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# John Calabrese, Special Colloquium

## December 11, 2017 @ 4:00 pm - 5:00 pm

**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.