Fan Chung

In 1974, Fan Chung graduated from the University of Pennsylvania and became a member of Technical Staff working for the Mathematical Foundations of Computing Department at Bell Laboratories 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,[2] 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.

Usually with positions in management you obtain more influence and you certainly have more power to make decisions. But I do not want people to respect me because of that power. I'd rather win their admiration because of the mathematics I'm doing.

— Fan Chung, in Donald J. Albers, Making Connections: A Profile of Fan Chung, Math Horizons, September 1995, 14–18[3]

In 1990, she was one of the first to receive a Bellcore university fellowship, a sabbatical she spent at Harvard university.

After twenty years of work at Bell Laboratories and Bellcore, Chung decided to go back to the University of Pennsylvania to become a professor of mathematics. In 1998, she was named Distinguished Professor of Mathematics at the University of California, San Diego.[4]

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.”[5]

Chung's life was profiled in the 2017 documentary film Girls who fell in love with Math.[6]

In 2012, she became a fellow of the American Mathematical Society.[7]

Chung was an American Mathematical Society (AMS) Council member at large.[8]

Chung has two children; the first child was born during her graduate studies from her first marriage.[9][1]

Fan Chung's first marriage ended in divorce in 1982. However, when she worked at Bell Laboratories, she met Ronald Graham. 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.[10]

Both Chung and Graham were close friends of the mathematician Paul Erdős, and have both published papers with him – 13 in her case;[11] thus, both have Erdős numbers of one. In 1998, Graham and Chung co-wrote the book Erdős on Graphs.[4]

Among Fan Chung's publications, her contributions to spectral graph theory 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 spectral graph theory 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 studies how the spectrum of the Laplacian of a graph is related to its combinatorial properties.".

In 1997, the American Mathematical Society published Chung's book Spectral graph theory. This book became a standard textbook at many universities and is the key to study Spectral graph theory for many mathematics students who are interested in this area. Fan Chung's study in the spectral graph theory brings this “algebraic connectivity” of graphs into a new and higher level.[4]

Fan Chung's work in random graph models shed new light on the field of network science. 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. 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.[13] 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.

Fan Chung, together with Ronald Graham 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.

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 Paul Erdős, 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.