### CHAO, Kuok Fai 周國暉

#### Affiliation

Lui Che Woo College

#### Tel

+853 8822 9139

#### Office

Room G041

Lui Che Woo College

University of Macau, W22

Avenida da Universidade

Taipa, Macau, China

### CHAO, Kuok Fai 周國暉 (Prof.)

Associate Master, Lui Che Woo College

#### Academic Qualifications

PhD in Pure Mathematics, The University of Manchester, United Kingdom

MSc in Pure Mathematics with Distinction, The University of Manchester, United Kingdom

Bachelor of Science, Sun Yat-Sen University, China

#### Research Interests

Representation Theory of real and p-adic groups

Langlands Programme

Non-commutative Geometry

#### Teaching Areas

**Courses Designed and Taught for undergraduate students**

General Mathematics

Number Theory

Algebra

Galois Theory

Information Theory and Coding

Topological Groups

Harmonic Analysis on Locally Compact Groups

Advanced Topics in Algebra

**Courses Designed and Taught for postgraduate students**

Algebraic Number Theory

Analytic Number Theory

Lie Groups and Lie Algebras

Group Representation Theory

#### Working Experiences

Associate Master, Lui Che Woo College, University of Macau, China

2016-2021

Associate Professor, Department in Mathematics, College of Sciences, Shanghai University, China

2013-2016

Associate Research Fellow, Shanghai Center for Mathematical Science and Fudan University, China

2011-2013

Postdoctoral Fellow, Academy of Mathematics and Systems Science and Morningside Center of Mathematics, Chinese Academy of Sciences, China

2010-2011

Postdoctoral Fellow, National Sun Yat-sen University, Taiwan, China

Visiting scholar, The School of Mathematics and Statistics, Henan University, China

Jul 2018

Visiting scholar, School of Mathematics and Statistics, University of Sheffield, United Kingdom

Dec 2017

Visiting scholar, School of Mathematical Sciences, University of Adelaide, Australia

Apr 2017

Visiting scholar, The School of Mathematics and Statistics, Henan University, China

Nov 2016

Visiting scholar, Research Center for Operator Algebras, East China Normal University, China

Jul 2015

Visiting scholar, School of Mathematical Sciences, University of Adelaide, Australia

Nov 2014

Visiting scholar, Morningside Center of Mathematical Science, Chinese Academy of Science, China

May 2014

Visiting scholar, School of Mathematics, Hunan University, China

Jun 2013

Visiting scholar, Department of Mathematics, University of Manchester, United Kingdom

Nov – Dec 2012

Visiting scholar, Department of Applied Mathematics, National Sun Yat-Sen University, Taiwan, China

Oct – Dec 2012

Visiting scholar, Mathematical Sciences Center, Tsinghua University, Beijing, China

Jun 2012

Visiting scholar, Department of Mathematics, University of Macau, China

2006 – 2009

Junior member, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, United Kingdom

- AMS MathSciNet Reviewer
- Member of American Mathematical Society
- Journal Reviewers: Ramanujan Journal, Research in Number Theory, Integers and etc.
- Founding President, Macau Association for Youth Scientists, 2023 –
- Advisor, The Committee on Inter-College Affairs (CICA), 2023-2024
- Deputy Advisor, The Committee on Inter-College Affairs(CICA), 2022-2023

