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The seminar usually takes place on Thursdays from 4pm to 5pm in room ADB-1020
of the School of Mathematics, Statistcs and Applied Mathematics, which is located
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 (ADB-G022) 30 minutes before the seminar starts.
A list of seminars from the 2013/2014 academic year as also available.
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.
If you wish to receive email announcements/reminders of these seminars, go to https://listserv.heanet.ie/cgi-bin/wa?A0=NUIG-MATHS-SEMINARS where you can join the circulation list.
|Sep 11||Rob Craigen
University of Manitoba
|Structure and Permutation Symmetry of Matrices
Say that two matrices are (permutation) equivalent if one can be
obtained by permuting the rows and columns of the other. Suppose a
matrix is equivalent to its transpose. Must it necessarily also
be equivalent to a symmetric matrix? More generally, what sort of
matrix is equivalent to its own transpose?
The answers are elegant and perhaps a little startling; we will derive an essentially complete solution, and discuss a couple of contexts in which these questions arise naturally.
National University of Ireland Maynooth
|Improving data visualisations with dendrogram seriationVisualisation is a key but often neglected step in data and model exploration.
Data visualisation is about comparisons, perhaps between variables, cases, groups, and or models. Stock visualisations provided in packages such as R benefit from systematic ordering (i.e. seriation) of data objects to highlight features and structure. The theme of this talk will be the use of seriation to improve data graphics. We describe a general-purpose seriation algorithm based on dendrograms which easily adapts to different visualization settings.
University of Alberta
|Robustness of Design: A SurveyWhen 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, dose-response, etc.||Jerome Sheahan|
|Oct 9||Graham Ellis
|Pictures from AustriaI will describe some computational analyses of real data involving basic notions and results from topology.||Sejong Park|
|Oct 16||Paul Bankston
|A betweenness perspective on dendrons and their kinThe betweenness condition that defines a dendron to be a continuum in which each pair of points have a third point whose removal separates the first two points in the remainder is weakened in two different ways: the first says that the first two points are maybe not separated in the remainder of the third, but at least they're in different components of that remainder; the second says that the first two points are in separate continuum components of the remainder of the third. We examine the idea of being a dendron relative to these weakened betweenness conditions.||Aisling McCluskey|
|Oct 23||No Seminar: Graduation
||No Seminar: Graduation|
|Nov 6||Aodhan de Bruen
|The basics of basesLet V=V(n,F) be an n-dimensional vector space over the field F and let S be a spanning set in V. We discuss the following 2 questions:
a.What is the minimum number of bases contained in S?
b.What is the maximum number of bases contained in S if F is finite?
Biographical sketch. Aodhan de Bruen(Aiden A Bruen) was born in County Galway and read mathematics at UCD.He took a PhD in Toronto where he worked with F.A.Sherk and H.S.M.Coxeter and is a research professor at Carleton University. He has held academic positions at Universities in North America and spent some time on the staff at the Los Alamos National Laboratories in New Mexico. His interests are in geometry and groups,codes and cryptography. He is a keen tennis player ,a fan of the Montreal Canadiens and the Galway hurling team
|Cryptosystems made in Galway - closing a gap in internet security?The encryption systems used to secure online bank accounts and keep critical communications private could be undone in just a few years, security researchers warned at the Black Hat conference last year. The only alternative to the threatened currently used encryption systems which is so far recognised for yielding systematic security improvements is Elliptic Curve Cryptography (ECC). Implementations of ECC were patented by a company called Certicom. Companies that want to use ECC will need to make expensive deals with Certicom to avoid lawsuits, writes the MIT Technology Review. This is why it is time now to develop new cryptosystems and to prove their security. NUI Galway already has experience on patenting cryptosystems, but resources were not available so far for establishing security proofs that would convince the markets. This is why Emil Skoldberg, Alexander D. Rahm and Nghia Thi Hieu Tran want to build up a research group for the development of Bianchi groups cryptosystems, which will lay the foundations for a cryptography research cluster with the critical mass to release a worldwide recognised encryption system.||Emil Skoeldberg|
|Nov 20||Antonio Díaz
Universidad de Málaga
|The cohomology of J_2 at p=3We describe the cohomology ring of the second Janko group J_2 with coefficients in the field of 3 elements. To compute it, we use the new spectral sequence that I described in this seminar last year. It turns out that this ring is Cohen-Macaulay and its quotient by the polynomial part satisfies Poincaré duality. This raises the question of whether this quotient ring is the cohomology of some manifold. The answer is positive and the manifold is a quotient of the compact Lie group G_2 by a discrete subgroup. We also present other instances of this interaction between sporadic finite simple groups and compact Lie groups related to Dickson's algebras of invariants at p=2.||Sejong Park|
