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Seminar
FIELD Math:Geometry
DATE May 06 (Thu), 2021
TIME 16:00-17:00
PLACE Online
SPEAKER Nabijou, Navid
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.
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