Date  Speaker  Title  Contact 
Sep 12 
Willem de Graaf University of Trento 
Computation with linear algebraic groups
Linear algebraic groups appear in many contexts as
symmetry groups, for example in differential Galois theory, or
algebraic geometry. So it is of interest to be able to compute
with these groups. In this talk I will discuss some computational
problems, and towards the end focus on the problem of computing
generators of the arithmetic group corresponding to a toral
algebraic group. Algorithms for the latter problem can be used to
compute the unit groups of integral group rings of abelian groups.

Dane Flannery 
Sep 19 
Sejong Park NUI, Galway 
Fusion, bisets and cyclic subgroups
This talk is intended as an introduction to the main
characters in my research. We start with a curious characterization of
(finite) cyclic groups (Th\'evenaz 1989) as groups G whose numbers of
double cosets form a nonsingular matrix M. We discuss how the biset
structure of the group G determines the fusion pattern in G and in
turn the matrix M. Then we introduce fusion systems and discuss why
it is interesting. Finally we formulate fusion version of Th\'evenaz'
theorem and sketch a proof. Time permitting, connection between the
matrix M and the theory of biset functors will be discussed.

Michael Mc Gettrick 
Sep 26 
JeongSook Im NUI, Galway 
Applications of a boundary integral method for unsteady water waves
We have applied a spectral boundary integral method to study the nonlinear evolution of water waves in various geometries. A similar method has previously been used to study periodic water waves, for which it generated highly accurate solutions in the many previous works. We have adapted the method to a nonperiodic geometry and used the method of images to satisfy the boundary condition of no flux on the walls. We use Chebyshev polynomials as basis functions and the ClenshawCurtis method to evaluate the boundary integral with spectral accuracy. Function evaluations are only required at the Chebyshev points. We have tested the method and then used it to simulate the flipthrough phenomenon and breaking waves. I will illustrate the numerical results with a variety geometries.

Michel Destrade 
Oct 2 Wednesday
3pm(ADB2018)

Antonio Augusto Franco Garcia
Department of Genetics, ESALQ/USP, Brazil

Statistical models for genetic mapping in autopolyploids, with applications in sugarcane
Sugarcane is a complex autopolyploid, since it has a high number of chromosomes on each homology group, with frequent aneuploidy. In fact, the ploidy level could be different for each homology group. This species, and a number of similar ones, do not fully benefit from modern marker technology (specially SNPs), since the statistical methods available are based on unrealistic assumptions and are in general based on the genetical behavior of diploids. In this lecture, I will show a number of new models that have been developed to: a) make the SNP call and estimate ploidy level; b) building linkage maps; c) perform QTL mapping. Examples will be presented and discussed.

John Hinde

Oct 10

John Burns
NUI, Galway

The Geometry of Maximal Tori, Continuous and Discrete
Motivated by a question in Statistical Mechanics, we classify the conjugacy classes of maximal order Abelian subgroups of Weyl groups. The classification and its applications will encounter many old friends and some new ones (Symmetric spaces, branching rules, del Pezzo surfaces, Fano planes and Qubits).

Haixuan Yang

Oct 16 Wednesday
2pm(ENG2052)

Ray W. Ogden FRS
University of Glasgow

Elasticity of biopolymer filaments and crosslinked Factin networks with compliant binding proteins
Crosslinked actin networks are important constituents of the cytoskeleton. In order to gain deeper insight into the interpretation of experimental data on the mechanics of actin networks,
adequate models are required. Here we introduce an affine constitutive network model for crosslinked Factin networks based on nonlinear continuum mechanics, and specialize it in order to reproduce the experimental behaviour of in vitro reconstituted
model networks. The model is based on the elastic properties of single filaments embedded in an isotropic matrix. In particular, the model is able to reflect the experimentally determined
shear and normal stress responses of crosslinked actin networks typically observed in rheometer tests. The single filament model is then extended by incorporating the compliance of crosslinker
proteins and further extended by including viscoelasticity. The model facilitates parameter studies of experimental setups such as micropipette aspiration experiments, and an illustrative
example is presented.

Michel Destrade

Oct 17

Shaun Mahony
Penn State University

Characterizing contextdependent transcription factor activity during direct motor neuron programming

Cathal Seoighe

Oct 24 
Sune Reeh University of Copenhagen 
Burnside rings and fusion systems
The Burnside ring of a finite pgroup S consists of isomorphism classes
of finite Ssets, with disjoint union as addition, and completed
with additive inverses. We will consider in particular those Ssets
where the action of S is stable with respect to the additional
structure of a fusion system over S. We discuss the subring of these
fusionstable sets, transfer maps constructing stable Ssets from
unstable ones, and how this all relates to topology and the socalled
classifying spectrum of a fusion system.

