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Arithmetic of Algebraic Curves

AMS Southeastern Spring Sectional Meeting,

University of Tennessee, Knoxville, Knoxville, TN

March 21-23, 2014 (Friday - Sunday)

Meeting #1097

Special Session:
   Arithmetic of Algebraic Curves


  • Caleb Shor, Western New England University
  • Lubjana Beshaj, Oakland University
  • Andreas Malmendier, Colby College


Algebraic curves have been studied for a long time, however there are still many problems left unanswered some of which with a long history. The goal of this session is to look at some of these problems from a computational point of view. Furthermore, we want to explore how new computational techniques can be used to study algebraic curves and their moduli.

Motivation and Importance

The development of new computational techniques has made it possible to attack some classical problems of algebraic geometry. The goal of this session is to highlight such computational techniques related to algebraic curves and moduli spaces of curves. Especially, we would like to explore recent developments in the geometry of algebraic curves, moduli spaces of curves, Jacobians of curves, etc and their applications.

Topics of the session include, but are not limited to:

  • Algebraic curves and their automorphisms, Hurwitz curves,

  • Jacobians of algebraic curves, curves with split Jacobian, rational torsion points in the Jacobian etc.

  • Applications of algebraic curves and their moduli spaces in string theory and gauge theory.

  • Computational number theory, rational points on curves,

  • Field of moduli and field of definition of algebraic curves,

  • Covering of the Riemann sphere by a generic curve of genus g, solvable monodromy groups,

  • Interaction between computational group theory and algebraic curves,

  • Groups acting on surfaces

  • Moduli of curves and Gromov-Witten theory

  • Invariant theory and algebraic curves

  • Thetanulls of algebraic curves and applications to integrable systems, solitons, differentiable equations

  • Families of curves with prescribed automorphism group and the loci that they define in the moduli space.

  • Algorithms and computations of cohomology of moduli spaces of curves. Recent developments on the tautological ring and the Gorenstein conjecture.

  • Experimental and computer-assisted results on the birational geometry of the moduli space.

  • others

Speakers (The following have tentatively accepted our invitation to speak at the special session)
  • Andrew Sutherland, MIT
  • Tony Shaska, Oakland Univ.
  • Wade Hindes, Brown
  • David Zureick-Brown, Emory University
  • Atoshi Chowdhury , Berkeley
  • Stefan Mendez-Diez, University of Alberta
  • Alan Thompson, Fields Institute Toronto
  • Jesse Leo Kass, University of South Carolina
  • Matthew Boylan, University of South Carolina
  • Álvaro Lozano-Robledo, University of Connecticut
  • Michael Filaseta, University of South Carolina
  • Milagros Izquierdo, Linkoping, Sweden
  • Ricardo Conceição, Emory University
  • Ursula Whitcher, University of Wisconsin - Eau Claire.
  • Fred Thompson, Oakland University
  • Caleb Shor, Western New England University
  • Kit Ho Mak, Georgia Institute of Technology

Contact for Organizers:

C. Shor (
Department of Mathematics
Western New England University
Springfield, MA 01119

L. Beshaj (
Department of Mathematics and Statistics
Oakland University
Rochester, MI 48386

A. Malmendier (
Department of Mathematics and Statistics
Colby College
Waterville, ME 04901