MathMeetings.net

The last 10 years have brought a burst of activity at the intersection of algebraic topology, number theory and algebraic geometry. This has led to a wealth of: New theorems, such as Ellenberg–Venkatesh–Westerland’s breakthrough results on the Cohen–Lenstra heuristics for function fields; New sources of heuristics in topology, such as Vakil–Wood’s predictions from the Grothendieck ring, or the notion and coincidences of homological densities as in Farb– Wolfson–Wood; Refinements of classical enumerative theorems using modern topological tools, such as Kass–Wickelgren’s arithmetic count of the 27 lines on a cubic surface; and A renewed focus on unstable homology, as in Galatius–Kupers–Randal-Williams and Miller–Wilson. We believe that these results are just the beginning of the emerging area of arithmetic topology.

This 5 day workshop will bring together junior and senior researchers from across these areas with the goal of:

Giving participants a global view of a fast emerging and multidisciplinary area,
Giving participants a detailed awareness on the range of methods available, and
Emerging with a robust problem list which can help guide activity in the area for the next 5-10 years.