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Algebra and geometry of link homology

Name: Algebra and geometry of link homology
Keywords: Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, FOS: Mathematics, Mathematics - Combinatorics, Geometric Topology (math.GT), Combinatorics (math.CO), Representation Theory (math.RT), Algebraic Geometry (math.AG), Mathematics - Representation Theory

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2021Embargo end date: 01 Jan 2021Publisher:arXiv

Authors: Gorsky, Eugene; Kivinen, Oscar; Simental, José;

doi: 10.48550/arxiv.2108.10356

arXiv: http://arxiv.org/abs/2108.10356

Algebra and geometry of link homology

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Abstract

These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, its basic properties and recent advances, as well as three algebro-geometric models for link homology: braid varieties, Hilbert schemes of singular curves and affine Springer fibers, and Hilbert schemes of points on the plane.

49 pages

Related Organizations

Max Planck Society
Germany
University of California, Davis
United States

Keywords

Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, FOS: Mathematics, Mathematics - Combinatorics, Geometric Topology (math.GT), Combinatorics (math.CO), Representation Theory (math.RT), Algebraic Geometry (math.AG), Mathematics - Representation Theory

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