Sejong Park 
Oct 31 
Sebastian Schoennenbeck RWTH Aachen 
Resolutions for unit groups of maximal orders 
Alexander Rahm 
Nov 7 
(1) Thong Nguyen (PhD defence talk)
10am, Plant Science seminar room (2) Antonio Díaz 3.45pm (1) NUI, Galway (2) Universidad de Málaga 
(1) Novel Insights into Chromatin Structure and Gene Regulation
through Integrative Analysis of High Throughput Genomics Data
(2) A generalization of the LyndonHochschildSerre spectral sequence(2)
Fusion systems are algebraic models for the structure of a
finite group at a given prime p. In this talk we construct a
LyndonHochschildSerre(LHSss)type spectral sequence for fusion systems.
This new spectral sequence computes the cohomology of a fusion system with
a strongly closed subgroup and it coincides with the classical LHSss. in
the case of an extension of finite groups. On the other hand, it might be
applied in situations where the LHSss cannot. For instance, to compute the
cohomology of the finite simple groups which possess a strongly closed
subgroup. We will describe an example in detail to show how the new
spectral sequence works.

(1) Cathal Seoighe (2) Sejong Park 
Nov 8 
Jorge Bruno (PhD defence talk) 10am NUI, Galway 
A Metric Approach to Topology: the epsilondelta obsession 
Aisling McCluskey 
Nov 14

Ted Hurley
NUI, Galway

Algebraic structures for communications
'Abstract algebra methods are fundamental and vital tools in the communications’ areas and are becoming even more so. This talk looks at various design requirements for communications with emphasis on abstract algebraic structures required.

Haixuan Yang

Nov 21 Thursday
(1) 10am (2) 3.45pm

(1) Deirdre Wall (PhD defence talk)
10am, ADB1019 (2) Bent Nielsen 3.45pm
(1) NUI, Galway
(2) Oxford University

(1) Integration of Genetic Biomarkers in Prognostic Models for Breast Cancer Survival
(2) Inference and forecasting in the ageperiodcohort model with unknown exposure with an
application to mesothelioma mortality

(1) John Newell (2) Milovan Krnjajic

Nov 28

Grant Lythe
University of Leeds

Stochastic modelling and immunology: how many populations? how many cells? how many encounters?
More than 0^{11}$ T cells circulate through the human body, using
Tcell receptors (TCRs) to probe the surfaces of antigenpresenting
cells they come into contact with. One T cell has only one type of TCR
on its surface, on average about 30,000 of them. How many different
types of T cells do you have? Tcell activation relies on encounters
with dendritic cells in lymph nodes. How many dendritic cells are
required to initiate a Tcell response?
We present a stochastic model of the T cell repertoire, based on
competition between large numbers of clonotypes. We also present a
simplified theoretical model, approximating the movement of cells in a
lymph node by Brownian motion, that yields simple expressions for the rate
of contacts between two types of immune cells that are compared with
direct experimental measurements from Institut Pasteur.

Cathal Seoighe

Dec 5 
Rupert Levene University College Dublin 
Distance formulaeWe will discuss formulae and estimates for the distance to
various linear subspaces of B(H), the bounded operators on a Hilbert
space. This will touch on some joint work in progress with Ivan
Todorov and Georgios Eleftherakis. 
Niall Madden 
Dec 12 
Martin Stynes University College Cork 
A finite difference method for a twopoint boundary value problem
with a Caputo fractional derivativeThis talk assumes no prior knowledge of fractionalorder
derivatives, which will be introduced gently. A twopoint boundary value
problem whose highestorder term is a Caputo fractional derivative of order
δ ∈ (1,2) is considered. We discuss a suitable comparison/maximum
principle for this problem and describe sharp a priori bounds on the
derivatives of its solution u.
These show that u''(x) may be unbounded at the interval endpoint
x=0 which hints that the numerical analysis of
this problem will not be routine. We describe a finite difference method for
the problem, in which linear algebra considerations lead us to discretize
the convective term using simple upwinding in order to get a stable method
for all values of δ. A pointwise convergence result is stated for
this method and numerical results are presented to illustrate its
performance.
While a basic knowledge of finite difference methods and their analysis
would be helpful in following the later stages of the talk, most of the
material should be accessible to everyone. 
Niall Madden 
Dec 19
11am