||Nghia Thi Hieu Tran
Ho Chi Minh City
|The Artinianess of graded generalized local cohomology modulesThis talk wants to present the Artinianess of some classes of graded generalized local cohomology modules. Generalized local cohomology was introduced by J. Herzog in 1974. It is a generalization of Grothendieck's local cohomology theory. In particular, we consider it for a given Noetherian commutative local ring R with the unit element 1 different from 0, for each pair of modules M, N over R. A recent result of the speaker is that under certain additional assumptions, this cohomology vanishes in high enough dimensions. This allows to obtain partial information about the projective dimension of M and the Krull dimension of N.||Alexander D. Rahm|
|Dec 4||Seventh de Brun Workshop on Homological Perturbation Theory
||Seventh de Brun Workshop on Homological Perturbation Theory||Graham Ellis|
|The colored cubes puzzle: a tribute to Percy MacMahonStart with a collection of cubes and a palette of six colors. We paint the cubes so that each cube face is one color, and all six colors appear on every cube. Take n^3 cubes colored in this manner. When is it possible to assemble these cubes into an n × n × n large cube so that each face on the large cube is one color, and all six colors appear on the cube faces? For the 2 × 2 × 2 case we give necessary and sufficient conditions for a set of eight cubes to have a solution. Furthermore, we show that the (colored cubes)^3 puzzle always has a solution for n > 2.||Alexander Rahm|
|Dec 11||No Seminar
||Research students meeting||Niall Madden|
University of Helsinki
|Commutator Maps and ChaosLinear dynamics has been a rapidly evolving area of operator theory since the late 1980s. I will begin by recalling some basic examples and results to introduce the notion of hypercyclicity of bounded linear operators in the setting of separable, infinite-dimensional spaces. The primary goal is to discuss the dynamics of commutator maps $S\mapsto AS-SA$, for a fixed operator $A$, on spaces of operators. Hitherto the only results in this setting have been the characterisation of the hypercyclicity of the left and right multipliers. The main non-trivial example I will show is that scalar multiples of the backward shift operator, which is hypercyclic on the sequence space $\ell^2$, never induce a hypercyclic commutator map on separable Banach ideals. This is joint work with Eero Saksman and Hans-Olav Tylli.||Ray Ryan|
|The Markov Chain Tree Theorem in the Max Algebra and SemiringsThe classical Markov Chain Tree Theorem relates the stationary vector of an irreducible Markov chain to the weights of directed spanning trees in the associated digraph. In this talk I will discuss some recent work extending the Markov Chain Tree Theorem to matrices defined over the Max Algebra. I will describe two independent proofs of this result and discuss the relation of the spanning tree vector'' to the Kleene Star and the critical subgraph. An extension of the result to general commutative semirings will also be discussed.||Niall Madden|
IBM Research – Zurich
|Re-imagining the radio telescope and sampling from Gaussian processesThe Square Kilometre Array (SKA) is a global science and engineering project to build the world’s largest radio telescope. The sheer enormity of the planned antenna array leads to scaling issues, in terms of power consumption (in the desert and centrally), and computation (from the vast quantity of data). The current state of the art is afraid of losing data, implicitly leaning on over-engineering to compensate for uncertainty. I will first present an overview of our team’s work in novel algorithms for the SKA and other telescopes. Our approach is inherently holistic, considering the algorithms from acquisition to image creation. Ultimately, radio interferometry is a method for parameter estimation, of the location and brightness of sources in sky. So, in the second part, I will look at parameter estimation from signal samples at antennas. In particular, I will derive accuracy of statistical estimators given filtered stationary, circularly-symmetric complex Gaussian stochastic processes. One nice insight is that, contrary to what one would think given the sampling theorem, sampling beyond Nyquist can increase accuracy.||Jerome Sheahan|
||final year project presentations
|Some comments on the ranks of subspaces of Mn(F)'We consider 2-dimensional subspaces of Mn(F) where F=F_q is a finite field. The theme is to study the distribution of ranks which arise in these subspaces. This is a report back on a period of study leave during 2014.||H Yang|
|Equivalences between blocks of cohomological algebrasLet G be a finite group and k be a field of characteristic p. There is a bijection between the blocks of the so-called cohomological Mackey algebra and the blocks of the group algebra. In this talk we will show that the existence of a splendid derived equivalence between blocks of group algebras implies the existence of a derived equivalence between the corresponding blocks of the cohomological Mackey algebras. As application of this theorem, we give an example of a finite group with surprising representation theory.||Sejong Park|
|Triangulating the permutahedronFor an Artin group G of finite type we relate the K(G, 1) of Salvetti with the K(G,1) given by noncrossing partitions. This is work in progress with Emanuele Delucchi and Colum Watt||Emil Skoldberg|
|Timothy J. Healey
University of Bath
Polish Academy of Sciences
Institut de Mathématiques de Toulouse