Frobenius Structure and p-adic Zeta Function

Explore the intricate relationship between p-adic Frobenius structures and p-adic zeta functions in this advanced mathematics lecture. Delve into the concept of ordinary linear differential equations and their p-adic Frobenius structures, which establish an equivalence between the local system of solutions and its pullback under the map t → t^p over the field of p-adic analytic elements. Examine the significance of this property in the context of differential equations arising from the Gauss-Manin connection in algebraic geometry. Investigate how p-adic Frobenius structures near singular points can be characterized by a set of p-adic constants. Discover examples of hypersurface families where these constants are revealed to be p-adic zeta values, based on joint work with Frits Beukers. This hour-long talk by Masha Vlasenko at the Hausdorff Center for Mathematics offers a deep dive into advanced mathematical concepts at the intersection of p-adic analysis and algebraic geometry.