Arithmetic, Geometry, Cryptography and Coding Theory
June 19 – 23, 2017

This conference will be the sixteenth edition of a conference which began in 1987 with the best specialists of the field. Students and young researchers are invited to collaborate with senior researchers.

The talks will focus on new theoretical mathematical results and will also present effective or algorithmic results.

The conference will be organised as such:
— One or two plenary talks each day at the beginning of the session, given by high level researchers. Our hope is that part of these talks will be given by researchers outside our community, in order to present new directions and new applications of arithmetic and/or algebraic geometry.
— Other short, specialized talks.

Topics will include:
— Number theory, asymptotic behavior of families of global fields and statistic arithmetic
— Arithmetic geometry, algebraic curves over finite fields or over number fields, Abelian varieties: point counting methods, theoretical, effective and algorithmic aspects in arithmetic geometry
— Error correcting codes, algebraic codes, geometric codes on algebraic curves or on high dimensional varieties, algebraic decoding algorithms, etc.
— Cryptography, elliptic curves and Abelian varieties: discrete logarithm problem, pairings, explicit computing of isognies, invariant theory and curves classification
— Boolean functions, bent functions, APN functions: construction of families of bent functions and hyperbent functions, etc.

We plan to publish proceedings of this conference in the Contemporary Mathematics collection of the AMS.

• Irene Bouw (Universität Ulm)   Picard curves with small conductor   (pdf)
• Wouter Castryck (KU Leuven & Université Lille 1)   Counting quartic extensions of Fq [t]   (pdf)
• Alina Carmen Cojocaru (University of Illinois-Chicago)   Arithmetic properties of the Frobenius traces of an abelian variety   (pdf)
• Marc Hindry (Université Paris Diderot)   Brauer-Siegel theorem and analogues for varieties over global fields
• Bjorn Poonen (MIT)   Abelian varieties isogenous to a power of an elliptic curve
• Alice Silverberg (University of California, Irvine)   Orders, lattices, and an application to principal ideal testing
• John Voight (Dartmouth College)    Computing classical modular forms as orthogonal modular forms   (pdf)
• Felipe Voloch (​University of Canterbury)   Maps between curves and diophantine obstructions

Speakers
​

• ​Jeff Achter (Colorado State University)   Local densities compute isogeny classes   (pdf)
• Elise Barelli (INRIA)    Short McEliece Key from Alternant Algebraic-geometry codes with automorphisms   (pdf)
• Nils Bruin (Simon Fraser University)    Arithmetic aspects of the Burkhardt quartic  (pdf)
• Mrinmoy Datta (Danmarks Tekniske Universitet)    An upper bound for the number of zeros of a system of homogeneous polynomials   (pdf)
• Lucile Devin (Université Paris Sud 11)    Divisibility properties of the number of Fp-points of schemes defined over Z   (pdf)
• Iwan Duursma (University of Illinois at Urbana-Champaign)   Rank two root systems and maximal curves   (pdf)
• Elena Egorova (Skoltech, Moscow)   Zero-error coding for multiple-access channels as a new test bed for AG-codes   (pdf)
• Sudhir Ghorpade (IIT Bombay)   Linear codes associated to Grassmann and flag varieties    (pdf)
• Nathan Kaplan (UC Irvine)    Rational Point Count Distributions for del Pezzo Surfaces over Finite Fields   (pdf)
• Valentijn Karemaker (University of Pennsylvania)   Fully maximal and minimal supersingular abelian varieties   (pdf)
• Daniel J. Katz (California State University)    A New Generating Function for Calculating the Igusa Local Zeta Function
• Kiran Kedlaya (University of California, San Diego) Computing zeta functions of nondegenerate toric hypersurfaces   (pdf)
• Pinar Kilicer (University of Oldenburg)    Primes dividing the invariants of CM Picard Curves   (pdf)
• Gilles Lachaud (Aix-Marseille Université)    Distribution of the trace in the compact group of type G2 and applications to exponential sums   (pdf)
• Philippe Lebacque (Université de Franche-Comté)    M-functions associated with modular forms   (pdf)
• Elisa Lorenzo García (Université de Rennes 1)   Primes of bad reduction of curves of genus 3 with CM   (pdf)
• Stefano Marseglia (Stockholm University)   Computing isomorphism classes of abelian varieties over finite fields   (pdf)
• Ivan Pogildiakov (University of French Polynesia)    On the linear bounds on the genus of pointless curves   (pdf)
• Rachel Pries (Colorado State University)   Galois action on  Fermat curves: non-vanishing of obstruction map   (pdf)
• Matthieu Rambaud (Télécom Paris-tech)     Intertwinned towers of Shimura curves and bilinear multiplication   (pdf)
• Prasant Singh  (IIT Bombay)  
   Minimum Weight Codewords of Schubert Codes   (pdf)
• Andrew Sutherland (MIT)    Strong arithmetic equivalence   (pdf)
• Mehdi Tibouchi (NTT Corporation, Tokyo)    Generalized Howgrave-Graham-Szydlo and Side-Channel Attacks Against BLISS   (pdf)
• Andrey Trepalin (IITP and NRU HSE, Moscow)   Del Pezzo surfaces over finite fields
• Michael Tsfasman (IITP, Moscow & Aix-Marseille Unibversité)    Measures associated to curves and abelian varieties over finite fields
• Marius Vuille (EPFL)   Computing cyclic isogenies between abelian surfaces over finite fields   (pdf)
• Chia-Fu Yu (Academia Sinica)  Explicit formulas for superspecial abelian surfaces over finite fields   (pdf)