Association for Symbolic Logic (ASL)

Association for Symbolic Logic Tutorial: Hilbert's Tenth Problem: Between logic and number theory, Parts I & II, organized by David Solomon, ASL; Wednesday, 9:00–10:00 am and 1:00–2:00 pm. The tenth of Hilbert's Problems (H10), posed in 1900, asked for an algorithm to decided correctly whether or not a given polynomial $f\in\mathbb{Z}[X_{1},\ldots,X_{n}]$ has a solution in $\mathbb{Z}$. Culminating in 1970, work of Davis, Matiyasevich, Putnam, and Robinson showed that no such algorithm exists --- a `{\em negative solution}' to H10. Since then, a body of work has developed tackling the analogous questions in a variety of other rings and fields, where one is interested in solutions in a ring $R$, and sometimes also with coefficients in $R$.

In these two tutorial lectures, I will focus on recent developments in the subject, both in the more `global' world of finitely generated fields (including the prominent open case $R=\mathbb{Q}$), and their subrings, and in the more `local' world of henselian valued fields, and their valuation rings. The speaker for these tutorial sessions is Sylvy Anscombe, Université Paris Cité and Sorbonne Université.

Invited Addresses: The ASL Invited address program will take place on Friday and Saturday. The program will include invited addresses by Jeremy Avigad, Carnegie Mellon University, The promise of formal mathematics; Peter Cholak, University of Notre Dame, Ramsey like theorems on the rationals; Franziska Jahnke, University of Münster, Model theory of perfectoids fields; Sandra Müller, Technical University of Vienna, Universally Baire sets, determinacy and inner models; Lynn Scow, California State San Bernadino, Semi-retractions and the Ramsey Property; Assaf Shani, Harvard University, Classifying invariants for Borel equivalence relations; and Erik Walsberg, Vassar College, Model theory of large fields.

Contributed Paper Session: ASL will also host an ASL Contributed Paper Session on Friday afternoon and two ASL Special Sessions on Thursday.