Combinatorics seminar (Thursday 10:10)
Student Combinatorics and Algebra Seminar (TBA)
Topology Seminar (Mondays at 2:30)
Syzygies and Mirror Symmetry Virtual Seminar (Thursdays at 1:00)
The King Conjecture proposed that every smooth, projective toric variety had an incredibly well-behaved category of sheaves, in a particular sense. While the conjecture turned out to be false, it has continued to inspire a huge amount of research on derived categories of toric varieties. I will explain how King’s Conjecture can be remedied, and proven, by incorporating a birational geometry perspective. This is joint work with Berkesch, Favero, and more.
Hilbert’s Syzygy Conjecture is a a fundamental finiteness result in algebra which has had major repercussions for modern algebraic geometry (and more). About a decade ago, Berkesch, Smith and myself conjectured a multigraded analogue of Hilbert’s Theorem. Our conjecture was recently proven, by several different groups largely different perspectives. I’ll summarize the circle of ideas that went into this result and some of the open questions it raised.
Orlov’s Theorem for dg-algebras
A landmark theorem of Orlov relates the singularity category of a graded Gorenstein algebra to the derived category of the associated noncommutative projective scheme. I will discuss a generalization of this theorem to the setting of differential graded algebras. This is joint work with Prashanth Sridhar.
Hilbert’s Syzygy Conjecture is a a fundamental finiteness result in algebra which has had major repercussions for modern algebraic geometry (and more). About a decade ago, Berkesch, Smith and myself conjectured a multigraded analogue of Hilbert’s Theorem. Our conjecture was recently proven, by several different groups largely different perspectives. I’ll summarize the circle of ideas that went into this result and some of the open questions it raised.