Program

• 14:00 – 14:45  Dan Haran (Tel Aviv University)
  On Free Profinite Products of Infinitely Many Absolute Galois Groups

  Koenigsmann (2002) showed that the free profinite product of finitely many absolute Galois groups is also the absolute Galois group of some field. Recently the question to what extent this can be extended to infinitely many groups has arisen. Jarden (2025) gives examples of free profinite products of copies of the same absolute Galois group G converging to 1 that are not absolute Galois groups. Bar-On (2025) gives an exact condition for a free pro-p product of countably many Demushkin groups of rank ℵ₀ to be an absolute Galois group.

  We will show that

  • the free profinite product of copies of a single absolute Galois group over any constant sheaf is an absolute Galois group;
  • the free profinite product of absolute Galois groups Gal(E_i) converging to 1 is an absolute Galois group, provided every E_i contains an algebraically closed field.

  We intend to provide the necessary background as much as possible.

• 15:00 – 15:45  Or Ben Porath (Tel Aviv University)
  Polynomial Counting for Primitive Wreath Product, k-Transitive, and Regular Actions
• 15:45 – 16:30  Coffee Break
• 16:30 – 17:15  Eden Granot (The Hebrew University)
  Interpolation of Low Degree Points on Curves
• 17:30 – 18:15  Arno Fehm (TU Dresden)
  Decidability Problems for Global and Local Fields
  Can one algorithmically decide whether a system of polynomial equations has a solution in the field of rational numbers? I will discuss several variations of this question, for different fields (global and local), different kinds of equations (polynomial, linear, ...), and with arithmetic extra conditions (absolute values, heights).
• 19:30  Conference Dinner