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.

References

  1. ^ "CURRICULUM VITAE: Francis G. Garvan" (PDF). qseries.org. 18 July 2016. Retrieved 7 April 2019.
  2. ^ "George Andrews' Students". sites.math.rutgers.edu. Retrieved 7 April 2019.
  3. ^ Garvan, Francis G. (May 1986). "1". Generalizations of Dyson's rank (Thesis). Retrieved 22 March 2019.
  4. ^ Garvan, Francis G. "Frank Garvan: List of Publications". Retrieved 22 March 2019.
  5. ^ Askey, Richard (1999). "The work of George Andrews: a Madison perspective" (PDF). Séminaire Lotharingien de Combinatoire. 42: Art. B42b, 24pp. MR 1701581.
  6. ^ Dyson, Freeman J. (1944). "Some Guesses in The Theory of Partitions". Eureka (Cambridge). 8: 10–15. ISBN 9780821805619.

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