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Logarithmic intersection theory and enumerative geometry

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KAH2 - K-theory, algebraic cycles and motivic homotopy theory

A logarithmic structure on an algebraic variety equips it with, among other things, a natural stratification. In the context of intersection theory, this means that logarithmic structures select natural principal component contributions in an intersection problem. The analysis of these principal components has led to recent new directions in Gromov-Witten theory and in the study of the cohomology of the moduli space of curves. I will try to give a tour of these problems and the tools we have to analyze them, focusing especially on geometry related to the double ramification cycle in the moduli space of curves. The talk will encompass work with Battistella, Nabijou, and Molcho, as well as touch on independent work of Holmes, Pandharipande, Pixton, Schmitt, and Schwarz

This talk is part of the Isaac Newton Institute Seminar Series series.

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