# and Related Topics Interest Group

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### Automorphisms of Curves - University of Arizona, Tucson AZ - April 21-22, 2007

#### Organizers:

Description of the session: Automorphism groups of surfaces have been studied for many years with major results dating back to Klein and Wiman. In recent years there has been a major revival in this area mainly due to the great advances in computer algebra systems, such as GAP, and the advances in finite group theory such as the classification of finite simple groups. The goal of this session is to explore recent advances in this area and applications to other areas of mathematics. Topics of the session include, but are not limited to:

• Compact Riemann surfaces and their automorphisms,
• Hurwitz curves, and quasiplatonic surfaces,
• Klein surfaces and their automorphisms,
• Galois extensions of function fields,
• Finite subgroups of mapping class groups,
• Defining equations for surfaces,
• Strong symmetric genus of groups,
• Genus spectra of families of groups ,
• Automorphisms of curves of over arbitrary fields
• Applications to moduli and Teichm\"uller problems

#### List of talks oredered by presenter

 Presenter Title (click for abstract) Links Allen Broughton Classifying Pairs of Fuchsian Groups of Finite Type slides page Francisco Javier Cirre Double coverings of hyperelliptic real algebraic curves Marston Conder Combinatorial group-theoretic methods in the study of automorphisms of maps and surfaces Arsen Elkin On endomorphism algebras of hyperelliptic jacobians. Jose Javier Etayo The symmetric crosscap number of the groups $C_{m}\times D_{n}$ Frederick P. Gardiner Finite earthquakes and the associahedron paper Jane Gilman Canonical Forms for Conjugacy Classes of Prime Order Symplectic Matrices in Sp(2g,Z) Ernesto Girondo Triangle Fuchsian groups and surfaces with many automorphisms Darren Glass The relationship between p-ranks and automorphism groups Gabino Gonzalez-Diez Generalized Fermat curves. Michael Jackson Strong Symmetric Genus and Generalized Symmetric Groups of Type $G(n,3)$ Gareth Jones Complete bipartite maps, factorisations of groups, and generalised Fermat curves Sudeb Mitra Some metric properties of the Teichm\"uller space of a Riemann surface rel a closed subset Denis Sjerve Invariant Spin Structures on Riemann Surfaces Tom Tucker Gap-filling for the Symmetric Genus of a Group Anthony Weaver The largest non-genus of ${\Bbb Z}_{pq}$ and the Frobenius problem James S Wolper Vanishings of Theta on the Jacobian of Bring's Curve (Numerical Results) Aaron Wootton The Full Automorphism Group of a Cyclic $p$-gonal Surface