| Date | Speaker | Title | Contact |
|---|
| Sep 10 |
Chris Leininger
Urbana-Champaign |
Homeomorphisms of surfaces and dynamicsWe will start by describing a standard measure of the dynamics of a
homeomorphism of a surface. For a certain generic class of
homeomorphisms, we will discuss how this measure relates to algebraic and
topological properties. |
Javier Aramayona |
| Sep 17 |
Kevin Jennings
Galway |
A dissection of an abelian (341,85,21) difference setA (perfect) difference set is a subset D of a group such that each nonidentity element of the group has exactly L representations as a difference ab^{-1} where a and b are in D. In this talk I will focus on a difference set with 85 elements in a group of order 341. L=21 in this case and this difference set exists, belonging to a classical family.
This group has a subgroup of order 31 and we can show by a few different arguments that there are 15 elements from the normalized difference set in this subgroup. (arguments range from basic counting, to looking at the orbits of the Hall multiplier, to simple applications of more technical combinatoric arguments). Unfortunately, I can not establish that these 15 elements must a priori express each element of this subgroup exactly 7 times i.e. that there is a (31,15,7)-difference set embedded in this larger difference set. This is the problem I will discuss.
In this talk I will give an overview of the known techniques for attacking such a problem, and explain briefly where this particular case might lead and why it is interesting. The talk will be elementary and I will keep it as non-technical as possible. The problem posed is low-hanging fruit. |
|
Sep 21
Monday 9.15am
|
Ian McLoughlin
Galway |
Dihedral Codes |
|
Sep 21
Monday 2.00pm
|
Bent Jørgensen
Odense |
Efficient Estimation for Incomplete Multivariate DataWe compare the Fisher scoring and EM algorithms for incomplete multivariate data, and investigate the corresponding estimating functions under second-moment assumptions. We propose a hybrid algorithm, where Fisher scoring is used for the mean vector and the EM algorithm for the covariance matrix. A bias-corrected estimate for the covariance matrix is obtained. This is joint work with Hans Chr. Petersen. |
John Hinde |
| Sep 24 |
James Gleeson
Limerick |
Cascade dynamics on complex networksNetwork models underlie many complex systems, e.g. the Internet, the World Wide Web, gene-regulatory networks, etc. Cascade dynamics can occur when the (binary) state of a node is affected by the states of its neighbours in the network. Such models have been used to aid understanding of the spread of cultural fads and the diffusion of innovations, and can be generalized to include percolation problems, k-core sizes, and the study of (SIR-type) epidemics on networks. For this class of problems, I present recent results on the analytic determination of the expected size of cascades on networks of arbitrary degree distribution, and outline extensions and applications of this research. |
Petri Piiroinen |
| Oct 1 |
Brian Marx
Baton Rouge |
Variations on the Varying Coefficient ModelAlthough the literature on varying coefficient models (VCMs) is vast, we believe that there remains room to make these models more widely accessible and provide a unified and practical implementation for a variety of complex data settings. The adaptive nature and strength of P-spline VCMs allow for a full range of models: from simple to additive structures, from standard to generalized linear models, from one-dimensional coefficient curves to two-dimensional (or higher) coefficient surfaces, among others, including bilinear models and signal regression. As P-spline VCMs are grounded in classical or generalized (penalized) regression, fitting is swift and desirable diagnostics are available. We will see that in higher dimensions, tractability is only ensured if efficient array regression approaches are implemented. We also motivate our approaches through several examples to highlight the breadth and utility of our approach.
|
John Hinde |
| Oct 8 |
Cyril Lecuire
Toulouse |
Convex cores of hyperbolic 3-manifoldsThe study of 3-dimensional hyperbolic manifolds with infinte volume can
be reduced to the study of their convex cores. I will explain how the
volume of such a convex core is related to its end invariants, in
contrast with the 2-dimensional case. |
Javier Aramayona |
Oct 14
Wednesday 3.00pm
|
Efim Zelmanov
San Diego |
Asymptotic properties of finite groups and finite dimensional algebrasThis is a public lecture to be held in the NCBES Seminar Room at 3pm |
Dane Flannery |
| Oct 22 |
|
Student Autumn GraduationsStudents' graduations will be from 2:30pm till 5:30pm |
|
| Oct 29 |
Natalia Iyudu
Belfast |
Quadratic algebras: the Anick conjecture, representation spaces and Novikov structuresI will explain new results on the Anick conjecture (1983) on attaining of the Golod-Shafarevich estimate for the Hilbert series of quadratic algebras. Then I mention some results which describe representation spaces of one quadratic algebra, well-known in non-commutative geometry: Jordan algebra. These include classifcation of irreducible components of the space of n-dimensional representations. As a consequence, the number of irreducible components turned out to be equal to the number of partitions of n. If time permits I also explain a surprising connection between representation theory of quadratic algebras with questions on existance of Novicov structures, prominent by their appearance in the study of Poisson brackets of hydrodynamic type in integrable systems and by their connections to the conformal Lie theory.
