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Orlando 2017

Algebraic curves and their applications

Fall Southeastern Sectional Meeting

University of Central Florida, Orlando, Orlando, FL

September 23-24, 2017 (Saturday - Sunday)

Meeting #1133



Organizers:  

  • Lubjana Beshaj, West Point Military Academy Email:  Lubjana.Beshaj@usma.edu


Overview:


Algebraic curves are one of the most studied areas of mathematics which create a very nice mixture of classical theoretical results with applications. In this session we intend to bring together researchers from academia and industry and provide a platform for discussing algebraic curves and their applications in industry such as robotics, automotive security, cryptography, mathematical physics, etc.



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


  • Curves defined over the complex numbers

  • Thetanulls for superelliptic curves

  • Moduli spaces and their stratification

  • Equations of curves over their minimal field of definition

  • Field of moduli versus the field of definition

  • Models of curves with minimal height

  • Neron-Tate models of superelliptic curves

  • Moduli height of curves

  • Counting of curves in the moduli space

  • Jacobians of curves and their decompositions

  • Algebraic curves and mathematical physics

  • Tropical Curves

  • Tropical curves and their automorphisms

  • Tropical superelliptic curves

  • Algebraic curves and cryptography

  • Algebraic curves and their use in industrial applications

  • others


Deadline for
abstracts:

August 1, 2017


Website

            Here is the website of the session from AMS including instructions how to submit    abstracts

Talks (in the order they were received)
  • From hyperelliptic to superelliptic curves,
    T. Shaska

  • A Family of Non-normal Double Planes Associated to Hyperelliptic Curves,  
    Timothy J. Ford

  • Covers of elliptic curves and good reduction,
    James Phillips

  • Bounds for the Mordell-Weil rank of certain families of jacobians of hyperelliptic curves defined over Q, Alvaro Lozano-Robledo, Harris B. Daniels, Erik Wallace

  • Loci of genus two curves with marked Weierstrass points,  
    Renzo Cavalieri, Nicola Tarasca

  • Constructing hyperelliptic curves of genus 3 whose Jacobians have CM,
    Jennifer S. Balakrishnan, Sorina Ionica, Kristin Lauter, Christelle Vincent

  • Local-to-Global Principles for Galois Covers of Curves in Characteristic p,
    Renee Hyunjeong Bell

  • Some Applications of the Hasse-Weil Bound,  
    Xiang-dong Hou

  • Torsion subgroups of rational elliptic curves over infinite extensions of Q,
    Harris B. Daniels

  • Interpolation problems for curves in projective space,
    Isabel Vogt

  • The Local Lifting Problem for D4D4,  
    Bradley Weaver

  • Degrees of CM Points on X1(M,N)X1(M,N).
    A. Bourdon, P. L. Clark

  • The auto-Igusa zeta function of a plane curve singularity is rational,
    A. Stout 

  • Reduction of Binary Forms via the Hyperbolic Centroid,
    A. Elezi, T. Shaska

  • A Quantum Algorithm for Computing Isogenies between Supersingular Elliptic Curves,   Jean-Francois Biasse

Proceedings

    Title: Algebraic Curves and Applications 
    Editors: Lubjana Beshaj and Tony Shaska
    Publisher: Contemporary Math. (AMS)
    
    Deadline for papers  October 30

Topics
  • Elliptic Curve Cryptography
  • Hyperelliptic Curve Cryptography
  • Decomposition of Jacobians of Hyperelliptic Curves
  • Algebraic curves and automotive security
  • Arithmetic of genus 2 curves
  • Genus 3 hyperelliptic curves
  • Superelliptic curves and cryptography
  • Isogeny-based cryptography
  • Arithmetic of superelliptic curves
  • From hyperelliptic to superelliptic curves
  • Tropical superelliptic curves
  • others 




Dinner

    There will be a dinner for all the session participants and their guests in one of the local restaurants.  More details to come soon. 

Schedule


 Time   Title Speaker
   
 Saturday Morning  
   
 8:00-8:20 The Local Lifting Problem for D4D4  B. Weaver
 8:30-8:50Reduction of Binary Forms via the Hyperbolic Centroid  A. Elezi
9:00-9:20 Constructing hyperelliptic curves of genus 3 whose Jacobians have CM  C. Vincent
9:30-9:50 A Family of Nonnormal Double Planes Associated to Hyperelliptic Curves  T. Ford
10:00-10:50 From hyperelliptic to superelliptic curves  T. Shaska
   
  Saturday Afternoon 
   
 3:00-3:20

Covers of elliptic curves and good reduction.

J. Phillips 
3:30-3:50 Loci of genus two curves with marked Weierstrass points  N. Tarasca
4:00-4:20 Interpolation problems for curves in projective space  I. Vogt
4:30-4:50 Torsion subgroups of rational elliptic curves over infinite extensions of Q H. Daniels 
 5:00-5:50Bounds for the Mordell-Weil rank of certain families of Jacobians of hyperelliptic curves defined over  Q A. Lozano-Robledo 
   
  Sunday Morning 
   
8:00-8:20 The auto-Igusa zeta function of a plane curve singularity is rational A. Stout 
 8:30-8:50Some Applications of the Hasse-Weil Bound X. Hou 
 9:00-9:20Local-to-Global Principles for Galois Covers of Curves in Characteristic p  R. Bell
 9:30-9:50Degrees of CM Points on X1(M,N)X1(M,N) A. Bourdon 
 10:00-10:20Computing isogenies between elliptic curves and applications to cryptography  J. Biasse

Orlando: Algebraic Curves


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