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Mathematics, Statistics and Applied Mathematics Seminar 2011/12

The seminar usually takes place on Thursdays from 3.45pm to 4.45pm in room C219 of the School of Mathematics, Statistcs and Applied Mathematics, which is located in Áras de Brún (Block C).
   The talks are directed towards a general mathematical audience and everyone interested is very welcome to attend. Tea/coffee/biscuits/cake will be available in the ground floor research room from 3.15pm.
   Previous seminars are listed here.

Abstracts when available can be obtained by rolling the mouse over a title. Clicking a title sometimes provides a longer version of the talk in PDF format.

Academic year 2011 to 2012

Date	Speaker	Title	Contact
Sep 8	Carlo Di Franco University College Cork	Two-dimensional quantum walks with reduced experimental resourcesQuantum walks, being the analogue of classical random walks, have recently emerged as a topic arising the interest of a wide scientific community, in the same way that their classical counterparts have found applications in different fields, ranging from physics to computer science and from economics to biology. The behaviour of quantum walks has been analysed in literature and a striking application in quantum computation for a particular two-dimensional quantum walk, known as Grover walk, has been found. And yet, the experimental realisation of known two-dimensional quantum walks is extremely challenging, due to the significant technological effort required. One of the difficulties is clearly the dimension of the coin space, larger than the one necessary for the implementation of one-dimensional walks. A simplification in this respect is highly desirable, especially from a practical perspective. In this talk, I present a significant step forward in this direction: a scheme for a two-dimensional quantum walk that requires only a two-dimensional coin space. I formally prove that this protocol is able to generate the same spatial probability distribution of the Grover walk in its non-localised case. Another interesting aspect in quantum information science is the generation of entanglement, a particular kind of quantum correlations that is a critical requirement for quantum metrology, quantum computation and communication. I show that the proposed scheme is actually more efficient in the generation of x-y spatial entanglement with respect to the original Grover walk. A very clear explanation can be found, also in this case, in the smaller dimension of the coin space.	Michael Mc Gettrick
Sep 15	Marlos Viana University of Illinois at Chicago	Dihedral Fourier Analysis of Symmetry Preference Data (joint colloquium with the School of Physics)http://www.maths.nuigalway.ie/research/vianaABS.pdf	John Hinde
Sep 16 Friday in C218 12.00	Chris Glasbey Biomathematics and Statistics Scotland (BioSS)	Dynamic programming versus graph cut algorithmsImage restoration, segmentation and template matching are generic problems in image processing that can often be formulated as non-parametric model fitting: maximising a penalised likelihood or Bayesian posterior probability for an I-dimensional array of B-dimensional vectors. The global optimum can be found by dynamic programming provided I=1, with no restrictions on B, whereas graph cut algorithms require B=1 and a convex smoothness penalty, but place no restrictions on I. I compare conditions and results for the two algorithms, using restoration of a synthetic aperture radar (SAR) image for illustration.	John Hinde
Sep 22		Reserved for visit to the School by the University President
Sep 29	Rachel Quinlan NUI, Galway	What I did on my sabbaticalThe following question, arising from a construction involving automorphisms of finite p-groups, was posed by F. Szechtman in a 2003 paper in the AMS Proceedings : for a vector space V of dimension n over a field F, what is the minimum possible dimension of a (non-linear) affine subspace of EndF(V) that contains elements annihilating all hyperplanes of V? This question is equivalent, under a duality arising from the trace bilinear form on Mn(F), to the problem of determining the maximum possible dimension of a linear subspace of Mn(F) in which no element possesses a non-zero eigenvalue that belongs to the field F. This talk will explain this duality and show how it can be used to solve both of the problems mentioned above, independently of the field under consideration. The duality relation will then be explored in a wider context involving affine spaces of square and rectangular matrices that have special rank properties and special covering properties. One application that will be discussed is to the problem of characterizing partial matrices whose completions have ranks satisfying a prescribed lower bound. The only background needed for this talk is basic linear algebra and a little bit about bilinear forms.	Michael Mc Gettrick
