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ACA 2013: Arithmetic of Algebraic Curves

Special Session on Arithmetic of Algebraic Curves,  Malaga, Spain, July 2-6, 2013



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.
    • 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 


Important Information & Dates:

May 27th: Deadline for talk submissions.
May 30th: Notification of acceptance.
May 15th: Final day for standard registration.
May 20th: Final day for special rates at Málaga Palacio Hotel.
July 02nd - 6th: ACA 2013 Conference.

Abstracts can be sent to any of the session organizers directly. Notification of acceptance of the report for this session: one week after receiving the material.

History of the session

A special session on algebraic curves for ACA since 2003. Here are the links for previous special sessions
  • Computational aspects of algebraic curves, ACA 03
  • Computational Aspects of Algebraic Curves, ACA 2004.
  • Special Session: Coding theory and cryptography, ACA 2006.
  • Computational aspects of algebraic curves, ACA 07
  • Computational aspects of algebraic curves, ACA 2010

For accommodations and directions please visit the main conference webpage at ACA 2013
Subpages (2): Participants Talks