|DATE||May 06 (Thu), 2021|
|HOST||Bhamidi, S.S Sreedhar|
|INSTITUTE||University of Cambridge|
|TITLE||( 2 + 1 ) ways of counting tangent curves|
|ABSTRACT||Logarithmic Gromov-Witten theory is a framework for counting curves in a fixed variety X, with specified tangency orders to a fixed normal crossings divisor D. The associated moduli spaces of logarithmic stable maps have been extensively studied over the past decade. Despite this, calculating invariants remains a hard problem, and there are relatively few targets for which the theory has been "solved".
In this talk I will explain how tropical combinatorics can be leveraged to control the geometry of these moduli spaces and, ultimately, compute numbers. This point of view leads us to construct a natural iterated blowup of the moduli space of (ordinary) stable maps, whose intersection theory can then be exploited to relate the logarithmic Gromov-Witten invariants to other, better-understood curve counts.
This is joint work with Dhruv Ranganathan. No prior knowledge of logarithmic geometry will be assumed.