Workshop of the DeCaDE 2016

The Derived Categories Day Edinburgh 2016 will take place on April 12/13 at JCMB and ICMS. Please contact Arend Bayer with any questions.


April 12, JCMB 5327

2.30pm-3.30Lightning round Short talks by Spela Spenko, Martin Kalck, Agnieszka Bodzenta, Matthew Woolf, Chunyi Li
3.30-4.00 Coffee break (Common Room)
4.00-4.45Joe Karmazyn (Bath)Nakayama's lemma and the generation of derived categories

I aim to talk about several lemmas that can be used to deduce when an object generates the derived category and that apply outside the setting of smooth projective varieties. In particular I will discuss how a variant of Nakayama's lemma can be used to show that a vector bundle on a flat family is
a tilting bundle if and only if it restricts to a tilting bundle on all the fibres.

5.00-5.45Nathan Broomhead (Münster) Thick subcategories via geometric modelsI will explain some current work, in which I aim to describe the lattices of thick subcategories of discrete derived categories and derived categories of certain orbifold projective lines. This is done using collections of exceptional and sphere-like objects related to non-crossing configurations of arcs in a geometric model.

April 13, ICMS Lecture room

10.30-11.15Tyler Kelly (Cambridge)A Derived Bestiary for Gorenstein ConesGorenstein cones have been a means to an end in toric mirror symmetry for over twenty years. Although they are usually thought of as the support of the fan of a toric vector bundle whose generic global section cuts out a Calabi-Yau variety, Gorenstein cones have an interesting story themselves, which can be unpacked geometrically. In this talk, we provide a glossary for how different types of Gorenstein cones manifest in the wild in the context of derived categories. This work is joint with David Favero.
11.15-11.45 Break
11.45-12.30Jørgen Rennemo (Oxford)Homological projective duality for (anti-)symmetric rank loci

Kuznetsov's theory of homological projective duality relates the derived categories of complete intersections in a smooth variety X to complete intersections in a different variety Y, the "homological projective dual of X". We compute Y when X is the space of rank k (anti-)symmetric (n x n)-matrices, for k and n satisfying a parity condition. In this case X is singular and must be replaced by a non-commutative/categorical resolution - we use a resolution which has recently been constructed by Spenko and Van den Bergh.

This is motivated by work in physics by Hori, who has proposed a duality between certain pairs of gauged linear sigma models with non-abelian gauge groups. Our main statement follows from considering the category of B-branes associated with such theories (interpreted as the non-commutative resolution of X) and extracting from the proposed physical equivalence an equivalence of B-brane categories. This is joint work with Ed Segal.

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