Arithmetic Statistics
Statistiques arithmétiques

15 – 19 May 2023

Scientific Committee 
Comité scientifique 

Alina Carmen Cojocaru (University of Illinois Chicago)
Tim Dokchitser (University of Bristol),
Wei Ho (University of Michigan)
Andrew Sutherland (MIT)

Organizing Committee
Comité d’organisation

Samuele Anni (Aix-Marseille Université),
Elisa Lorenzo Garcia (Université de Neuchâtel),
Peter Stevenhagen (Leiden University),
Jan Vonk (Leiden University)

The theme of the conference is a type of number theory that has become very popular over the last decades, and that is influenced by the possibility of « experimentally » studying arithmetic objects with the help of a computer. Thanks to the wide availability of computer algebra systems, essentially any number theorist nowadays has this possibility at his fingertips. There are concrete objects that are not so easily determined « by hand », such as fundamental units in number fields of higher degree, or Mordell-Weil generators of point groups of elliptic curves, and a first impression of « what these typically look like » is often obtained by numerical experimentation.
Over the years, substantial datasets relating to number fields, elliptic curves and L-series have become available, enhancing our understanding of the arithmetic world somewhat beyond only the smallest examples, which may fail to show the true asymptotic behaviour.



Manjul Bhargava (Princeton University)     Integers expressible as the sum of two rational cubes
Alina Bucur (University of California San Diego)    Counting D4 quartic extensions of a number field ordered by discriminant
Francesc Fité (Universitat de Barbcelona)     On a local-global principle for quadratic twists of abelian varieties
Matilde Lalin (Université de Montréal)     Vanishing of twisted L-functions of elliptic curves over function fields
Hendrik Lenstra (Leiden University)     Subrings of number fields
Guillermo Mantilla-Soler (National University of Colombia)     On zeta functions of number fields and related arithmetic invariants
Melanie Matchett Wood (Harvard University)     The average size of 3-torsion in class groups of 2-extensions
Alexander Smith (Stanford University)     Quadratic twist families of elliptic curves with unusual 2∞-Selmer groups
Peter Stevenhagen (Leiden University)     On arithmetic statistics
Andrew Sutherland (Massachusetts Institute of Technology)    Murmurations of L-functions



Brandon Alberts (Eastern Michigan University)     A Random Group with Local Data
Nuno Arala Santos (University of Warwick)      A density problem on elliptic curves
Santiago Arango-Piñeros (Emory University)       q-Frobenius distributions of abelian varieties
Sam Chow (University of Warwick)    A Galois counting problem for number fields
Rainer Dietmann (Royal Holloway University of London)     Probabilistic Galois theory for reciprocal polynomials of degree four
Jakob Glas (Institute of Science and Technology Austria)    Rational points on del Pezzo surfaces of low degree
Fabian Gundlach (Harvard University)     Malle’s conjecture with multiple invariants
Jean Kieffer (Harvard University)      Isogeny classes of typical principally polarized abelian surfaces over Q
Peter Koymans (University of Michigan)       Counting nilpotent extensions
Alvaro Lozano-Robledo (University of Connecticut)     On the minimal degree of a torsion point of prime-power order on an elliptic curve over Q
Alison Miller (University of Michigan)     Arithmetic Statistics Questions Inspired by Classical Knot Invariants
Sebastian Monnet (University College London)      S4-quartics with prescribed norms
Ajith Anilkumar Nair (City University of New York)      Gauss Composition and Higher Composition Laws
Sun Woo Park (University of Wisconsin-Madison)     On the prime Selmer ranks of cyclic prime twist families of elliptic curves over global function fields
Ross Paterson (University of Bristol)      Average Ranks of Elliptic Curves after p-Extension
Lazar Radicevic (Université de Franche-Comté)      Structure constants of rings of finite rank and minimal free resolutions
Christophe Ritzenthaler (Université de Rennes)    On the distribution of curves over finite fields according to their number of rational points
Soumya Sankar (The Ohio State University)     Counting rational points on stacks
Ashvin Swaminathan (Harvard University)      Heuristics for class groups of orders in quadratic fields
Anne-Edgar Wilke (Université de Bordeaux)      Effective enumeration of quartic number fields