Final Schedule, 29th British Topology Meeting
All lectures will take place in the Lecture room A (= room 1041) of the Shackleton Building, which is building 44 near the bottom left corner
of
this map.
There will be a wine reception on the evening of Monday 8th, jointly with the International Conference on Generalized Functions.
This will be held in the Ketley Room on level 4 of the Mathematics Building, which is Building 54 on the top left of on
the same map.
For lunch, participants are recommended to visit the Staff Social Club, in Building 38 near the centre of the map.
Monday 8 September
13:00-14:00 Registration
14:00-15:00 Brendle
15:30-16:00 Kaji
Tea
16:30-17:30 Vershinin
18:00-19:00 Wine Reception
Tuesday 9 September
10:00-11:00 Madsen
Coffee
11:30-12:00 Spacil
12:00-12:30 Kurlin
Lunch
14:30-15:00 Beben
15:30-16:00 Huismann
Tea
16:30-17:30 Murillo
19:00 Conference Dinner at Ceno Restaurant.
Wednesday 10 September
10:00-11:00 Richter
Coffee
11:30-12:00 Tene
12:00-13:00 Wilton
Titles and Abstracts
1. Tara Brendle (Glasgow): Combinatorial models for mapping class groups
2. Shizuo Kaji (Yamaguchi and Southampton): Mod-p decompositions
of the loop spaces of compact symmetric spaces
Abstract: We give homotopy decompositions of the based loop spaces
of compact symmetric spaces after they are localised at large
primes. The factors are fairly simple; namely spheres, sphere
bundles over spheres, and their loop spaces. As an application,
upper bounds for the homotopy exponents are determined. This is
a joint work with A. Ohsita and S. Theriault.
3. Vladimir Vershinin (Montpelier 2): Lie algebras and Vassiliev invariants
Abstract: We start with a general construction of the Lie algebra
(over the integers) of the descending central series of a group. Then
we give presentations for the corresponding Lie algebras for classical
braids, for braids on the 2-dimensional sphere and for braids on a
surface of arbitrary genus. Finally we give a construction of the
universal Vassiliev invariant for braids on a 2-sphere.
4. Ib Madsen (Copenhagen): Real Algebraic K-theory
5. Oldrich Spacil (UCL): Homotopy type of the group of contactomorphisms of the 3-sphere
Abstract: After recalling basic notions of contact topology I will
present a simple proof showing that the homotopy type of the group of
contactomorphisms of the standard contact 3-sphere is that of the
unitary group U(2). The tools used are almost elementary algebraic
topology, but the starting line is a hard geometric result of
Eliashberg.
6. Vitaliy Kurlin (Durham): Topological Data Analysis: Applications to Computer Vision
Abstract: Topological Data Analysis is a new research area on the
interface between algebraic topology, computational geometry, machine
learning and statistics. The key aims are to efficiently represent
real-life shapes and to measure shapes by using topological invariants
such as homology groups. The usual input is a big unstructured point
cloud, which is a finite metric space. The desired outputs are
persistent topological structures hidden in the given cloud. The
flagship method is persistent homology describing the evolution of
homology classes in the filtration on the data over all possible
scales. After reviewing basic concepts and results, we consider the
problem of counting holes in noisy 2D clouds. Such clouds emerge as
laser scans of building facades with holes representing windows or
doors. We design a fast algorithm to count holes that are most
persistent in the filtration of neighborhoods around points in the
given cloud. We prove theoretical guarantees when the algorithm finds
the correct number of holes (components in the complement) of an
unknown shape approximated by a cloud in the plane.
7. Piotr Beben (Southampton): Configuration spaces and polyhedral products
Abstract: We use configuration space models for spaces of maps into
certain subcomplexes of product spaces (including polyhedral products)
to obtain a single suspension splitting for the loop space of certain
polyhedral products, and show that the summands in these splittings
have a very direct bearing on the topology of polyhedral products,
and moment-angle complexes in particular.
8. Johannes Huisman (Brest): Chern-Stiefel-Whitney classes of real vector bundles
Abstract: Let X be a real algebraic variety and F a real vector bundle
over X. I will define Chern-Stiefel-Whitney classes of F with values
in certain hypercohomology groups on the quotient topological space
X(C)/G, where G is the Galois group of C/R. These classes unify the
ordinary characteristic classes in the sense that they induce the
Chern classes of F(C), on the one hand, and the Stiefel-Whitney
classes of F(R), on the other hand. The construction sheds a seemingly
new light on the fact that the mod-2 cohomology ring of a real
Grassmannian is the reduction modulo 2 of the integral cohomology ring
of a complex Grassmannian after dividing all degrees by 2.
9. Aniceto Murillo (Malaga): Deformation functors and homotoy theory of Lie algebras
Abstract: Having as reference and motivation the Deligne's principle
by which every deformation functor is governed by a differential
graded Lie algebra, we build a homotopy theory for these algebras
which include the classical Quillen approach.
10. Birgit Richter (Hamburg): Higher topological Hochschild homology of rings of
integers.
Abstract: This is a report on joint work in progress with Bj{\o}rn
Dundas and Ayelet Lindenstrauss. We calculate higher THH of the
integers with coefficients in F_p and also for (certain) rings of
integers in a number field. This builds on the calculation of THH in
these cases of B\"okstedt and Lindenstrauss-Madsen.
11. Haggai Tene (Bonn): A product in equivariant homology for compact Lie group actions
Abstract: In this talk we present a product in the (Borel) equivariant
homology of a smooth manifold with a compact Lie group action. This
construction generalizes a product in the homology of BG defined by
Kreck. We give some computational results, and relate the product to
the product in negative Tate cohomology in the case G is finite and
the manifold is a point. This is a joint work with S. Kaji.
12. Henry Wilton (Cambridge): Detecting hyperbolicity in finite covers
Abstract: In practice, one of the most common ways of proving that two
closed, aspherical 3-manifolds M, N are distinct is to compare their
finite-sheeted covers. An open question in 3-manifold topology asks
to what extent this method always works. In more sophisticated
terminology, the question asks: 'If the profinite completions of the
fundamental groups of M and N are isomorphic, does it follow that M
and N are homeomorphic (unless they both admit Solv geometry)?'
In this talk I will report on recent progress towards a positive
answer: the profinite completion 'sees' hyperbolicity, in the sense
that if M is hyperbolic then so is N. To prove this theorem, we
develop a profinite analogue of the quasiconvex hierarchy for
hyperbolic 3-manifolds employed by Wise and Agol in their work on the
Virtually Fibred conjecture.
This is joint work with Pavel Zalesskii.
Last updated on 3rd September 2014.