CHAO KUOK FAI, Coffee 周國暉

—This masterpiece was created by my wife, Tiana, nearly twenty years ago.

Associate Master of Lui Che Woo College

University of Macau

Email: kchao@um.edu.mo
Office: G041, Lui Che Woo College
University of Macau, W22
Avenida da Universidade
Taipa, Macau, China

The most amazing formula in the world

About ME

I am a mathematician (by definition, a person who is engaging with mathematics daily). Born and raised in Macau, China, I currently serve as the Associate Master of Lui Che Woo College at the University of Macau. I earned my bachelor’s degree from Sun Yat-Sen University in China, followed by a master’s degree and a doctorate in Pure Mathematics from the University of Manchester under supervision by Prof. Roger Plymen. Before joining the University of Macau, I have been working in National Sun Yat-Sen University, Morningside Center of Mathematics(晨興數學中心) at Chinese Academy of Sciences, Shanghai Center for Mathematical Sciences(上海數學中心) at Fudan University, and Shanghai University respectively. I am grateful to have several important mentors, including Prof. Lai King Fai, Prof. Xi Nanhua, Prof. Tian Ye, Prof. Anne Marie-Aubert and Prof. Paul Baum.

My research interests include Number Theory, Non-Commutative Geometry, Group Representation Theory, and related topics. Primarily, I am focused on the Langlands Program (朗蘭茲綱領). Additionally, I am pleased to supervise students in mathematical modeling and mathematics competitions in our college (of course, other colleges as well). If you have an interest in studying mathematics, particularly in the areas of number theory and algebra, please come to my office for a talk.

I have a strong passion for sports, especially badminton and basketball, along with a love for coffee and mathematics. I warmly invite you to visit my office for discussions on mathematical concepts, to exchange coffee-making tips, or to practice badminton together. Your interests are always welcome! By the way, I am an avid lover of mathematics books.

At LCWC, we offer various workshops on LaTeX, mathematical modeling, and mathematics sharing. One thing should be mentioned is that I have a blackboard in my office for discussions. Please feel free to join us! You can also find me around the corner at the college.

Here is a list of my mathematics heroes:

• Leonhard Euler 
• Carl Friedrich Gauss 
• Bernhard Riemann 
• André Weil 
• Alexander Grothendieck
• Hua Loo-keng (華羅庚)
• Jean-Pierre Serre 
• Robert Langlands 

Teaching Areas

Over the years, I have taught several courses for both undergraduate and postgraduate students, primarily focusing on algebra, number theory, and Lie theory.

Courses Designed and Taught for undergraduate students

• General Mathematics
• Calculus
• 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

Publications

My research spans a variety of fields, such as analytic number theory, algebraic number theory, the Langlands program, and the representation theory of real and p-adic groups, as well as their relationships with non-commutative geometry.

Academic Journal papers:

• 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 SL_l(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.

Academic Books:

I have written two textbooks, which are all published by Higher Education Press (高等教育出版社)

«Advance Linear Algebra (高等線性代數學) »with Lai King Fai (黎景輝), and Bai Zhengjian(白正簡) in 2014

This is an advanced textbook for students studying linear algebra, including topics such as tensor algebras, (co)homology and module theory.

«Theory of Buildings and Applications in Geometry and Topology (樓理論及其在几何和拓扑中的應用)»  with Ji Lizhen(季理真), Lai King Fai (黎景輝) and Liang Zhibin(梁志斌) in 2024

This book is designed for advanced students to explore the beautiful theory by Jacquet Tits, known as “Building Theory”. This theory is highly valuable for the study of Lie theory and the representation theory of p-adic groups.

«Langlands Program and his mathematical world (Langlands 綱領和他的數學世界)» 

I also contributed to a translation for a collection of Robert Langlands’ papers, some of which were selected by Langlands himself. He also wrote a notable 38-page preface for this volume. This book provides valuable insights into the development of the Langlands Program and includes the famous letter to André Weil. We hope it will help more Chinese scholars and students gain a deeper understanding of the Langlands Program.

Academic Services and Social Services

Grant & Awards

Supervision

Supervision