Anthony Cronin
UCD

Three Problems in Matrix Theory
In this talk I will outline three problems still outstanding in
Matrix Theory.
(1) The Nonnegative Inverse Eigenvalue Problem (NIEP), including history,
major results, and my contribution.
(2) Integral Similarity of Matrices. Given two matrices A and B with integer entries can we decide if
these are integrally similar i.e. can we find an invertible matrix P with integer entries such
that P^{1}AP=B?
(3) The Pascal Matrix. I will consider the problem of finding the multiplicative order of the
matrix S_{n} which is derived from the Pascal matrix and give some new results on this order.

Niall Madden

Jan 9 
Neil Dobbs University of Helsinki 
Typical behaviour in onedimensional dynamical systems 
Petri Piiroinen 
Jan 16

David Malone
NUI Maynooth

Guessing and Passwords
From the point of view of an attacker, passwords could be
regarded as a probabilistic guessing game. In this talk, I'll
review some information theoretic style results related to
password guessing, discuss the analysis of reallife password data,
and discuss how these results might be applied.

Niall Madden

Feb 13 



Feb 20 
Final Year Students NUI, Galway 
Project presentations (from 11.45 to 16.15) 
Emil Sköldberg 
Feb 27 
Marcelo Forets Université Joseph Fourier (Grenoble) 
The Cauchy problem for the continuous limit of Quantum Walks
Quantum walks (QW) are the quantum analogue of classical random walks. They are a promising framework for algorithmic applications and more recently for the modelisation of quantum physical phenomena. Essentially, a discrete time QW is a finite difference scheme with physically
motivated properties, such as: unitarity, translation invariance and causality. It is known that in the continuous limit the
QW gives the Dirac equation of relativistic quantum mechanics (to be introduced). However this correspondence is often given either via long time limits or carried out via numerical simulations.
In this talk I propose to explore convergence and error bounds in the Sobolev norm for the above Cauchy problem, where the Dirac equation is wellposed. I will use elementary tools of PDE theory (operator splitting techniques, Sobolev spaces, Lax equivalence theorem). Time permitting, the problem of sampling/reconstruction of the multidimensional wavefunction will be discussed.

Michael Mc Gettrick 
Mar 4 Tuesday
2pm

Kevin Doherty (PhD defence talk)

Mathematical Models of Centromere Associating Proteins

Marin Meere

Mar 6

Giuseppe Zurlo
National University of Ireland, Galway

The Mechanical Modelling of Cell Membranes
The lipid bilayer is the main component of cell membranes and its mechanical features are fundamental in cell functionality. During the last decades, the progresses of microscopy techniques unveiled that the lipid bilayer plays a fundamental role in shaping the cell surface, by the means of a complex chain of effects starting at the level of the single lipid molecule. Due to the complexity of the interactions among chemical and mechanical effects, the theoretical modelling of the lipid bilayer is still an open issue, which is of primary interest both for a deeper understanding of cell functionality, and for the design of liposomes, artificial biological membranes which can be used for targeted drug delivery in advanced pharmacological applications. In this seminar we will discuss some recent advances in the modelling of the lipid bilayer, showing how chemistry and the mechanics of thin, deformable bodies may provide a simple and effective theory supporting the most recent observations, and suggesting new possible experiments.

Michael Mc Gettrick

Mar 10 Monday 4.00pm

Paul Korir (PhD defence talk) National University of Ireland, Galway 
Estimation and Analysis of Gene Expression and Alternative Splicing: Perspectives from Development and Disease 
Cathal Seoighe 
Mar 13 
Nina Snigereva University College Dublin 
Dynamics of Lorenz maps
Lorenz maps arise naturally in the study of a geometric model
of Lorenz differential equations and have been investigated intensively.
In this talk I will first review some of the classical results in this
area. In particular, a piecewise continuous interval map whose
derivative is constant everywhere, apart from at a finite number of
points, is the simplest example of a Lorenz map and its dynamics is
fairly well understood. I will discuss on how some features of a general
Lorenz map can be studied via piecewise continuous interval maps.
Then I will present recent joint work with T. Samuel and A. Vince which
addresses the question on when the symbolic dynamics of a given Lorenz
map can be fully embedded in the symbolic dynamics of a piecewise
continuous interval map. As an application of this embedding result, I
will describe a new algorithm for calculating the topological entropy of
a Lorenz map. If time permits, I will discuss some related open questions. 
Götz Pfeiffer 
Mar 14 Friday
2pm

