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Automorphisms of Riemann Surfaces, Algebraic Curves

and Related Topics Interest Group



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Conferences and Participants
Milwaukee - 2024
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Tufts U, MA - 2020
Portland OR - 2018
Chicago IL - 2015
Penn State PA - 2009
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Contact Current Organizers
Allen Broughton
Jennifer Paulhus
Aaron Wooton
Tony Shaska

Publications
CONM 776 - Feb 2022

Last modified: 27 Jan 24

Automorphisms of Riemann Surfaces and Related Topics
Portland State University, Portland, OR - April 14-15, 2018

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 Hurwitz, Klein, and Wiman. In recent years there has been a major revival in this area, due to its close relationship to Teichmuller theory, mapping class groups, and the Belyi/Grothendieck theory of maps and dessins d'enfant on algebraic curves. Advances in combinatorial and computational group theory have made many more examples available as opportunities to test conjectures and new approaches. 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 (in no particular order)

  • Compact Riemann surfaces and their automorphisms
  • Klein surfaces and their automorphisms
  • Galois extensions of function fields
  • Dessins d’enfant and quasi-platonic surfaces
  • Fields of definition and moduli fields
  • Defining equations for surfaces
  • Finite subgroups of mapping class groups
  • Applications to moduli and Teichmüller problems
  • Action of the mapping class group on Teichmuller space
  • Jacobians of curves with automorphisms
  • Group theoretic computational methods

List of participants/authors and talks, ordered by presenter

A star indicates the presenter of multi-author papers.
Participant/Authors Title (click for abstract) Links
Lubjana Beshaj Minimal Models for Superelliptic Riemann Surfaces with Extra Automorphisms slides
S. Allen Broughton Topological and $\mathcal{H}_q$ Equivalence of Prime Cyclic $p$-gonal Actions on Riemann Surfaces. slides tables  paper
Charles Camacho Dessins d'Enfants, Topological Cyclic Actions on Surfaces, and Counting Quasiplatonic Surfaces slides
Mariela Carvacho*, Víctor González-Aguilera Structure of M4 slides
Rachel Davis Comparing the deck group and Veech group of an origami slides
Edray Herber Goins*, Rachel Davis Metabelian Galois Representations slides
Antonio F. Costa, Milagros Izquierdo* One-dimensional families of Riemann surfaces of genus g with 4g + 4 automorphisms. slides
S Joseph Lippert*, Aaron D Wootton Bounding Skeletal Signature Spaces slides
Mariela Carvacho, Jennifer Paulhus*, Aaron Wootton Potential Versus Actual Signature Space slides
Sebasti\'an Reyes-Carocca On the one-dimensional family of Riemann surfaces of genus $q$ with $4q$ automorphisms. slides
Tony Shaska Riemann surfaces with extra automorphisms and endomorphism rings of their Jacobians slides
Thomas W. Tucker Unfaithful Maps slides
Anthony Weaver (unable to attend) Counting Topological Types of Finite Group Actions on Surfaces
James S. Wolper Periods of an Interesting Family of Curves with Automorphisms slides
Aaron D Wootton*, James W Anderson The Lattice Structure of the Potential Signature Space. (for consideration) slides