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Automorphisms of Riemann Surfaces, Algebraic Curves

and Related Topics Interest Group

Conferences and Particpants
Portland OR - 2018
Chicago IL -2015
Penn State PA - 2009
Tucson AZ - 2007
Santa Barbara CA - 2005
Contact Organizers
Allen Broughton
Mariela Carvacho
Tony Weaver
Aaron Wooton
Last modified: 28 Oct 09

Automorphisms of Riemann Surfaces and Related Topics
Pennsylvania State University, University Park, PA - October 24-25, 2009

AMS Info, Organizers, Invitation and Abstract Submission


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 Grothendieck-Teichm\"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.

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 non-orientable 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 Gonzalez-Diez*, 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 Gonzalez-Diez) Beauville surfaces and finite groups slides
Ewa Kozlowska-Walania Pairs of symmetries of Riemann surfaces slides
Yaacov Kopeliovich Towards Thomae formula for general cyclic covers of the Sphere slides
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 Edge-transitive tessellations with non-negative 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 3-space slides
Ewa Tyszkowska Application of theory of coverings in a study of Riemann surfaces  
Anthony Weaver*,
Cormac O'Sullivan
The largest non-genus of a cyclic group slides
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 2-groups of odd strong symmetric genus slides