Attia Fatima (PhD defence talk)
National University of Ireland, Galway

Analysis of hepatic microRNA expression in postpartum dairy cows in negative energy balance

Cathal Seoighe

Mar 20 
Tom Weber National University of Ireland, Maynooth 
Quantifying the length and variance of the eukaryotic cell cycle phases by a stochastic model and dual nucleoside pulse labelling 
Cathal Seoighe 
Mar 26 Wednesday, SC200A (Main Concourse) 3.15pm

Tom Gilroy (PhD defence talk) NUI, Galway 
Genus Two Zhu Theory for Vertex Operator Algebras 
Michael Tuite 
Mar 27

Stephen Power
Lancaster university

The Rigidity of Infinite Graphs and Crystals
Geometric rigidity theory has its origins in the theory of barjoint linkages and Cauchy's
rigidity theorem for convex simplicial polyhedra. A foundational result of G. Laman in 1970 characterises those finite simple graphs whose
generic realisations in R^{2} give
rigid barjoint frameworks. Rigidity theory is also relevant in the condensed matter physics of crystals in connection with low energy phonon modes (rigid unit modes or RUMs) and displacive phase transitions. Here the barjoint frameworks in mathematical models are infinite and crystallographic.
I intend to give a nontechnical overview of some recent work with Derek Kitson. On the generic side, we obtain generalisations of the Cauchy and Laman theorems for nonEuclidean norms and for infinite graphs. On the crystallographic side we characterise almost periodic rigidity in terms of the RUM spectrum (or Bohr spectrum) of the crystal framework. I hope to convey the fact that geometric rigidity theory is a wonderfully hybrid research area with interesting pure and applied directions. In particular infinite frameworks and their infinite rigidity matrices invite methods from harmonic analysis and operator theory.

James Cruickshank

Apr 3 
Norbert Hoffmann Mary Immaculate College (University of Limerick) 
Rational families of instanton bundles on P^{2n+1}
Instanton bundles are algebraic vector bundles of
rank 2n on complex projective (2n+1)space having a particular
Chern polynomial and with certain cohomology groups vanishing.
The talk is about two natural irreducible loci in the moduli space
of symplectic instanton bundles. One result is that these loci
are often rational. I will also present some evidence for Ottaviani's
conjecture that one of the loci is an irreducible component for n > 1,
and deduce that the moduli space is then reducible. This is
joint work with L. Costa, R.M. MiroRoig and A. Schmitt.

Götz Pfeiffer 
Apr 10

1) Le Van Luyen (NUI, Galway) 10am 2) John Murray (NUI, Maynooth) 3:45pm

1) Homology of ntypes (PhD defence talk) 2) Symplectic Modules and Induction
1) To be announced
2) Given a group G and a field k, a kGmodule is a kvector space M on which G acts as klinear transformations i.e. there is a group homomorphism G>GL(M). When char(k) is a prime divisor p of the group order G, there is a welldeveloped theory of vertices and sources (due to J. A. Green) which uses induction and restriction to relate kGmodules to kPmodules, where P ranges over the psubgroups of G.
We can replace GL(M) by one of the smaller groups O(M), Sp(M) or U(M), as M affords an orthogonal, symplectic or unitary geometry. Unfortunately much of the module theory (e.g. unique decomposition into indecomposables) and vertex theory does not carry over to modules with Ginvariant forms. We outline our investigations into what can be retrieved, when char(k)=2 and M is a nontrivial selfdual irreducible kGmodule. A result of P. Fong's guarantees that M has a unique symplectic geometry. We make use of an elaboration of Galgebra theory due to L. Puig.

1) Graham Ellis 2) Rachel Quinlan

Apr 17 



Apr 24 



May 1

Research Day

Research Day


May 8

Robert Osburn
UCD


Rachel Quinlan

Oct 2

Doug Wiens
University of Alberta

Robustness of Design: A Survey
When an experiment is conducted for purposes which include fitting a particular model to the data, then the 'optimal' experimental design is highly dependent upon the model assumptions  linearity of the response function, independence and homoscedasticity of the errors, etc. When these assumptions are violated the design can be far from optimal, and so a more robust approach is called for. We should seek a design which behaves reasonably well over a large class of plausible models.
I will review the progress which has been made on such problems, in a variety of experimental and modelling scenarios  prediction, extrapolation, discrimination, survey sampling, doseresponse, etc.

Jerome Sheahan
