Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 863: Advanced Topics in Algebraic Geometry (Spring)

Andrei Caldararu (Spring 2017): 

 This course will be a gentle introduction to the ideas of homological mirror symmetry and curve counting invariants using homological algebra methods. Some of the topics that will be covered are

  • A-infinity algebras
  • Hochschild homology and cohomology
  • operads
  • Gerstenhaber and Batalin-Vilkovisky algebras
  • Fukaya categories
  • Kontsevich's Homological Mirror Symmetry conjecture
  • Costello's constructions of Topological Field Theories from A-infinity algebras

The course should be reasonably self-contained, but a good knowledge of basic homological algebra will be very useful. Basic algebraic geometry will also be used, but is not absolutely necessary.

semester: 
Spring
prereqs: 
Math 750 or Math 763 are highly recommended

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, Wi  53706

(608) 263-3054

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