Francis G. Garvan (born March 9, 1955) is an Australian-born mathematician who specializes in number theory and combinatorics. He holds the position Professor of Mathematics at the University of Florida.[1] He received his Ph.D. from Pennsylvania State University (January, 1986) with George E. Andrews as his thesis advisor.[2] Garvan's thesis, Generalizations of Dyson's rank, concerned the rank of a partition[3] and formed the groundwork for several of his later papers.[4]
Garvan is well-known for his work in the fields of q-series and integer partitions. Most famously, in 1988, Garvan and Andrews discovered a definition of the crank of a partition.[5] The crank of a partition is an elusive combinatorial statistic similar to the rank of a partition which provides a key to the study of Ramanujan congruences in partition theory. It was first described by Freeman Dyson in a paper on ranks for the journal Eureka in 1944.[6] Andrews and Garvan's definition was the first definition of a crank to satisfy the properties hypothesized for it in Dyson's paper.