W-operators and generating functions of hurwitz numbers
Sun, Hao
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https://hdl.handle.net/2142/101336
Description
Title
W-operators and generating functions of hurwitz numbers
Author(s)
Sun, Hao
Issue Date
2018-04-18
Director of Research (if dissertation) or Advisor (if thesis)
Bergvelt, Maarten
Doctoral Committee Chair(s)
Kedem, Rinat
Committee Member(s)
Di Francesco, Philippe
Nevins, Thomas
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
W-operator, Hurwitz number, Cut-and-join operator
Abstract
This thesis is motivated by the W-operators introduced by Mironov et al. We prove that the W-operators are generalizations of the cut-and-join operator studied by Goulden and Jackson. We give a new description of the structure of W-operators, using the combinations of symmetric groups. As an application, we prove new formulas about generating functions of connected Hurwitz numbers and give topological recursion formulas for d-Hurwitz numbers.
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