Oct 6	Giuseppe Tinaglia King's College London	The geometry of constant mean curvature surfaces embedded in R^3In this talk I will discuss recent results on the geometry of constant mean curvature (H\neq 0) surfaces embedded in R^3. Among other things I will prove radius and curvature estimates for simply connected surfaces embedded in R^3 with constant mean curvature. It follows from the radius estimate that the only complete, simply connected surface embedded in R^3 with constant mean curvature is the round sphere. This is joint work with Bill Meeks.	John Burns
Oct 13	Avi Berman Technion (Israel Institute of Technology)	Diagonal stability and completely positive matrices.The talk will consist of a short survey of the theory of completely positive matrices and relate it to a newly defined concept of a common diagonal Lyapunov matrix. A necessary and sufficient condition for the existence of such a matrix will be derived. The second part of the talk is based on a recent paper with C. King	Rachel Quinlan
Oct 20	Niall Madden NUI, Galway	Fast solvers for singularly perturbed problemsIn recent years there has been great interest in the design and analysis of numerical schemes that yield robust solutions to singularly perturbed problems. However, these schemes lead to systems of linear equations that must be solved. It is usually assumed that this is easily done. However, as I'll outline in this talk, there are difficulties in applying standard direct solvers to popular finite element and finite difference discretizations. I'll then report on some developments of multigrid approaches for these problems. This is joint work with Scott MacLachlan, Tufts University.	Michael Mc Gettrick
Oct 27	Ben McKay University College Cork	Rolling balls, complex manifolds and the Lie algebra G2Hilbert wrote out an example of an underdetermined ODE system that he proved cannot be solved by elementary methods. Cartan described the same ODE system geometrically, in terms of rolling balls, and algebraically in terms of an exceptional simple Lie algebra. This system complexifies to a complex analytic ODE on a compact complex manifold. I found a surprising characterization of Hilbert's ODE in terms of complex manifolds.	Javier Aramayona
Nov 3	Clifford Nolan University of Limerick	Microlocal Analysis of Bistatic Synthetic Aperture Radar ImagingWe consider radar imaging of ground terrain from a pair of moving radar systems. Radio waves are emitted from one radar, scatter off the ground topography and are measured by the other radar system. High frequency variations of the index of refraction on the ground are responsible for the scattered waves and we model the measured radar data as the output of a linear scattering operator F acting on the latter index of refraction. We show that F is a Fourier integral operator and we analyse the image obtained by backprojecting the data, i.e., applying the formal L2 adjoint F* of F to the data. The analysis hinges on the normal operator F*F whose distribution kernel which is an oscillatory integral associated to a pair of cleanly intersecting Lagrangian submanifolds of phase space.	Niall Madden
Nov 17	Götz Pfeiffer NUI, Galway	Monomial representations of finite Coxeter groups A square matrix is called monomial if it has exactly one nonzero entry in each row and column. If G is a finite group, then each 1-dimensional representation of a subgroup H of G gives rise to a representation of G by monomial matrices, and each monomial representation of G can be described in terms of these. But, in general, not every matrix representation of G is monomial. In this talk I will discuss the significance of monomial representations in finite group theory and report about some recent research on surprising properties of certain monomial representations in case G is a finite Coxeter group (such as the symmetric groups or the dihedral groups). This is joint work with M. Bishop, G. Röhrle and J. M. Douglass.	Michael Mc Gettrick
