Fan-Rong King Chung Graham (; born October 9, 1949), known professionally as Fan Chung, is a Taiwanese-born American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who works mainly in the areas of

spectral graph theory In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matri ...

extremal graph theory Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local ...

and

random graphs In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs ...

, in particular in generalizing the

Erdős–Rényi model In the mathematical field of graph theory, the Erdős–Rényi model is either of two closely related models for generating random graphs or the evolution of a random network. They are named after Hungarian mathematicians Paul Erdős and Alfr� ...

for graphs with general degree distribution (including

power-law In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one q ...

graphs in the study of large information networks). Since 1998, Chung has been the Paul Erdős Professor in Combinatorics at the

University of California, San Diego The University of California, San Diego (UC San Diego or colloquially, UCSD) is a public land-grant research university in San Diego, California. Established in 1960 near the pre-existing Scripps Institution of Oceanography, UC San Diego is ...

(UCSD). She received her doctorate from the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a Private university, private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest- ...

in 1974, under the direction of Herbert Wilf. After working at

Bell Laboratories Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial Research and development, research and scientific developm ...

and Bellcore for nineteen years, she joined the faculty of the University of Pennsylvania as the first female

tenure Tenure is a category of academic appointment existing in some countries. A tenured post is an indefinite academic appointment that can be terminated only for cause or under extraordinary circumstances, such as financial exigency or program disco ...

d professor in mathematics. She serves on the editorial boards of more than a dozen international journals. Since 2003 she has been the editor-in-chief of ''Internet Mathematics''. She has been invited to give lectures at many conferences, including the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rena ...

in 1994 and a plenary lecture on the mathematics of PageRank at the 2008 Annual meeting of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meeting ...

. She was selected to be a

Noether Lecturer The Noether Lecture is a distinguished lecture series that honors women "who have made fundamental and sustained contributions to the mathematical sciences". The Association for Women in Mathematics (AWM) established the annual lectures in 1980 as t ...

in 2009.

Biography

Fan Chung was born on October 9, 1949 in

Kaohsiung Kaohsiung City ( Mandarin Chinese: ; Wade–Giles: ''Kao¹-hsiung²;'' Pinyin: ''Gāoxióng'') is a special municipality located in southern Taiwan. It ranges from the coastal urban center to the rural Yushan Range with an area of . Ka ...

, Taiwan. Under the influence of her father, an engineer, she became interested in mathematics, especially in the area of

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

in high school in Kaohsiung. After high school, Chung entered the

National Taiwan University National Taiwan University (NTU; ) is a public research university in Taipei, Taiwan. The university was founded in 1928 during Japanese rule as the seventh of the Imperial Universities. It was named Taihoku Imperial University and served d ...

(NTU) to start her career in mathematics formally. While Chung was an undergraduate, she was surrounded by many female mathematicians, and this helped encourage her to pursue and study mathematics. After graduating from NTU with a B.S. in mathematics, Chung went on to the

to pursue a career in mathematics. There she obtained the highest score in the qualifying exam by a wide margin, catching the attention of Herbert Wilf, who would eventually become her doctoral advisor. Wilf suggested

Ramsey theory Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask ...

as a subject Chung could work on. During a single week studying material Chung had come up with new proofs for established results in the field. Wilf said: "My eyes were bulging. I was very excited. I asked her to go to the blackboard and show me. What she wrote was incredible! In just one week, from a cold start, she had a major result in Ramsey theory. I told her she had just done two-thirds of a doctoral dissertation." Chung was awarded a M.S. in 1972 and a Ph.D. two years later. By this time, she was married and had already given birth to her first child. The same year she received her Ph.D. and started working for the Mathematical Foundations of Computing Department at

in Murray Hill, New Jersey. The position at

was an opportunity to work with other excellent mathematicians, but also it contributed to her mathematical world powerfully. She has published many impressive mathematical papers, and published many joint papers with Ron Graham.

Bell Laboratories

In 1974, Fan Chung graduated from the

and became a member of Technical Staff working for the Mathematical Foundations of Computing Department at

in Murray Hill, New Jersey. She worked under Henry Pollak. During this time, Chung collaborated with many leading mathematicians who work for Bell Laboratories such as Ron Graham. In 1975, Chung published her first joint paper with Graham, ''On multicolor Ramsey numbers for complete bipartite graphs'', which was published in the ''Journal of Combinatorial Theory (Series B)''. In 1983 the Bell Telephone Company was split up. Since Pollak joined and became head of a research unit within a new company, he asked Chung to become Research Manager. She supervised many mathematicians in the unit. In 1990, she was one of the first to receive a Bellcore university fellowship, a sabbatical she spent at Harvard university.

