Research Interests

• Complex Algebraic Geometry
  • Algebraic Models for Riemann Surfaces
  • Belyi Surfaces and Dessins D'Enfants
  • Automorphism Groups of Compact Riemann Surfaces
• Group Theory
  • Finite Groups (Group Actions and Structure Theory)
  • Finitely Presented Groups
• Geometric Group Theory
  • Discrete Groups (Fuchsian Groups and Fundamental Groups)
  • Mapping Class Groups of Compact Connected Surfaces

Recent Publications

• "The Genus Level of a Group" (with M. Arbo, K. Benkowski, B. Coate, H. Norsdtrom & C. Peterson) Involve, A Journal of Mathematics, Vol. 2 (2009), No. 3, 323--340
• "Topologically Unique Maximal Elementary Abelian Group Actions on Compact Oriented Surfaces" (with S. Allen Broughton) Journal of Pure and Applied Algebra, 213 (2009), no. 4, 557--572

Preprints and Works in Progress

• "Full Automorphism Groups of Cyclic n-gonal Surfaces" (with S. A. Broughton)
• "On Gonality of Surfaces" (with A. Weaver & G. Gromadzki)
• "Bounding the Number of Topological Group Actions on a Compact Oriented Surfaces" (with J. W. Anderson)
• "Quasiplatonic Cyclic n-gonal Surfaces" (with S. A. Broughton)
• "Topological Classification of the cyclic p-gonal locus"

Undergraduate Research (both collaborative and as a mentor)

• "Groups of Genus Level 1 and 2", Chris Peterson, Ben Coate, Kristin Benkowski, Matthew Arbo, Michael Sawdy, University of Portland REU, Summer 2007 (collaborative work with H. Nordstrom)
• "Classification of Quasplatonic Abelian Groups and Signatures", Robert Benim, University of Portland, Academic Year 2006-07. Awarded best honors thesis 2007 (University of Portland), and published in Rose-Hulman Undergraduate Journal of Mathematics (faculty mentor).
• "Cryptography Using Non-Abelian Groups", Emile Doering, University of Arizona, Fall 2004 (faculty mentor)
• "A Study of "Primes is in P," Jeff Gilbert, University of Arizona, Fall 2004 (faculty mentor)

Selected Seminar Talks

• "Bounding the Number of Group Actions on a Surface of Fixed Genus," AMS Eastern Sectional Meeting, Pennsylvania State University, University Park, October 2009
• "Cyclic n-gonal Surfaces," (Invited) 25th Nordic and 1st British-Nordic Congress of Mathematicians, Oslo, Norway, June 2009
• "Quasiplatonic Cyclic n-gonal Surfaces," (Invited) ICMS Workshop, Edinburgh, September 2008
• "Finite Abelian Group Actions on Closed Oriented Surfaces," (Invited) Southampton University Mathematics Colloquium, May 2008
• "Determining defining equations for compact Riemann surfaces which admit non-trivial automorphisms," (Invited) Rice University Algebraic Geometry Seminar, October 2006
• "Finite Subgroups of the Mapping Class Group," (Invited) Oregon State University, Math Colloquium, June 2006