Nov 24	Carmen Molina-Paris University of Leeds	Lymphocyte populations: homeostatic regulation and receptor diversity maintenance -- a stochastic modelling approach T cells are specialised white blood cells (lymphocytes) that protect the body from infection and are also able to kill infected cells. T cells are characterised by the presence of a special receptor on their cell surface called T cell receptor (TCR). The specificity of the T cell, namely which pathogens it can recognise, is determined by the molecular structure of its TCR. T cells can be classified according to their TCRs. All T cells that have identical TCRs are said to belong to the same clonotype. There are two types of T cells: naive and memory. Naive T cells have not yet encountered pathogens and memory T cells have already encountered pathogen. In this talk, I will only consider the class of naive T cells. A diverse naive T cell pool is essential to protect against novel infections, as the immune system cannot predict which pathogens the organism will be exposed to during its life-time. A healthy adult human possesses approximately 10^{11} naive T cells, which belong to about 10^7-10^8 different clonotypes. The reliability of the immune response to pathogenic challenge depends critically on the size (how many cells) and diversity (how many different TCRs or clonotypes) of the naive T cell pool of the individual. Experimental evidence suggests that interactions between TCRs with self-peptides (self-peptide = a fragment of a household protein) displayed on the surface of specialised cells, called antigen presenting cells (APCs), are important in controlling naive T cell numbers. Naive T cells undergo one round of cell division after receiving a survival stimulus from these specialised APCs. Whether or not a particular naive T cell can receive a survival signal from an specialised APC depends both on the TCR it expresses and the array of self-peptides displayed on the surface of the APC. Competition amongst naive T cells for these interactions regulates the diversity of the naive T cell pool. We have made use of a probabilistic (stochastic) model to describe this competition. In particular, we have modelled the time evolution of the number of T cells belonging to a particular clonotype. Our results indicate that competition maximises TCR diversity by promoting the survival of T cell clonotypes that are most different from each other in terms of the self-peptides they are able to recognise.	Cathal Seoighe
Dec 1	Victor Bovdi University of Debrecen	Lie nilpotency indices of modular group algebrasLet R be an associative algebra with identity. The algebra R can be regarded as a Lie algebra, called the associated Lie algebra of R, via the Lie commutator [x,y]=xy-yx, for every x,y\in R. Set [x1, ...,xn]=[[x1, ...,xn-1],xn], (xi in R). The n-th lower Lie power R[n] of R is the associative ideal generated by all the Lie commutators [x1,...,xn], where R[1]=R and xi \in R. By induction, we define the \emph{n-th upper Lie power} R(n) of R as the associative ideal generated by all the Lie commutators [x,y], where x\in R(n-1), y\in R and R(1)=R. An algebra R is called lower Lie nilpotent (respectively upper Lie nilpotent) if there exists m such that R[m]=0 (R(m)=0). The minimal integers m,n such that R[m]=0 and R(n)=0 are called the lower Lie nilpotency index and the upper Lie nilpotency index of R and these are denoted by tL(R) and tL(R), respectively. In my talk we discuss relations between tL(R) and tL(R) in the case when R is a modular group algebra	Ted Hurley
Dec 8	Stephen Kirkland NUI Maynooth	Load balancing for Markov chainsA square matrix T is called stochastic if its entries are nonnegative and its row sums are all equal to one. Stochastic matrices are the centrepiece of the theory of discrete-time, time homogenous Markov chains on a finite state space. If some power of the stochastic matrix T has all positive entries, then there is a unique left eigenvector for T, known as the stationary distribution, to which the iterates of the Markov chain converge, regardless of what the initial distribution for the chain is. Thus, in this setting, the stationary distribution can be thought of as giving the probability that the chain is in a particular state over the long run. In many applications, the stochastic matrix under consideration is equipped with an underlying combinatorial structure, which can be recorded in a directed graph. Given a stochastic matrix T, how are the entries in the stationary distribution influenced by the structure of the directed graph associated with T? In this talk we investigate a question of that type by finding the minimum value of the maximum entry in the stationary distribution for T, as T ranges over the set of stochastic matrices with a given directed graph. The solution involves techniques from matrix theory, graph theory, and nonlinear programming.	Niall Madden
Jan 12	Alexander Rahm NUI, Galway	Torsion subcomplex reduction and conjugacy classes graphs An innovation in the study of arithmetic groups comes with the recently introduced technique of torsion subcomplex reduction. Given a cell complex acted on by an arithmetic group, the torsion subcomplexes are extracted from the quotient space by collecting the cells with elements of a given prime order in their stabiliser. The torsion subcomplexes determine a great deal of the homological torsion of a group. The conjugacy classes graph is constructed purely group-theoretically, without involving any cell complex. We can show that for all the Bianchi groups with units {+/- 1}, and all prime numbers, the reduced torsion subcomplex is isomorphic to the conjugacy classes graph. The latter can be computed very efficiently.	Graham Ellis
