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Conference: "Arithmetic Statistics" - August 24-28, 2026
Inverse problems in number theory are refined by studying their quantitative counterparts. Typical examples are the distribution of Galois groups and class groups of number fields, whose behavior is predicted by celebrated conjectures of Malle and Cohen—Lenstra—Martinet. Analogous questions for function fields have received much attention, including the case that the characteristic divides the group order.
The purpose of this workshop is to offer the opportunity to present recent results in this area and to have plenty of time for collaboration.
The conference "Arithmetic Statistics" will take place at the Institute of Mathematics in Paderborn (Germany) . Please apply here.
Link to Website: Conference: "Arithmetic Statistics"
Everything at a glance
The main goal of computer algebra is the symbolic solution of mathematical problems on a computer. Therefore, on the one hand, new algorithms are theoretically developed and reviewed and on the other hand implemented into existing computer algebra systems, like Kant or Magma. For many years, a database for number fields has been provided via web-interface, which contains of more than 3 million number fields with "interesting" Galois groups. The developed algorithms and its calculated data are used to establish hypotheses for mathematical problems or to verify them experimentally. Several members of our work group are working on so called asymptotic problems, e.g. the distribution of fields with a given Galois group or the distribution of class groups in algebraic (of algebraic) number fields. In this case, using the computer for experiments has turned out to be very useful.