Seminar in Real and Complex Geometry

Thursday, January 4, 2024, 16:15-17:45, online via zoom




Dhruv Ranganathan
(University of Cambridge)

Logarithmic enumerative geometry for curves and sheaves


Abstract
             

I will outline a conjectural relationship between logarithmic DT theory and GW theory. This conjecture extends the usual GW/DT conjectures, and we now have a fairly complete understanding of how these conjectures interact with degeneration techniques and tropical geometry. I will then focus on perhaps the most basic instance of this setup, namely the logarithmic enumerative geometry of the algebraic torus of dimension 3, and explain what we know on the two sides. The theories have a number of interesting links to nearby mathematics, for example with tropical refined curve counting, double ramification cycles, and integrable hierarchies. I will try to explain these connections.
The picture is based on recent and ongoing joint work with Maulik, but also touches upon work of Kennedy-Hunt, Shafi, and Urundolil Kumaran.