Speakers: Dan Correy (Embry-Riddle Aeronautical University) and Caelan Ritter (University of Washingon) 

Title: Tropical Abel--Jacobi theory

Speaker: Dan Corey

Abstract: Intermediate Jacobians and Abel-Jacobi maps are powerful tools for studying higher-dimensional algebraic varieties.
They generalize the classical Jacobian and Abel-Jacobi map for curves. While they do not classify higher-dimensional varieties
(as in the curve case), they may be used find obstructions to rational and algebraic equivalence of cycles. In this talk,
I will explain how to extend these constructions to tropical varieties of arbitrary dimension. As in the classical setting, the tropical
versions yield obstructions to rational and algebraic equivalence. We will apply this framework to the Ceresa cycle - a canonical
cycle associated to an algebraic curve that has been the subject of significant recent interest. In particular, I will present a combinatorial
formula for the Abel-Jacobi image of the tropical Ceresa cycle and discuss its relationship with the complex and l-adic Ceresa classes.
This is joint work with Omid Amini and Leonid Monin.

Title: A canonical superform on tropical Jacobians

Speaker: Caelan Ritter

Abstract:There is a natural (1,1)-form on the Jacobian of a compact Riemann surface that features prominently in Arakelov geometry,
appearing, for example, in Wilm's computation of Faltings' delta-invariant.  In joint work with Junaid Hasan and Farbod Shokrieh,
we construct an analogous (1,1)-form on the tropical Jacobian of a metric graph using the formalism of Lagerberg superforms,
which mimics Dolbeault cohomology for tropical varieties.  In this talk, I will outline the construction and show that the form we obtain
satisfies integral formulas that one expects from the classical setting.  Then we will explore how it captures interesting combinatorial
properties of the underlying edge-weighted graph, relating it in particular to random walks, spanning trees, and effective resistance.

(Contact person: Wanlin Li)