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The derived category of a cubic 4-fold contains a semi-orthogonal component which famously behaves as a `non-commutative K3 surface'. The symmetric square of this component is thus a `non-commutative hyperkaehler 4-fold'. Galkin conjectured that it should be equivalent to the derived category of an actual hyperkaehler 4-fold: the Fano of lines in the cubic.
I'll give an informal…

Since at least the 1970s, social scientists have been using graphs to model social systems. A typical model is a collection of graphs sharing the same set of vertices: the vertices represent individual actors within the system, and each graph a distinct relation among them. There are various long-established methods to extract information about the structure of a social system from such a model. For instance, to identify the ‘social roles’ present in a system one studies the semigroup it generates under composition of relations, and to identify ‘social positions’ one studies certain especially nice congruences in the category of graphs.

Graphs, however, can record only pairwise connections between actors; to incorporate ties of higher dimension, one might prefer to work with simplicial complexes or hypergraphs. What is a ‘role’ or a ‘position’ in a social system modelled by a collection of hypergraphs? This talk is about joint work with Nima Motamed and Nina Otter, in which we propose an answer to that question by reframing it in terms of universal coalgebra.

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12:30  Lunch at Pizza Posto