Enumerative Geometry and Arithmetic

11 - 15 March 2024

Venue: Lorentz Center@Oort

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Enumerative geometry is concerned with counting geometric objects satisfying certain constraints. It dates back to the Apollonian Problem 22 centuries ago, counting circles in the plane tangent to 3 other circles. The modern approach through Gromov-Witten theory has flourished in the last 50 years. It rephrases the counts as invariants of moduli spaces of stable maps and deals with enumerative questions involving incidence conditions of curves. Most recently, logarithmic structures have been used to encode higher tangency conditions, giving rise to logarithmic Gromov-Witten theory. Recent developments in analytic number theory over global function fields and their motivic analogs have found applications to determining some geometric properties of moduli spaces such as dimension and irreducibility of certain components.

This workshop will bring together two research communities that rarely meet but would benefit from more interaction: number theory and enumerative (logarithmic) geometry. To facilitate the interactions, there will be three introductory minicourses, selected talks that survey the latest developments, and ample space for discussions.

Cristina Manolache (University of Sheffield): Introduction to enumerative geometry.
Pankaj Vishe (Durham University): Introduction to number theory of function fields.
Jonathan Wise (University of Colorado Boulder): Introduction to logarithmic geometry. 

Margaret Bilu (Université de Bordeaux)
Samir Canning (ETH Zürich)
Leo Herr (Universiteit Leiden)
Navid Nabijou (Queen Mary University of London)
Emmanuel Peyre (Université de Grenoble)
Angelina Zheng (Università Roma Tre)


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