**Academic Talks**

- National Conference on Number Theory, Jintan, China, 2021
- Workshop on Number Theory and Automorphic Forms, Soochow University, Suzhou, China, 2020
- Seminar, East China Normal University, Shanghai, China, 2019
- International Workshop on Operator Theory and Applications, Shanghai, China,2018
- Workshop on Noncommutative Geometry and Representation Theory, Sichuan University, Chengdu, China, 2018
- Seminar, Henan University, Kaifeng, China, 2017
- Workshop for Modern Mathematics, University of Macau, Macau, China, 2017
- Fudan-KAIST Workshop on Algebra and Geometry, Dajeon, Korea, 2016
- Seminar, Zhejiang University, Hangzhou, China, 2016
- p-adic day, Fudan University, Shanghai, China, 2014
- Seminar, Hunan University, Changsha, China, 2014
- International Conference on Banach methods in Noncommutative Geometry, Wuhan, China, 2014
- Series Lectures on decent method for classical groups, Mathematical Sciences Center, Tsinghua University, China 2013
- China-Japan Conference on Noncommutative Geometry and K-Theory, Changchun, China, 2013
- 2nd Youth Forum of Algebra, Wen-Tsun Wu Key Laboratory of Mathematics, Anhui, China, 2012
- Series Lectures on representation theory and index theory, Mathematical Sciences Center, Tsinghua University, China, 2012
- International Conference on Galois Representations, Automorphic Forms and Shimura Varieties, NCTS, Taiwan, China, 2011
- Workshop on Automorphic Forms and Representations, AMSS, CAS, Beijing, China 2011
- Seminar, Sichuan University, Sichuan, China, 2011
- Seminar, University of Luxembourg, Luxembourg, 2010
- Seminar, Center for Theoretical Sciences (South), Taiwan, China, 2010
- Series Lectures on p-adic representations, Center for Theoretical Sciences (South), Taiwan, China, Sept-Dec, 2010
- Seminar, National Sun Yat-sen University, Taiwan, China, 2010
- 46th K-theory day, University of Manchester, UK, 2008
- 44th K-theory day, University of Manchester, UK, 2007

**Conferences Attended (selected)**

- IASM-BIRS Workshop on Arthur Packets, Hangzhou, China, 2023
- National Conference on Number Theory, Jintan, China, 2021
- Workshop on Representations of Reductive Groups, Shanghai Jiao Tong University, Shanghai, China, 2021
- Workshop on Number Theory and Automorphic Forms, Soochow University, Suzhou, China, 2020
- Workshop on Noncommutative Geometry and Representation Theory, Chengdu, China, 2018
- International Workshop on Operator Theory and Applications, Shanghai, China, 2018
- International Conference on Matrix Inequalities and Matrix Equations, Shanghai, China, 2018
- 2017 Noncommutative Geometry Conference, Fudan University, China, 2017
- Fudan-KAIST Workshop on Algebra and Geometry, Dajeon, Korea, 2016
- Representation Theory, Number theory, and Invariant Theory, Yale University, New Haven, Connecticut, US, 2015
- International Conference on Functional Analysis, Hangzhou, China, 2014
- International Conference on Banach methods in Noncommutative Geometry, Wuhan, China, 2014
- Further Development of Atiyah-Singer Theorem and K-theory, Kyoto University, Japan, 2013
- China-Japan Conference on Noncommutative Geometry and K-Theory, Changchun, China, 2013
- International Consortium of Chinese Mathematicians, Taipei, Taiwan, China, 2013
- Workshop on Automorphic Forms, CAS, Beijing, China, 2012
- Non-Commutative Geometry, Fudan University, Shanghai, China, 2012
- 2nd Youth forum of algebra, Wen-Tsun Wu key laboratory of mathematics, University of Science and Technology of China, Anhui, China, 2012
- The Third Pan Asian Number Theory Conference, AMSS, CAS, China, 2011
- Workshop on Automorphic Forms and Representations, AMSS, CAS, China, 2011
- NCTS International Conference on Galois Representations, Automorphic Forms and Shimura Varieties, National Tsing-Hua University, Hsinchu, Taiwan, 2011
- NCTS Serre lecture on Sato-Tate conjecture, National Tsing-Hua University, Hsinchu, Taiwan, China 2011
- NSYSU-CUHK Workshop in Modern Mathematics, Taiwan, China, 2010
- Fifth National Conference on Number Theory, Zhaoqing, Guandong, China, 2010
- Eighth Annual NCGOA Spring Institute, Vanderbilt University, Tennessee, US, 2010
- Lie theory and representation, Isaac Newton Institute Workshop, Cambridge, UK, 2009
- New Direction in Non-Commutative Geometry, Manchester, UK, 2008
- Sixth Annual NCGOA Spring Institute, Vanderbilt University, Tennessee, US, 2008
- Geometric Langlands conjecture, University of Oxford, UK, 2007
- K-theory school, Sedano, SPAIN, 2007
- Noncommutative Geometry and Cyclic Cohomology, Isaac Newton Institute Workshop, Cambridge, UK, 2006

