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Peter Kronheimer, Zoom: Two months in Oberwolfach and the genus-minimizing property of algebraic curves
Thursday, September 17, 2020, 03:30pm - 04:30pm
Questions about smoothly embedded 2-manifolds in dimension 4 are central to the understanding of 4-manifolds. Among the most natural non-trivial examples of embedded 2-manifolds are the smooth algebraic curves in a complex algebraic surface. We know today that embedded 2-manifolds arising in this way have a genus-minimizing property: no embedded 2-manifold in the same homology class can have smaller genus than the algebraic curve. When I was an undergraduate, the best lower bound known, for most homology classes in most 4-manifolds, was zero, even if the algebraic curve had genus 496. I will try and give an account of how things started to change, focusing on my work with Tom Mrowka in the 1990s. Anecdotes will include the tale of sitting out a snow storm in LaGuardia, and weeks of social isolation outside a small village on the edge of the Black Forest.
Location: Zoom

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