Cycles in Algebraic and Tropical Geometry
Document Type
Event
Location
Math Conference Room: College of Arts and Sciences
Start Date
24-3-2026 11:00 AM
End Date
24-3-2026 12:00 PM
Description
Within algebraic geometry lies the deep and mysterious theory of rational and algebraic equivalence classes of algebraic cycles. This theory is a refinement of algebraic topology that incorporates the algebraic structure of algebraic varieties. In this talk, I will survey the theory of cycles in algebraic geometry, and in its combinatorial manifestation, tropical geometry. I will begin with the classical setting of divisors on curves. I will then demonstrate how this theory generalizes to higher (co)dimensions with a particular focus on two fundamental examples: the Ceresa and modified diagonal cycles. These are closely related canonical 1-dimensional cycles associated with an algebraic curve that capture phenomena invisible to homology and play a central role in the deeper algebraic theory of curves. Finally, I will describe my collaborative work on the combinatorial version.
Cycles in Algebraic and Tropical Geometry
Math Conference Room: College of Arts and Sciences
Within algebraic geometry lies the deep and mysterious theory of rational and algebraic equivalence classes of algebraic cycles. This theory is a refinement of algebraic topology that incorporates the algebraic structure of algebraic varieties. In this talk, I will survey the theory of cycles in algebraic geometry, and in its combinatorial manifestation, tropical geometry. I will begin with the classical setting of divisors on curves. I will then demonstrate how this theory generalizes to higher (co)dimensions with a particular focus on two fundamental examples: the Ceresa and modified diagonal cycles. These are closely related canonical 1-dimensional cycles associated with an algebraic curve that capture phenomena invisible to homology and play a central role in the deeper algebraic theory of curves. Finally, I will describe my collaborative work on the combinatorial version.