• Work out specific examples in geometric analytic number theory.

  • • • Work out the classical example of square-free integers and configuration spaces.

      • Develop new examples.

• Learn about the Grothendieck ring of varieties and motivic analytic number theory.

  • • • Understand the relationship between the analytic class number formula and Dold-Thom's theorem. (See this Twitter thread by Daniel Litt).

• Étale cohomology and the Grothendieck-Lefschetz trace formula.

• Configuration spaces and homological stabilization theorems.

• The Grothendieck ring of varieties.

• Zeta functions and motivic analytic number theory.

We will watch asynchronously Ellenberg's and then Vakil's past Arizona Winter School lectures, and meet once every two weeks to discuss questions and observations.

We will also have occasional lectures by GASES participants (on the same schedule) to emphasize certain important topics not covered in the AWS videos.

Participants optionally organize in groups to work out new examples as we follow the lectures. Each group will schedule problem sessions independently.

At the end of the semester, we will have a final meeting for the groups to present their examples to the rest of GASES.

• Representation stability in cohomology and asymptotics for families of varieties over finite fields - Thomas Church, Jordan S. Ellenberg, Benson Farb.

• Geometric analytic number theory course notes: 2014 Arizona Winter School - Jordan S. Ellenberg

• Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields - Jordan S. Ellenberg, Akshay Venkatesh, Craig Westerland.

• Statistics of number fields and function fields - Jordan S. Ellenberg, Akshay Venkatesh.

• A survey on k-freeness - Francesco Pappalardi.

• The Grothendieck ring of varieties is not a domain - Bjorn Poonen.

• Lectures on N_X(p) - Jean-Pierre Serre.

• Discriminants in the Grothendieck ring - Ravi Vakil, Melanie Matchett Wood.

• The Grothendieck ring of varieties and motivic analytic number theory: 2015 Arizona Winter School notes - Ravi Vakil.

Feel free to contact Santiago Arango-Piñeros, Chris Keyes, or David Zureick-Brown with questions or to be added to the mailing list.