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Future directions in automorphisms of surfaces, graphs, and other related topics
Contemporary Mathemtatics, accepted (2021)
  • Sean A Broughton, Rose-Hulman Institute of Technology
  • Jennifer Paulhus
  • Aaron Wootton, University of Portland
The study of Riemann surfaces and the groups which act on them
is a classical area of research dating back to the latter half of the 19th century.
Research in this field has wide-reaching implications in geometry and topology,
algebra, combinatorics, analysis, and number theory through related topics
such as the study of dessins d'enfants, mapping class groups, and graphs on
surfaces. Today, this is still a rich area of research with many open questions.
In this expository article we pose 78 open problems, contextualize them within
the field, and discuss partial results or progress toward answering the questions,
when relevant.
  • automorphisms and symmetries of Riemann surfaces,
  • moduli space,
  • algebraic curves,
  • mapping class group,
  • dessins d'enfant,
  • graphs on surfaces.
Publication Date
April 27, 2021
Citation Information
Sean A Broughton, Jennifer Paulhus and Aaron Wootton. "Future directions in automorphisms of surfaces, graphs, and other related topics" Contemporary Mathemtatics, accepted (2021)
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