Royal Holloway - Pure Mathematics Seminar
The PM-seminar takes place
on Wednesday at 2pm in McCrea 219.
is a campus plan.
January 10 !!Extra - Seminar at 2pm in McCrea 219!! Colin Reid
"Locally compact piecewise full groups"
Abstract: I will be talking about joint work
with Alejandra Garrido and David Robertson. Let X be the
Cantor set (or any compact zero-dimensional Hausdorff space) and
let G be a subgroup of the group Homeo(X) of homeomorphisms from
the Cantor set to itself. We say h in Homeo(X) is 'piecewise
in G' if there is an open cover O of X, such that for every Y in
O, there is some g_Y in G such that hx = g_Yx for all x in
Y. The piecewise elements of G themselves form a group,
called the piecewise full group [[G]] of G (also known as the
topological full group). Piecewise full groups have been
extensively studied since the 1990s, but mostly in the context of
countable groups. We consider instead those piecewise full
groups that admit a nondiscrete locally compact group
topology. In this context, we find that given a locally
compact group acting on the Cantor set, then the group topology
extends to the piecewise full group if and only if the action is
locally decomposable, meaning that for every clopen partition of
the space, there is an open subgroup that acts independently on
each part of the partition. Moreover, if in addition G is
compactly generated and acts minimally and expansively, then the
derived group of [[G]] is open, compactly generated and abstractly
simple. This construction gives rise to all local
isomorphism types of compactly generated simple locally compact
groups in which some compact open subgroup admits a nontrivial
direct factorization; in this context, we note that there are
uncountably many such groups up to isomorphism (by a construction
of Smith), but it is unknown whether there are uncountably many up
to local isomorphism. The piecewise full group construction
also sheds light on a class of abstract commensurators of
profinite groups, in the sense of Barnea–Ershov–Weigel: we show
that a certain local condition suffices to ensure that the
abstract commensurator has a simple monolith, and also obtain
sufficient conditions for the abstract commensurator to be
January 11 !!Mini-conference "Geometric
Group Theory at Royal Holloway"!!
January 16 Derek Holt
"Computing in finitely presented groups"
survey algorithms for computing in (generally infinite) groups
defined by finite
presentations, with an emphasis on the existence and
availability of effective
The talk will focus mainly
on the Word Problem, the Generalised Word Problem and the Conjugacy Problem.
For the Word Problem we will
concentrate on the use of automatic structures for defining an effective
normal form for the groups elements, with some applications to
deciding finiteness, and to drawing pictures.
There are not many methods
available for the Generalised Word Problem when the index of the subgroup H of
G is infinite. The Stallings Folding method for subgroups of free groups
can be generalised to quasiconvex subgroups of automatic groups provided
that we can compute a so-called coset automatic structure. This is
possible, for example, for quasiconvex subgroups of
The Conjugacy Problem in
certain types of groups (braid groups and polycyclic groups, for example) has
received a lot of attention recently resulting from potential applications to
cryptography. But in this talk we focus on the problem in hyperbolic
groups, which can theoretically be solved in (almost) linear time, but for which
effective implementations seem to be more difficult.
January 23 Fredrik
"Computational aspects of Spectral theory for subgroups of
the modular group and Maass waveforms"
will give a brief introduction to the spectral theory of
Fuchsian groups and in particular finite index subgroups of
the modular group. There are many interesting and
fundamental questions in this area (e.g. Selberg’s
eigenvalue conjecture) which are (currently) mainly
approachable using computations and I will give an overview
of some of the computational methods, main problems and
January 30 Tamas Makai
"Bootstrap percolation on inhomogenous random graphs"
Bootstrap percolation is a deterministic process on a graph.
It starts out from a set of infected vertices and in every
step each vertex, which has at least r infected neighbours
becomes infected. Once a vertex becomes infected it remains
infected forever. The process stops once no additional
vertices can become infected.
this process on the Chung-Lu random graph. In this model
every vertex is assigned a weight and the vertices are
connected proportional to the product of the vertex weigths.
Each edge is inserted independently.
the weight sequences where a small number of randomly
infected vertices leads with high probability to the
infection of a linear fraction of the vertices by the end of
the process. We also establish the threshold on the number
of initially infected vertices required for this linear
outbreak to occur.
February 6 Ana Khukhro
"Geometry and topology of finite quotients"
Abstract: A group's natural
habitat is surely in the world of geometry - whether
acting on metric or topological spaces, or being viewed as
geometric objects themselves, groups are happiest when
coupled with geometric notions. Geometric group
theory is now a thriving topic in pure mathematics, with many
connections to areas as varied as analysis, dynamics, and cryptography. One of the fundamental
ideas of this subject is that a finitely generated group can be
viewed as graph, called a Cayley graph, which can encode many of its
algebraic properties geometrically. In this talk, we will introduce a variant on
this geometric object for groups with many finite quotients, and see
how its geometry can be used to create and study examples of interest
in a coarse geometric setting.
February 13 Kitty Meeks
"Reducing Reachability in Temporal Networks"
The concept of reachability sets (i.e. which vertices in a
network can be reached by travelling along edges from a
given starting vertex) is central to many network-based
processes, including the dissemination of information or the
spread of disease through a network. Depending on the
application, it might be desirable to increase or decrease
the number of vertices that are reachable from any one
starting vertex. In most applications, time plays a crucial
role: each contact between individuals, represented by an
edge, will only occur at certain time(s), when the
corresponding edge is "active". The relative timing of edges
is clearly crucial in determining the reachability set of
any vertex in the network.
talk, I will address the problems of reducing the maximum
reachability of any vertex in a given temporal network by
two different means:
(1) we can
remove a limited number of time-edges (times at which a
single edge is active) from the network, or
number of timesteps at which each edge is active is fixed,
but we can change the relative order in which different
edges are active (perhaps subject to constraints on which
edges must be active simultaneously, or restrictions on the
timesteps available for each edge). Mostly, we
find that these problems are computationally intractable
even when very strong restrictions are placed on the input,
but we identify a small number of special cases which admit
polynomial-time algorithms, as well as some general upper
and lower bounds on what can be achieved.
in this talk is based on joint work with Jessica Enright
(University of Edinburgh); I will also mention some joint
results with George B. Mertzios and Viktor Zamaraev
(University of Durham) and Fiona Skerman (Uppsala
February 20 No Seminar!
February 27 Wajid
Mannan (Queen Mary)
"An exotic presentation of Q_28"
Abstract: Whether or not the
quaternion group of order 28 has a finite balanced
presentation with non-standard homotopy has been an open
problem for some time. I will provide such a
presentation, recently discovered, and convey why it is of
interest in low-dimensional topology.
March 6 Chris Smyth
"Coxeter-Dynkin diagrams: old mysteries and new extensions"
Abstract: I first survey
some of the wide variety of mathematical objects that turn out, mysteriously, to
be classified by Coxeter-Dynkin diagrams.
Then I describe how, in
joint work with James McKee, we extended these diagrams in a new but
natural way. However, these extensions seem to generate further mysteries.
March 13 Alexandre
March 20 Gareth Tracey
"Generation properties in finite groups: Tools and
March 27 Jan-Christoph Schlage-Puchta (Rostock)
Summer term 2019:
May 22 Imre Leader
Pure Mathematics Seminars