Automorphisms of Riemann Surfaces and Related Topics
Pennsylvania State University, University Park, PA  October 2425, 2009
AMS Info, Organizers, Invitation and Abstract Submission
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.
Moreover the area has strong links to topology, number theory and
combinatorics in the area of Teichm\"uller spaces, mapping class groups and
the GrothendieckTeichm\"uller theory of Dessins D'enfants. 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:
Topics suggested for special attention at the Penn State conference
 more on the dictionary between categories e.g., finding the equation of surfaces
 group theoretic computational methods
 action of the mapping class group on Teichmuller space including actions on Teichmuller discs
 Kleinian Groups
 Veech groups
 Riemann surfaces and vector bundles  moduli spaces
 Riemann surfaces of infinite type
 Fields of definition and moduli fields
 Jacobians of curves with automorphisms
Tucson Topics
 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
Location of movie shown by Martson Conder
Video and the paper showing 3D visualisations of regular maps.
These were both created by Jarke J. van Wijk, from Eindhoven. http://www.win.tue.nl/~vanwijk/regularmaps
List of talks, ordered by presenter
Presenter and authors 
Title (click for abstract) 
Links 
Gabriel Bartolini
Antonio F. Costa
Milagros Izquiedo* 
On the connectedness of the branch locus of the moduli space of Riemann Surfaces I. 
slides 
Gabriel Bartolini*
Milagros Izquiedo 
On the connectedness of the branch locus of the moduli space of Riemann Surfaces II. 

Allen Broughton*,
Chris Judge 
Flat Surfaces, Teichmueller Discs, Veech Groups, and the Veech Tessellation 
slides 
Marston Conder*,
Emilio Bujalance,
Francisco Javier Cirre 
Extendability of group actions on nonorientable surfaces 
slides 
Emilio Bujalance,
Francisco Javier Cirre* 
A family of Riemann surfaces with orientation reversing automorphisms (for consideration) 
slides 
Ernesto Girondo*,
David Torres 
Algebraic equations of genus 2 Riemann surfaces with a hyperelliptic uniform dessin 
slides 
J. Gilman*,
L. Keen 
Automorphisms of Pants and Tori:
Primitives and Palindromes 

Yolanda Fuertes, Gabino GonzalezDiez*, Ruben A Hidalgo, Maximiliano Leyton 
The full automorphism group of a family of generalized Fermat curves 
slides 
Michael Jackson 
Which $(2,3,r)$ triangle groups give rise to the strong symmetric genus of some finite group? 
slides 
Gareth Jones, Yolanda Fuertes (delivered by Gabino GonzalezDiez) 
Beauville surfaces and finite groups 
slides
paper 
Ewa KozlowskaWalania 
Pairs of symmetries of Riemann surfaces 
slides 
Yaacov Kopeliovich 
Towards Thomae formula for general cyclic covers of the Sphere 
slides
preprint 
Jennifer Paulhus (unable to attend) 
Decomposing Jacobian varieties using automorphism groups 
slides 
Pisanski Toma\v z, Alen Orbani\' c, Daniel Pellicer*, Thomas W Tucker, Arjana \v Zitnik 
Edgetransitive tessellations with nonnegative Euler characteristic 
slides 
Emma Previato 
Riemann surfaces with automorphisms: Aspects of dynamics 

Ernesto Girondo,
David Torres* 
Genus 2 Bely\u{\i} surfaces with a unicellular uniform dessin 
slides 
Tom Tucker 
Seeing symmetries of surfaces in 3space 
slides 
Ewa Tyszkowska 
Application of theory of coverings in a study of Riemann surfaces 

Anthony Weaver*,
Cormac O'Sullivan 
The largest nongenus of a cyclic group 
slides
paper 
Gareth Jones,
M. Streit,
Jurgen Wolfart*

Wilson's
operations on regular dessins and cyclotomic fields of definition 
slides 
James Wolper (unable to attend) 
Automorphism Groups and Moduli Spaces of Vector Bundles 

Aaron Wootton*,
J.W. Anderson 
Bounding the Number of Group Actions on a Surface of Fixed Genus 

Coy L.May,
Jay Zimmerman* 
The 2groups of odd strong symmetric genus 
slides 
