Ninety Fifth Meeting of the
MIMS - School of Mathematics
Alan Turing Building
University of Manchester
Monday 23 March 2015
The talks will take place in Lecture Room G209 (note the unusual
venue), on the ground floor of the Alan
Turing Building. The building is number 46 on the University
After the last talk, there will be a visit to a local restaurant (in the
vicinity of Piccadilly and Oxford Road Stations) for dinner with the speakers.
Participants will meet for coffee from 1100AM onwards in the Atrium
Bridge Common Room (the usual venue!).
- 11.00-11.30: COFFEE (Atrium Bridge)
- 11.30-12.30: Jelena Grbic (Southampton)
Homotopy Rigidity of the Functor ΣΩ
The main problem of this talk is the study of the homotopy rigidity of
the functor ΣΩ. Our solution to this problem depends heavily on
new decompositions of looped co-H-spaces. I shall start by recalling
some classical homotopy theoretical decomposition type results.
Thereafter, I shall state new achievements and discuss how new functorial
decompositions of looped co-H-spaces arise from an algebraic analysis of
functorial coalgebra decompositions of tensor algebras. This is a joint
work with Jie Wu.
- 12.30-2.00: LUNCH
- 2.00-3.00: Ilia Pirashvili (Leicester)
The fundamental groupoid as a terminal costack
The notion of a stack, which is the 2-mathematical analogue of a sheaf,
has been studied for some time. In this talk, we will introduce the notion of
a costack, which is essentially what we get by reversing the arrows. We then
show that this rather neglected object has a very nice property. For a
topological space X, the final object of the 2-category of costacks over X is
the assignment U → Π1(X). The same also holds for the etale
fundamental groupoid. This implies that we essentially get a purely categorical
description of the fundamental groupoid. At the end, we will also mention
some generalisations of this result.
- 3.00-4.00: TEA BREAK (Atrium Bridge)
- 4.00-5.00: Hendrik Suess (Manchester)
Lower dimensional torus actions
manifolds are studied from at least three viewpoints, namely that of
algebraic geometry, symplectic geometry and topology. These manifolds
are completely described by a convex polytope (the moment polytope).
in all three fields attempts were made to generalise this description
by combinatorial data and the corresponding results for toric manifolds
to the case of lower dimensional torus actions. I will describe the
algebraic setting and sketch the relations to what has been done in the
Everyone who wishes to participate is welcome, particularly
postgraduate students. We shall operate the usual criterea for
assistance with travel expenses, but beneficiaries will need to
complete the standard forms, which are available at the
Please send an empty email (with subject TTT95YES) to
nigel.ray(at)manchester.ac.uk if you expect to attend, so that we
can cater for appropriate numbers.