Tropical Geometry and Moduli Spaces: Satellite Conference of the 2018 International Congress of Mathematicians (ICM)

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This award will support US based participants and speakers at Tropical Geometry and Moduli Spaces, a satellite conference of the 2018 International Congress of Mathematicians (ICM), to be held August 13-17 in Cabo Frio, Brazil. This event will leverage the assembly of a vast number of mathematicians at the ICM in Rio de Janeiro as an opportunity to bring together a global community of leading experts and early career researchers in an especially active and rapidly developing field. This conference will be the largest ever in tropical geometry with over 80 participants anticipated.The scientific focus of the conference will be broadly centered on connections to moduli spaces, including interactions logarithmic structures, Berkovich spaces, and enumerative geometry. In just the past few years, there have been a number of significant advances in building explicit links among these different geometric theories, especially for curves and abelian varieties, using skeletons of nonarchimedean analytic spaces as a shared common tool. These links explain many older correspondence theorems, from the beginnings of tropical enumerative geometry, and are being used to establish new correspondences and to prove new enumerative results of classical flavor, e.g. for counting curves with fixed invariants, and to prove degeneration formulas for logarithmic Gromov-Witten invariants as part of a broader program linking tropical geometry to mirror symmetry. At the same time, new algebraic foundations are emerging for scheme-theoretic tropical geometry, built out of idempotent semirings, which will also be featured at the conference.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.