Program

Enumerative Geometry Beyond Numbers

January 16, 2018 to May 25, 2018

Organizers

Mina Aganagic (University of California, Berkeley), Denis Auroux (University of California, Berkeley), Jim Bryan (University of British Columbia), LEAD Andrei Okounkov (Columbia University; University of California, Berkeley), Balazs Szendroi (University of Vienna)

Description

Traditional enumerative geometry asks certain questions to which the expected answer is a number: for instance, the number of lines incident with two points in the plane (1, Euclid), or the number of twisted cubic curves on a quintic threefold (317 206 375). It has however been recognized for some time that the numerics is often just the tip of the iceberg: a deeper exploration reveals interesting geometric, topological, representation-, or knot-theoretic structures. This semester-long program will be devoted to these hidden structures behind enumerative invariants, concentrating on the core fields where these questions start: algebraic and symplectic geometry. Bibliography

Keywords and Mathematics Subject Classification (MSC)

Primary Mathematics Subject Classification

14-XX - Algebraic geometry

Secondary Mathematics Subject Classification

53-XX - Differential geometry {For differential topology, see 57Rxx; for foundational questions of differentiable manifolds, see 58Axx}

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Programmatic Workshops

January 18, 2018 - January 19, 2018	Connections for Women: Enumerative Geometry Beyond Numbers
January 22, 2018 - January 26, 2018	Introductory Workshop: Enumerative Geometry Beyond Numbers
March 19, 2018 - March 23, 2018	Structures in Enumerative Geometry