|
Alexander Zuevsky |
| Nov 5 |
Viacheslav V. Nikulin
Liverpool |
On classification of arithmetic hyperbolic reflection groups.I would like to speak about old and new results on
finiteness and classification of arithmetic groups generated by reflections
(in hyperplanes) of hyperbolic spaces. |
Alexander Zuevsky |
| Nov 12 |
Stephen Wills
Cork |
Markov processes and semigroups and their noncommutative counterpartsI will outline the connections between Markov processes (memory-less
stochastic processes) and semigroups in the classical theory, before
going on to explain their noncommutative counterparts in quantum
probability. A large part of the talk will be devoted to discussing how
to produce a quantum Markov process from a given quantum Markov
semigroup, the problems one typically encounters, and how these have
recently been overcome for (some cases of) the quantum exclusion
process. |
Edwin O'Shea |
Nov 17
Tuesday 3.00pm
|
Alexander Rahm
Grenoble |
The integral homology of PSL_2 of imaginary quadratic integers with
non-trivial class groupWe show that a cellular complex described by Floege allows to determine
the integral homology of the Bianchi groups PSL_2(O_{-m}), where
O_{-m} is the ring of integers of an imaginary quadratic number field
Q[\sqrt{-m}] for a square-free natural number m. We use this to
compute the integral homology in the cases m = 5, 6, 10, 13 and 15, which
before was known only in the cases of trivial class group m = 1, 2, 3, 7
and 11. |
Graham Ellis |
| Nov 19 |
Jim Anderson
Southampton |
Small filling sets of curves on surfacesThis talk is about joint work with Hugo Parlier and Alexandra Pettet. The
general problem we are considering is the structure of sets of simple closed
curves on a closed surface that fill; that is, sets of curves whose
complement is the union of (topological) discs. I will give a brief history
of where and why the question arose and discuss our first results, which
involve bounding the minimal number of curves in a set of filling curves. |
Javier Aramayona |
| Nov 26 |
Mathieu Dutour
Zagreb |
Lattice Packings and CoveringsA family of balls in Euclidean space is called a packing if for
any two balls B and B' their interior do not self-intersect. It is called
a covering if every point belong to at least one ball.
We focus here on packings and coverings for which the calls are of the form
x + B(0,R) with x belonging to a lattice L. If L is fixed then we adjust the
value of R to a value R0 to find the best packing. Alternatively we can
adjust the value of R to a value R1 to find the best covering. This allow
us to define the packing density pack(L) and covering density cov(L) of L.
The geometry of the function pack on the space of lattices has been
elucidated by Minkovski, Voronoi and Ash. They showed that the function
pack has no local minimum, that it is a Morse function and they give
a characterization of the local maximum in terms of the algebraic notions
of perfection and eutaxy.
The covering function cov is much more complex. It has local minimum and
local maximum and it is not a Morse function. We also characterize the
local maximum of the covering density in terms of the corresponding notions
of perfection and eutaxy this time for Delaunay polytope. |
Graham Ellis |
| Dec 3 |
Jochen Einbeck
Durham |
Data compression and regression based on local principal curves and surfaces.
In a multivariate regression problem with p-dimensional predictor space, the intrinsic dimensionality of the latter is often far smaller than p, sometimes even just one or two. Usual modelling attempts such as the additive model, which try to reduce the complexity of the regression problem by making additional structural assumptions, are then inefficient as they ignore the inherent structure of the predictor space and involve complicated model and variable selection stages.
In a fundamentally different approach, one may consider first approximating the predictor space by a (usually nonlinear) curve, and then regressing the response only against the one-dimensional projections onto this curve. This entails the reduction from a p- to a one- dimensional regression problem. As a tool for the compression of the predictor space we apply local principal curves. We show how local principal curves can be parametrized and how the projections are obtained. The actual regression step can then be carried out using any nonparametric smoother. If the intrinsic dimension of the predictor space is 2 (or more), one needs to replace the local principal curve by an adequate structure of higher dimension. We demonstrate how the idea of local principal curves can be extended towards local principal surfaces (or manifolds) through relatively simple means. The proposed techniques are illustrated using astronomical and oceanographic data examples. |
John Newell |