Topological invariants in arithmetic geometry

Abstract: This will be a gentle introduction to two independent themes.

The first half of the talk will focus on conductors and discriminants, two invariants that measure degeneration in a family of a hyperelliptic curves. We will show how a combinatorial refinement helps us compare these two invariants.

The second half of the talk will be be an introduction to A^1 enumerative geometry, i.e., how we may use quadratic forms to encode additional arithmetic information in enumerative problems in algebraic geometry.

algebraic geometryalgebraic topologyK-theory and homologynumber theory

Audience: researchers in the topic

CMI seminar series

Series comments: Please visit the seminar series homepage for streaming details. Timings of the seminar vary from week to week.