Skip to main content
Browse by:

Until further notice, in-person public events have been canceled. Event listings include how to access online content.
Please check before coming to campus.

Derived categories of cubic fourfolds and their geometric applications

Math Colloquium Alex Perry 1/15 @ 3:15pm
Icon calendar
Wednesday, January 15, 2020
Icon time
3:15 pm - 4:15 pm
Icon speaker
Alex Perry (Columbia University)
Icon series
Algebraic Geometry Seminar

A fundamental problem in algebraic geometry is to determine whether a given algebraic variety is birational to projective space. This is most prominently open for cubic fourfolds, i.e. hypersurfaces defined by a cubic polynomial in a five-dimensional projective space. A decade ago, Kuznetsov suggested an approach to this problem using the derived category of coherent sheaves. I will explain recent applications of this perspective to fundamental questions in hyperkahler geometry and Hodge theory, which in turn shed light on the original question about cubic fourfolds.