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Algebraic geometry

Combinatorics of non-crossing partitions

Iain Gordon whiteboard
The board is a result of of Bin Shu from East China Normal University visiting Iain Gordon at the University of Edinburgh. In Iain’s words: “We were discussing the combinatorics of non-crossing partitions, and its generalisations to a bunch of different finite groups. The two diagrams are Cayley graphs of symmetric groups where one calculates this combinatorics. Most of that text is in black, but we were lazybones, so there is also a bit of green writing from my PhD student, about braid group actions on tensor categories and their asymptotic limits. Amazingly, the two topics are linked, through moduli spaces in algebraic geometry!”

Deformation theory and 3-folds

blackboard in University of Edinburgh common roomThis photo is of the blackboard in the common room of the School of Mathematics at the University of Edinburgh. The workings on the left are by Michael Wemyss, drawn while he was talking about deformation theory (a generalization of differential calculus) with Will Donovan, as part of their work on the geometry of certain spaces, known as 3-folds. Will says, “Deformation theory lets us express the way in which a curve in a 3-fold can `move’ infinitesimally: we can then relate this to the (quantum) geometry of the 3-fold. I’ve tried to emulate Michael’s calligraphic F’s and G’s, but I haven’t had any success yet.” We don’t know who did the workings on the right.

The topology of algebraic varieties


Mikael Vejdemo-Johansson, from the University of St Andrews, sent in this photo some time ago, saying “we were discussing computational approaches to the topology of algebraic varieties, and sampling issues we were having. A very pleasantly geometric topic that generates a lot of sketches and pictures.”