Later career

After twenty years of work at

and

Bellcore iconectiv is a supplier of network planning and network management services to telecommunications providers. Known as Bellcore after its establishment in the United States in 1983 as part of the break-up of the Bell System, the company's name ...

, Chung decided to go back to the

to become a professor of mathematics. In 1998, she was named Distinguished Professor of Mathematics at the

.J J O'Connor and E F Roberson, ''Fan Rong K Chung Graham'', web
www-history.mcs.st-andrews.ac.uk/Biographies/Chung.html
Beyond her contributions to graph theory, Chung has used her knowledge to connect different fields of science. As she wrote in "Graph Theory in the Information Age", : “In the past decade, graph theory has gone through a remarkable shift and a profound transformation. The change is in large part due to the humongous amount of information that we are confronted with. A main way to sort through massive data sets is to build and examine the network formed by interrelations. For example, Google’s successful Web search algorithms are based on the WWW graph, which contains all Web pages as vertices and hyperlinks as edges. There are all sorts of information networks, such as biological networks built from biological databases and social networks formed by email, phone calls, instant messaging, etc., as well as various types of physical networks. Of particular interest to mathematicians is the collaboration graph, which is based on the data from Mathematical Reviews. In the collaboration graph, every mathematician is a vertex, and two mathematicians who wrote a joint paper are connected.” Chung's life was profiled in the 2017 documentary film ''Girls who fell in love with Math''. In 2012, she became a fellow of the

.List of Fellows of the American Mathematical Society
retrieved 2012-11-10.

Personal life

Chung has two children; the first child was born during her graduate studies from her first marriage. Fan Chung's first marriage ended in divorce in 1982. However, when she worked at

, she met

Ronald Graham Ronald Lewis Graham (October 31, 1935July 6, 2020) was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He ...

. During that time, they became close friends and published many joint papers in graph theory, eventually marrying in 1983. She was married to him until his death in 2020. In Paul Hoffman's book ''The Man Who Loved Only Numbers'', regarding her marriage with Graham, Chung said: :Many mathematicians would hate to marry someone in the profession. They fear their relationship would be too competitive. In our case, not only are we both mathematicians, we both do work in the same areas. So we can understand and appreciate what the other is working on, and we can work on things together and sometimes make good progress. Both Chung and Graham were close friends of the mathematician

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...

, and have both published papers with him – 13 in her case; thus, both have

Erdős number The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual ...

s of one. In 1998, Graham and Chung co-wrote the book ''Erdős on Graphs.''

Research

Chung has published more than 200 research papers and three books: * '' Erdős on Graphs: His Legacy of Unsolved Problems'' (with Ron Graham), A K Peters, Ltd., 1998, * ''Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92)'', American Mathematical Society, 1997, * ''Complex Graphs and Networks (CBMS Regional Conference Series in Mathematics, No. 107 " (with Linyuan Lu), American Mathematical Society, 2006,

Spectral graph theory

Among Fan Chung's publications, her contributions to

are important to this area of graph theory. From the first publications about undirected graphs to recent publications about directed graphs, Fan Chung creates the solid base in the

to the future graph theorist. Spectral graph theory, as one of the most important theories in graph theory, combines the algebra and graph perfectly. Historically, algebraic methods treat many types of graphs efficiently. Her work initiated a geometric approach to spectral graph theory with connections to differential geometry. According to the biography ''Fan Rong K Chung Graham'', "

Spectral graph theory In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matri ...

studies how the spectrum of the

Laplacian In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the ...

of a graph is related to its combinatorial properties.". In 1997, the

published Chung's book ''Spectral graph theory''. This book became a standard textbook at many universities and is the key to study

for many mathematics students who are interested in this area. Fan Chung's study in the

brings this “algebraic connectivity” of graphs into a new and higher level.

Network science

Fan Chung's work in random graph models shed new light on the field of

network science Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors rep ...

