Tropical Mathematics & its Applications
Supported by the LMS
23rd November 2016
School of Mathematics, University of Manchester
Local Organiser: Marianne Johnson
* Laure Daviaud (Warsaw)
* James Hook (Bath)
All talks will talk place in room 3.214 of University Place (third floor), University of Manchester. (See below for advice on how to get here.)
14:00 James Hook Max-plus statistical leverage scores
The statistical leverage scores of a complex matrix A record the degree of alignment between the column space of A and its containing space. These scores are used in random sampling algorithms for solving certain numerical linear algebra problems. In this talk I will present a max-plus algebraic analogue of statistical leverage scores. I will show that max-plus statistical leverage scores can be used to calculate the exact asymptotic behavior of the conventional statistical leverage scores of a generic matrix of Puiseux series and also provide a novel way to approximate the conventional statistical leverage scores of a fixed complex matrix. The advantage of approximating a complex matrices scores with max-plus scores is that the max-plus scores can be computed very quickly. This approximation is typically accurate to within an order or magnitude and should be useful in practical problems where the true scores are known to vary widely.
15:00 Laure Daviaud Max-plus automata or how to link automata theory with max-plus algebra
Max-plus automata are a kind of quantitative automata closely related with matrices over the max-plus semiring. They compute functions from a set of finite words to the set of integers. In this talk, I will present some results about the description of such functions. In particular, I will link the problem of comparing max-plus automata with the computation of a quantity associated with sets of matrices: the joint spectral (sub-)radius. This talk is based on joint works with Thomas Colcombet, Pierre Guillon, Glenn Merlet and Florian Zuleger.
16:00 Tea/Coffee in Alan Turing Building
We plan to go for an early dinner, somewhere near to the train station. It would be helpful if you could let Marianne know if you intend to join us for dinner.
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.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 past some constructions works - 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. Walk past what looks like an entrance (glass wall with fire doors) and turn right into a partially covered walk-way. The actual entrance to the Alan Turing building should no wbe on your right. To get to University Place, keep walking past Alan Turing, and past the grassy area up ahead, keeping this on your right. University Place is the building resemnling a 'tin can' which borders this walkway and Oxford Road (straight ahead of you).