John Calabrese, Special Colloquium

Title: Categorical reconstruction theorems in algebraic geometry

Abstract: A classic theorem of Gabriel states that a variety X may be recovered by Coh(X), its category of coherent sheaves. The latter play a central role in modern algebraic geometry, combining together vector bundles over topological spaces, and modules over rings. I will start by explaining why Gabriel’s theorem should be true and then discuss some generalizations and variants, including connections to birational geometry.