Jan 19	Conor Houghton Trinity College Dublin	The temporal structure of spike train noise In the brain, signals are carried from neuron to neuron in the form of spike trains, sequences of voltage pulses. Given that these signals support the analysis of external communications, along with all the other glories of our mental processes, they appear to be surprisingly noisy. The same stimuli prompt very variable results. Mathematically, the space of spike trains is best thought of as a metric space; here a trick based on a spike train metric is used to study one aspect of spike train noise.	Niall Madden
Jan 23 Monday 9.00am	Barry Hurley NUI Galway	Classification problems for finite linear groups	Niall Madden
Jan 24 Tuesday 3.00pm	Alan Rogerson	Developing Quality in Mathematics Education Bio: Dr. Alan Rogerson lives in Poland and has spent most of his life learning and teaching: mathematics, informatics, history, sociology, philosophy and English literature, in universities and schools in the UK, Italy, Australia and Brazil. He was Research Director of the SMP (School Mathematics Project in the UK) in the 1970s and has worked extensively since then with innovative projects in mathematics education and in the use of technology. He has traveled widely abroad, visiting schools and lecturing, and has written many articles and books, mainly in mathematics education. He is International Coordinator of the Mathematics Education into the 21st Century Project which holds conferences every two years to disseminate new and exciting ideas in education, especially technological innovations. After graduating in Mathematics at London University, he went on to complete research degrees in Education (at Cambridge), The History and Philosophy of Science (at London) and obtained his Doctorate at Oxford University in History & Sociology. He later obtained a degree in English Literature externally at London University and completed two years full time doctoral study on Shakespeare at Monash University, Melbourne. He was formerly Junior Research Fellow in History/Sociology at Wolfson College and a Lecturer in Mathematics at Queens College, Oxford University for ten years. He has taught graduates and undergraduates at Oxford, London and many other universities throughout the world, including a year as Visiting Professor at the University of Cagliari, Italy.	Kevin Jennings
Jan 26	PhD & MSc Students NUI, Galway	Postgrad blitz talks[What research I have recently completed] and/or [what I am currently working on]	Louise Nolan
Feb 2	Final Year Students NUIG	Final Year Project PresentationsClick title for a detailed schedule.	Claas Roever
Feb 9	Colin Wilmott Masaryk University (Brno)	Quantum sign permutation polytopes Convex polytopes are convex hulls of point sets in the n-dimensional space that generalise 2-dimensional convex polygons and 3-dimensional convex polyhedra. In this talk, we concentrate on the class of n-dimensional polytopes called sign permutation polytopes. We characterise sign permutation polytopes before relating their construction to constructions over the space of quantum density matrices. Finally, we consider the decade old problem of quantum W-state identification and show how sign permutation polytopes may be useful in addressing issues of robustness.	Michael Mc Gettrick
Feb 16
Feb 23	Michael Mackey UCD	Local triple derivationsA local derivation on an algebra is a linear map whose value at any point agrees with the value of an algebra derivation at that point. Richard Kadison introduced this definition and he proved that every continuous local derivation on a von Neumann algebra is a derivation. In this talk, we introduce the structure of complex Jordan Banach triples. Here, triple derivations can be considered to be the infinitesimal form of surjective isometries. We consider local triple derivations and provide a result analogous to that of Kadison.	Niall Madden
Mar 1	Kevin Hutchinson UCD	Polylogarithms and linear groups	Rachel Quinlan
Mar 8	Jesús Hernández Universidad Veracruzana (Mexico)	To be announced	Javier Aramayona
Mar 15
Mar 22
Mar 29
Apr 5	Easter
Apr 12	Aylwyn Scally Sanger Institute, Cambridge		Cathal Seoighe
Apr 19	Tim Downing NUI, Galway	To be announced	Michael Mc Gettrick
Apr 26	School Research Day	School Research Day	Michael Tuite
May 3
May 10
May 17
May 24
May 31

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