- J.-F. Xie, K. F. Chao, A note on 3-divisibility of class number of quadratic fields, Chinese Annals of Mathematics, Ser. B, 43, pages307–318 (2022)
- J. W. Zhang, K. F. Chao, On the construction of K_0 group for C∗ algebra of finite groups, Journal of Shanghai University, 2021.
- J. F. Xie, K. F. Chao, On the divisibility of class numbers of imaginary quadratic fields (Q(sqrt{D}), Q(sqrt{D+m})) The Ramanujan Journal, 2020, vol 53, 517-528.
- K. F. Chao, K. F. Lai, Buildings and groups II, Chinese Quarterly Journal of Mathematics 2020,Vol 35, No. 3 p.221-254.
- K. F. Chao, H. Wang, Langlands Functorality in K-theory for C∗-algebras. I. Base Change, Journal of Noncommutative Geometry, 11 (2017), 1001-1036.
- K. F. Chao, W. W. Li, Dual R-group of inner forms of SL(N), Pacific Journal of Mathematics, Vol 267, No. 1, 2014, pp.35-90.
- K. F. Chao, R. Plymen, Geometric structure in the tempered dual of SL(4), Bulletin London Math. Soc.44 (2012) 460-468.
- K. F. Chao, Geometric structure in the tempered dual of SLl(F): toral case, Bulletin of the Australian Mathematical Society December 2011, 84 : pp. 425-432.
- K. F. Chao, R. Plymen, A new bound for smallest x with π(x) > li(x), International Journal of Number Theory, Volume: 6, Issue: 3(2010) pp. 681-690.
- K. F. Chao, S. Tao, W. Yang, Trend forecast of COVID-19 outbreak based on Gompertz-ARIMA time series models, completed.
- K. F. Chao, K. F. Lai, Norm field and algebraic tori, submitted.

**Books**

- K. F. Lai, Z. J. Bai, K. F. Chao , “Advanced linear algebra”(高等線性代數學), Higher Education Press, ISBN 978-7-04-0410570-0.
- L. Z. Ji, K. F. Lai, Z. B. Liang, K. F. Chao, “Theory of Buildings and Applications in Geometry and Topology”(樓理論及其在几何和拓扑中的應用), Higher Education Press, to appear.

**Book Sections (Translations)**

- R. Langlands, “Langlands Program and his mathematical world”(朗蘭茲綱領及其數學世界), Higher Education Press, ISBN 978-7-04-049929-2.

__Grant__

- National Natural Science Fundation of China, Grant no: 11401105, “On the Local Langlands correspondences, representation of p-adic groups, K-theory and related topics”.

**Awards and Hounors**

- Finalist for top 10 of the best supervisors, Shanghai University, 2021
- K.C.Wong Postdoctoral fellow scholarship, Chinese Academy of Science, 2012
- Full PhD scholarship of School of Mathematics, University of Manchester, 2005
- Meritorious Winner, USA Interdisciplinary Contest in Modeling (ICM), 2004
- Scholarship of excellent student in Sun Yat-sen University, 2003
- First prize, China Undergraduate Mathematical Contest in Modeling, 2003
- First prize of excellent freshman, Sun Yat-sen University, 2000
- Contestant of International Mathematical Olympiad (IMO), 2000
- Top Six of Macau Mathematical Olympiad, 2000

- Supervisor of “The training plan of top-notch talent”, School of Mathematical Science, Fudan University;
- Supervisor of seminar in Number Theory, Shanghai Center for Mathematical Science;
- Supervisor of seminar in Number Theory, and Representation Theory, Shanghai University;
- Supervisor of ”Mathematics Forum for undergraduate”, Shanghai University;
- Supervisor of Undergraduate Seminar in mathematics, Shanghai University;
- Coach of China National Team of Mathematical Olympic 2017.
- Supervisions: 3 master degree students’ dissertation
- Supervisions: 11 undergraduate students’ dissertation

**Student Awards under my supervision**

- Finalist, USA Mathematical Contest In Modeling, 2021
- Honornable Mention, USA Interdisciplinary Contest In Modeling, 2021
- Third Prize (Two teams), China Undergraduate Mathematical Contest in Modeling, 2021
- Third Prize, ”HUAWEI Cup” National Graduate Student Mathematical Contest in Modeling, 2021
- Successful Participants (Three Teams), USA Interdisciplinary Contest In Modeling, 2024
- Second Prize, “Zhengda Cup” 14th National University Student Market Research and Analysis Competition, 2024