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Noncommutative Algebraic Geometry January 16, 2024 to May 24, 2024
Organizers Wendy Lowen (Universiteit Antwerp), Alexander Perry (University of Michigan), LEAD Alexander Polishchuk (University of Oregon), Susan Sierra (University of Edinburgh), Spela Spenko (Vrije Universiteit Brussel), Michel Van den Bergh (Hasselt University)
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Derived categories of coherent sheaves on algebraic varieties were originally conceived as technical tools for studying cohomology, but have since become central objects in fields ranging from algebraic geometry to mathematical physics, symplectic geometry, and representation theory. Noncommutative algebraic geometry is based on the idea that any category sufficiently similar to the derived category of a variety should be regarded as (the derived category of) a “noncommutative algebraic variety”; examples include semiorthogonal components of derived categories, categories of matrix factorizations, and derived categories of noncommutative dg-algebras. This perspective has led to progress on old problems, as well as surprising connections between seemingly unrelated areas. In recent years there have been great advances in this domain, including new tools for constructing semiorthogonal decompositions and derived equivalences, progress on conjectures relating birational geometry and singularities to derived categories, constructions of moduli spaces from noncommutative varieties, and instances of homological mirror symmetry for noncommutative varieties. The goal of this program is to explore and expand upon these developments. 
Keywords and Mathematics Subject Classification (MSC)
  • noncommutative algebraic geometry

  • derived categories

  • semiorthogonal decompositions

  • enhancements

  • homological mirror symmetry

  • dg/A-infinity categories

  • birational geometry

  • moduli spaces

  • stability conditions

  • quantum cohomology

  • Donaldson-Thomas invariants

  • noncommutative resolutions

  • homological minimal model program

  • homological projective duality

  • noncommutative projective geometry

  • deformation theory and associated cohomology theories

  • schobers

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Programmatic Workshops
April 08, 2024 - April 12, 2024 Recent Developments in Noncommutative Algebraic Geometry