The geometry of underwear: maths conference discusses ‘double pants decompositions’

Posted by mjs76 at Jun 21, 2012 02:45 PM |
We are not making this up, we are not joking. This really is what it seems.
The geometry of underwear: maths conference discusses ‘double pants decompositions’

A 'pair of pants' in mathematical terms (image: Wikipedia)

Mathematicians from across Europe are assembling in Leicester today for a three-day Workshop on Geometry, Representation Theory and Clusters. And pants.

Believe it or not, ‘pants’ is a genuine geometric term and Anna Felikson from Jakobs University Bremen will present a paper entitled ‘Double Pants Decompositions’. According to her abstract, “a pants decomposition of a 2-surface S is a maximal set of mutually non-intersecting closed curves on S whose complement is a union of ‘pants’ (i.e. spheres with 3 holes).”

So ‘pants’ are simple three-dimensional shapes which have three interconnected holes. In other words, anything which is topologically similar to … a pair of underpants. Who says there’s no humour in mathematics?

To extend the metaphor further, Wikipedia informs us that “In hyperbolic geometry all three holes are considered equivalent – no distinction is made between ‘legs’ and ‘waist’.”

Other intriguingly titled papers presented at the workshop include:

  • 'Oriented triangulations, double covers and maximal Green sequences'
  • 'Iyama-Yoshino reductions of cluster categories from surfaces’
  • 'Maximal rigid objects as noncrossing bipartite graphs'

and the glorious

  • 'On possible skew-symmetrizable extensions of Derksen-Weyman-Zelevinsky’s mutation theory of quivers with potentials'

Speakers at the event have travelled from the universities of Graz, Trondheim, Paris, Bremen, Hannover, Newcastle, Leeds, Amien, Caen and Durham. Professor Nicole Snashall from our own Department of Mathematics will present a paper on ‘Brauer graph algebras, Coverings and Ext algebras.’*

The first day of the workshop doubles up as the 57th meeting of BLOC, the Bristol Leicester Oxford Colloquium which has met approximately quarterly since it was founded in 1997. BLOC aims to “encourage research collaboration in the Representation Theory of Algebras between mathematicians at Bristol, City, Leeds, Leicester, Liverpool, Oxford and Sheffield universities.”

The three-day event has been organised by Sybille Schroll, Leverhulme Early Career Fellow in our Department of Mathematics, and Robert Marsh from the University of Leeds. It has been supported by a grant from the London Mathematical Society.

*This replaces Professor Snashall’s previously announced paper on ‘Hochschild cohomology and Happel’s question’. We apologise to cohomology fans who may have been especially looking forward to that one.