. Many real-world large information networks (such as Internet Graphs, Call Graphs, and Collaboration Graphs, etc.) have been observed to be well approximated by a

power law distribution In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one q ...

. Fan Chung's work in the Chung-Lu model, pioneered the theory of treating random graphs with arbitrary degree distributions, including the power law graphs. Her work provides a solid framework for quantitative and rigorous analysis for modeling and analyzing large complex networks. It also often serves as a popular benchmark for comparing new graph models in network science. In 2006, the American Mathematics Society and the Conference Board of the Mathematical Sciences co-published Fan Chung and Linyuan Lu's book ''Complex Graphs and Networks''. The book gave a well-structured exposition for using combinatorial, probabilistic, spectral methods as well as other new and improved tools to analyze real-world large information networks.

Quasi-random graphs

Fan Chung, together with

and Richard Wilson, introduced a strong notion of equivalence among graph properties through the control of error bounds and developed the theory of quasi-random graphs. In a series of research papers (with several coauthors), she showed that a large family of graph properties is equivalent in the sense that if a graph satisfies any one of the properties, it must satisfy all of them. The set of equivalent quasi-random properties includes a surprisingly diverse collection of properties, and therefore provides efficient methods for validating graph properties. Many (but not all) random graph properties are quasi-random. The notion of quasi-randomness has been extended to many other combinatorial structures, such as sequences, tournaments, hypergraphs and graph limits. In general, the theory of quasi-randomness gives a rigorous approach to 'random-like' or 'pseudorandom' alternatives.

Extremal graph theory

A basic question in extremal graph theory is to find unavoidable patterns and structures in graphs with given density or distribution. A complementary problem is to find a smallest graph which contains every member of a given family of graphs as subgraphs. In a series of work with

, Chung determined the sizes and structures of unavoidable graphs and hypergraphs. With several coauthors, she also derived many elegant and surprising results on universal graphs. Her fundamental contributions in these areas of extremal graph theory have many applications in parallel computations.

Awards and honors

* Allendoerfer Award of

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...

(1990) * Invited address,

(1994) *

Association for Women in Mathematics The Association for Women in Mathematics (AWM) is a professional society whose mission is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity for and the equal treatment o ...

(2009) * Fellow,

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, a ...

(1998) * Fellow, American Mathematics Society (2013) * Fellow,

Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific soci ...

(2015) * Academician,

Academia Sinica Academia Sinica (AS, la, 1=Academia Sinica, 3=Chinese Academy; ), headquartered in Nangang, Taipei, is the national academy of Taiwan. Founded in Nanking, the academy supports research activities in a wide variety of disciplines, ranging fro ...

(2016) *

Euler Medal The Institute of Combinatorics and its Applications (ICA) is an international scientific organization formed in 1990 to increase the visibility and influence of the combinatorial community. In pursuit of this goal, the ICA sponsors conferences, ...

Institute of Combinatorics and its Applications The Institute of Combinatorics and its Applications (ICA) is an international scientific organization formed in 1990 to increase the visibility and influence of the combinatorial community. In pursuit of this goal, the ICA sponsors conferences, ...

(2017) * She is included in a deck of playing cards featuring notable women mathematicians published by the Association of Women in Mathematics.

References

Sources

*''Notable Women in Mathematics, a Biographical Dictionary'', edited by Charlene Morrow and Teri Perl, Greenwood Press, 1998, pp. 29–34.

External links

Fan Chung's UCSD homepage

Agnes Scott College Agnes Scott College is a private women's liberal arts college in Decatur, Georgia. The college enrolls approximately 1,000 undergraduate and graduate students. The college is affiliated with the Presbyterian Church and is considered one of the ...

* *
Interview with Fan Chung created by Girls Talk Math
* {{DEFAULTSORT:Chung, Fan 1949 births 21st-century American mathematicians Living people Graph theorists Scientists from Kaohsiung National Taiwan University alumni Taiwanese emigrants to the United States University of California, San Diego faculty University of Pennsylvania alumni American women mathematicians Fellows of the American Mathematical Society Fellows of the American Academy of Arts and Sciences Fellows of the Society for Industrial and Applied Mathematics 20th-century Taiwanese mathematicians Chinese emigrants to the United States 20th-century women mathematicians 21st-century women mathematicians 20th-century American women scientists 21st-century American women scientists Members of Academia Sinica