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Research

Colloquium

【Science Lecture】Applications of matrix theory in combinatorics, and some contrasting approaches

Speaker: Richard M. Wilson(California Institute of Technology)
Time: May 16, 2024, 15:00-16:00
Location: M1001, College of Science Building

Abstract

We discuss some combinatorial subjects in, or related to, "extremal set theory", and which have been solved or approched using matrix theory. This would include the Erdos-Ko-Rado theorem, Fisher's inequality for designs, and a result on families of subsets with restricted intersections called the Frankl-Wilson inequality. It is also interesting to look at these subjects and results in other ways. For example, Fisher's inequality has a well-known proof with matrices, but this was not the way that Fisher first proved it (with a simple counting argument).

Biography

Richard M. (Rick) Wilson received his Ph.D. in 1969 from The Ohio State University, working under D. K. Ray-Chaudhuri. He remained there on the faculty for 11 years and then moved to the California Institute of Technology (Caltech). He is retired but remains a Professor Emeritus.In 1975 he was awarded the Polya Prize for his work on combinatorial designs. This subject has remained a main interest, but he strives to be diverse and has published papers on the related subjects of extremal set theory, coding theory, graph theory, linear algebra, and finite fields.Rick is the co-author (with J. H. van Lint) of a popular graduate level textbook "A Course in Combinatorics". He has been received three awards for excellence in teaching from the Associated Students of Caltech and has supervised 29 Ph.D. students.