Tropical Mathematics & its Applications
Supported by the LMS
26th February 2013
School of Mathematics, University of Manchester
Local Organisers: Marianne Johnson, Mark Kambites, Mark Muldoon
* Bas Lemmens (Kent)
* Felipe Rincon (Warwick)
* Sergei Sergeev (Birmingham)
* Simon Willerton (Sheffield)
All talks will talk place in the Frank Adams room of the Alan Turing building in the School of Mathematics, University of Manchester. (See below for advice on how to get here.)
12:00 Early arrivers meet for lunch
13:00 Simon Willerton Tight spans and semi-tropical modules
Tight spans (aka injective envelopes) for metric spaces have been rediscovered many times in the last 50 years, they have many applications in areas from group theory to phylogenetic analysis. Recently Hirai and Koichi generalized them to directed metric spaces. I will show how this construction is natural when viewed in the light of an enriched category approach to metric spaces, and how this approach leads to natural semi-tropical actions on the directed tight spans.
14:00 Felipe Rincon Tropical linear spaces and A-discriminants
Tropical linear spaces are one of the most basic objects in tropical geometry, playing a fundamental role in different contexts and applications. In this talk I will describe some of their nice polyhedral and combinatorial structure, and I will present an effective approach to computing them. As an application, I will show how we can use this to get a handle on classical A-discriminants.
15:30 Sergei Sergeev On Perron-Frobenius theorems in tropical spaces
This talk is on the eigenvector existence theorem in invariant subspaces (subcones) of max-linear operators, its proofs, generalizations and an application to the semigroups of pairwise commuting matrices. The talk is based on the work of G.B. Shpiz, G.L. Litvinov and the author.
16:30 Bas Lemmens Geometry of Hilbert's and Thompson's metric spaces
Max-times maps on the standard positive cone are nonexpansive with respect to Hilbert's and Thompson's metrics. These metrics are defined for general cones. Their geometric properties are very interesting. For example, Hilbert's metric spaces are a natural non-Riemannian generalisation of hyperbolic space. I will discuss some of the geometric properties of Hilbert's and Thompson's metrics. In particular, I will explain the structure of the unique geodesics and the possibility of quasi-isometric embeddings into finite dimensional normed spaces.
We plan to go for an early dinner shortly after the last talk, somewhere near to the train station. It would be helpful if you could let Marianne know if you intend to join us for dinner.
There are no registration fees, but it would be helpful if you could confirm your attendance by email (firstname.lastname@example.org). Financial support for UK-based postgraduate students is awarded on a first come first served basis; please give an estimate of your travel costs when confirming your attendance.Lunch
Please note that lunch will not be provided, however, you are most welcome to join us for lunch at one of the university cafeterias in University Place. If you would like to do so, we will meet at 12 on the atrium bridge area on the first floor of the Alan Turing building.Directions from Manchester Piccadilly station
Walking from Manchester Piccadilly to the Alan Turing Building should take around 20 mins. Leave the station by the Fairfield Street exit (head down the escalators or lift from the main concourse) which brings you out at a big road junction. Cross both main roads, and go along a smaller road (Granby Row) to the left of the Bull's Head pub. Keep straight on, as the road becomes a pedestrian walk and then a road again, and at the phoneboxes turn left onto Sackville Street. Go under the railway bridge and continue under a bridge between buildings, and where the road bends off to the right, follow the left-hand pavement which becomes a footpath and goes through an underpass. Afterwards, keep left under the motorway flyover (avoiding a deeper underpass ahead) before bearing right (avoiding yet another underpass to the left). After very carefully crossing the motorway sliproad, you find yourself on Brook Street. Walk down this (away from the flyover). At the intersection with Grosvenor Street, cross both roads and then continue along (now Upper) Brook Street on the opposite side. Cross the next side-road (Booth Street East, carefully again!), continue past the Aquatics Centre car park and then the Alan Turing Building is on your right. To get into the building, go into the walkway after the second "finger" and then the doors are on your right. Note that these directions (along with a map) can be found here.