maps having the KKM property
SOOCHOW JOURNAL OF MATHEMATICS, v. 28, (3), July 2002, p. 329-338
Jeng, Jyh-Chung; Huang, Young-Ye; Chang, Huai-Liang Article


No Publications






Teaching Assignment

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2021-22 Winter 0 2021-22 Fall 2 2020-21 Summer 0 2020-21 Spring 1 2020-21 Winter 0 2020-21 Fall 1

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MATH1013 Calculus IB
MATH6913O Reading Course: R Matrix Theory for Frobenius Manifolds


MATH3131 Honors in Linear and Abstract Algebra II


MATH1013 Calculus IB


No Teaching Assignments


No Teaching Assignments


No Teaching Assignments






Research Postgraduate (RPG) Supervision From January 2019 to December 2022 (As of 30 January 2022)

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Current RPGs

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Doctor of Philosophy ZHANG, Huaigong
Mathematics( 2021 - )

WANG, Zhiyong
Mathematics( 2017 - )









ProjectsFrom January 2020 to December 2022

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All Projects 4 Leading Projects 3 Participating Projects 1

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Gromov-Witten Invariants for Complete-Intersections Calabi-Yau Manifolds


全相交卡拉比-丘流形的Gromov Witten不变量 Leading


RGC - General Research Fund


Project Team (HKUST)
CHANG Huai-Liang (Lead)


2021 -




Feynman graph structures of quantumn singularity invariants of Fermat type


费马奇异点的量子不变量和其内部的费曼图结构 Leading


RGC - General Research Fund


Project Team (HKUST)
CHANG Huai-Liang (Lead)


2019 -




The mixed-spin P-field theory of stable quotients


稳定商的混合带旋P场的理论 Participating


RGC - General Research Fund


Project Team (HKUST)
LI Weiping (Lead)
CHANG Huai-Liang


2018 -




Algebraic construction of Fan-Jarvis-Ruan-Witten virtual cycle with broad sectors


可带广义边界条件 FJRW 不变量的代数构造 Leading


RGC - General Research Fund


Project Team (HKUST)
CHANG Huai-Liang (Lead)


2018 - 2021