Books


Algebraic Curves and their Applications

Eds: L. Beshaj, T. Shaska, Contemporary Math.  American Math. Soc. (2018),

Deadline for submission:  October 2017

Contents







Algebraic curves and their fibrations in mathematical physics and arithmetic geometry, Eds A. Malmendier, T. Shaska, Contemporary Math.  American Math. Soc. (2018), (to appear) xii+359 pp.

Contents

  • A Lower Bound for the Number of Finitely Maximal $C_p$-Actions on a Compact Oriented Surface, Jacob Russell, Aaron Wootton
  • Galois action on regular dessins d'enfant with simple group action, S. Allen Broughton
  • Equations of Riemann surfaces with automorphisms, David Swinarski 
  • On the field of moduli of superelliptic curves, Ruben Hidalgo, Tony Shaska
  • Minimal integral Weierstrass equations for genus 2 curves, Lubjana Beshaj
  • Rational points in the moduli space of genus two, Lubjana Beshaj, Ruben Hidalgo, Serge Kruk, Andreas Malmendier, Saul Quispe, Tony Shaska
  • Strong arithmetic mirror symmetry and toric isogenies, Chris Magyar, Ursula Whitcher
  • Inose's construction and elliptic K3 surfaces with Mordell-Weil rank~$15$ revisited, Abhinav Kumar, Masato Kuwata
  • Higher-order Weierstrass weights of branch points on superelliptic curves, Caleb McKinley Shor
  • Poncelet's Porism and Projective Fibrations, Emma Previato
  • Extending Runge's method for integral points, Aaron Levin
  • Self-inversive polynomials,   curves, and codes, David Joyner, Tony Shaska
  • Syzygy divisors on Hurwitz spaces, Anand Deopurkar, Anand Patel

Advances on superelliptic curves and their applications. Eds.  L. Beshaj, T. Shaska,  E. Zhupa, NATO Science for Peace and Security Series D: Information and Communication Security, 41. IOS Press, Amsterdam, 2015. xii+375 pp.

Contents

  • Preface L. Beshaj, T. Shaska, E. Zhupa
  • The case for superelliptic curves L. Beshaj, T. Shaska, E. Zhupa 
  • Weierstrass points of superelliptic curves T. Shaska, C. Shor 
  • Theta functions for superelliptic curves L. Beshaj, A. Elezi, T. Shaska 
  • Cyclic curves over the reals M. Izquierdo, T. Shaska 
  • Reduction of binary forms L. Beshaj 
  • Sato-Tate groups of genus 2 curves K. Kedlaya 
  • Heights of algebraic curves L. Beshaj, T. Shaska 
  • Descent and Covering Collections M. Stoll 
  • Chabauty and the Mordell–Weil Sieve S. Siksek 
  • Rational points on Jacobians of hyperelliptic curves S. Müller 
  • Explicit p-adic methods for elliptic and hyperelliptic curves, J. Balakrishnan 
  • Error Correcting Quantum Codes and Algebraic Curves , A. Elezi 
  • Graph based cubical multivariate maps and their cryptographical applications, M. Klisowski, V. Ustimenko 
  • Weight distributions, zeta functions and Riemann hypothesis for linear and algebraic geometry codes, A. Elezi, T. Shaska 
  • Galois geometries, codes, and new invariants for incidence structures, V. Tonchev
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