Enumerative geometry and Kontsevich's formula for counts of rational curves in a plane

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• Ajith Kumaran, University of Cambridge
• Friday 28 January 2022, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Macarena Arenas.

Enumerative geometry is about counting subvarieties in an ambient variety X. We consider the concrete question of how many rational plane curves of degree d pass through 3d-1 points in general position. Maxim Kontsevich gave a proof of a beautiful recursive formula that computes these numbers. We will give a sketch of his proof using Gromov-Witten theory. The basic idea is to turn this enumerative question into a computation in the cohomology ring of a certain moduli space M. This moduli space itself may be complicated but we have natural maps to other moduli spaces M’, which we understand better. This allows us to pullback relations in H to H(M). An instance of such a relation is the WDVV equation which will give us the aforementioned recursive formula.

This talk is part of the Junior Geometry Seminar series.

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