| 2012-05-11 | Fri | Andrew Gascoyne (Sheffield) | SP2RC Friday Seminars | |
| 13:05 | Lecture Theatre 9 | PARTICLE TRAJECTORIES AND ACCELERATION DUE TO 3D MAGNETIC RECONNECTION | ||
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Abstract: Magnetic reconnection is thought to be a primary mechanism in the acceleration of particles during flares in the solar corona. Particle acceleration by reconnection has been widely studied in 2D geometry, and thanks to recent work, particle acceleration in 3D is being investigated. We investigate the trajectories and acceleration of a particle injected into various 3D magnetic and electric field configurations by adopting a test particle approach. The electromagnetic fields studied here are solutions to the steady state, kinematic, resistive MHD equations (Wyper and Jain 2010). We numerically solve the equations that govern the motion of a charged particle in these electromagnetic fields and for various initial conditions, we analyse the kinetic energy of the particle and determine the regimes where efficient particle acceleration takes place. |
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| 2012-05-09 | Wed | Dr Anantanarayanan Thyagaraja (Culham) | ||
| 14:00 | LT6 | |||
| 2012-05-09 | Wed | Anantanarayanan Thyagaraja (Bristol) | Applied Maths Colloquium | |
| 14:00 | LT6 | A KdV-like advection-diffusion equation with remarkable properties | ||
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Abstract: Nonlinear partial differential equations which arise naturally in the the- ory of wave propagation in many branches of physics have both a rich history and wealth of novel properties, not shared by their linearized equivalents. The Korteweg-de Vries Equation (KdVE), which is now more than 100 years old, occupies a special place in this class, along with the complex Nonlinear Schro ̈dinger Equation (NLSE), and forms the core of the modern theory of the Inverse-Scattering-Transform tech- nique of solving equations of this type. Some colleagues and I have recently encountered a close ”cousin” of this equation [cf. Abhijit Sen et al, (2012), in press, Communications in Nonlinear Science and Numerical Simulations, also available as an ArXiv preprint] which has novel and interesting properties. It arose in a curious way during a ”ge- netic programming” search looking for equations which share solutions in common with the KdVE. In this talk, I will outline some of the more in- teresting features of this equation which also serves as a counter-example to some commonly held views about recurrent solutions in certain con- servative nonlinear dispersive wave equations. The new equation also has some properties which are not shared by the KdVE and appears to define a new class of interesting nonlinear partial differential equations describing wave motions. |
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| 2012-05-09 | Wed | Sotiris Bersimis (University of Piraeus) | Probability and Statistics Seminar | |
| 14:00 | LT-10 | Multivariate SPC with emphasis in multi-attribute processes | ||
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Abstract: Initially, the area of multivariate SPC will briefly overviewed and the basic procedures for implementing multivariate statistical process control via control charting will be reviewed. Specifically, multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart type control charts, MCUSUM control charts, and MEWMA control charts will be summarized and the problem of interpreting an out-of-control signal will be briefly discussed. Additionally, since in the literature, little work has been done to deal with multivariate attributes processes, which are very important in practical production processes, the presentation will close by presenting the special case, which arises when the quality of process of interest is not characterized by continuous characteristics. Furthermore, after the key points of multi-attribute process will presented, some procedures for controlling such processes will be discussed. |
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| 2012-05-04 | Fri | Michael Bareford (University of St Andrews) | SP2RC Friday Seminars | |
| 13:05 | Lecture Theatre 9 | The Energy Released from Relaxing Coronal Loops | ||
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Abstract: Relaxation theory offers a straightforward method for determining the energy released from a magnetic field when it undergoes an instability. Thus, an upper limit to the heating caused by ensembles of coronal loops can be estimated and compared with the coronal heating requirement. This talk will discuss the results obtained from the nonlinear magnetohydrodynamic (MHD) simulations of a sample of idealised coronal loops that are known to be linearly kink unstable. The principle aim is to determine whether or not these results agree with helicity-conserving Taylor relaxation (Taylor 1986, 1974). A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of specific line-tied field configurations based on a cylindrical coronal loop model. Initially, all configurations carry zero net current and are in ideally unstable equilibrium. Helicity is conserved to an acceptable level for all numerically-stable simulations. In addition, the energy release and final field profiles produced by the numerical simulations are in agreement with the predictions of relaxation theory: the relaxed field approximates a linear force-free state. Magnetic energy dissipation predominantly occurs within thin currents sheets. These results support the use of relaxation theory for calculating the heating-event distributions produced by ensembles of marginally unstable loops (Bareford et al. 2011). Bareford, M. R., Browning, P. K., | Van der Linden, R. A. M. 2011, Sol.Phys., 273, 93 Taylor, J. B. 1986, Rev. Mod. Phys., 58, 741 Taylor, J. B. 1974, Phys. Rev. Lett., 33, 1139 | |||
| 2012-05-03 | Thu | Simon Wood (University of Bath) | Probability and Statistics Seminar | |
| 14:00 | LT-6 | Simple statistical models for complex ecological data | ||
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Abstract: Much ecological theory is based on models that are relatively simple to write down and simulate from, while at the same time being capable of displaying very complicated dynamics. This talk suggests that such near chaotic dynamics provide a case where it is sensible to abandon conventional likelihood or Bayesian approaches in favour of inference based on carefully chosen statistics of the data. The statistics should be designed to avoid the irregularity produced by highly non-linear dynamics, while still being informative about the dynamic structure of the system being modelled. A simple approach to inference is proposed, which requires only the ability to simulate from the model. The approach has links to ABC, generalized method of moments, indirect inference and similar approaches, but requires rather little tuning. |
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| 2012-05-03 | Thu | Andrew Lobb (Durham) | Topology seminar | |
| 15:00 | Hicks Room J11 | Two-strand twisting and knot homologies | ||
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Abstract: We give an introduction to some quantum knot homologies and show how twisting up a pair of adjacent strands in a knot, combined with some straightforward homological algebra, allows us to deduce some interesting consequences. |
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| 2012-04-27 | Fri | Peter Whyper (University of Sheffield) | SP2RC Friday Seminars | |
| 13:05 | Lecture Theatre 9 | |||
| 2012-04-26 | Thu | Ronnie Loeffen (University of Manchester) | Probability and Statistics Seminar | |
| 14:00 | LT-6 | Spectral representations for affine processes | ||
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Abstract: Affine processes are widely used in various areas of mathematical finance, like credit risk modelling, interest rate modelling and stochastic volatility models. One of the advantages of working with affine processes is that one can compute European option prices via Laplace/Fourier inversion after solving a system of non-linear, first order ODEs. However, an explicit solution to this system exists only in a limited number of cases and numerically solving it seems cumbersome. Based on the work of Ogura (1974/75) on continuous-state branching processes, we discuss an alternative method in which the system of ODEs is replaced by a number of decoupled, linear, first order PDEs. Pros and cons of the method will be indicated and also some examples will be provided. |
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| 2012-04-26 | Thu | Martin Crossley (Swansea) | Topology seminar | |
| 15:00 | Hicks Room J11 | Conjugation Invariants in the Adem-free Steenrod algebra | ||
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Abstract: In work with Sarah Whitehouse we attempted to calculate the invariants of the mod 2 dual Steenrod algebra under the Hopf algebra conjugation. In work with Deniz Turgay we now tackle this problem by removing the Adem relations and working with a free associative algebra instead. We give a description of the linear structure of the conjugation invariants there, and comment on the remaining problem of deriving information on the Steenrod algebra. |
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| 2012-04-26 | Thu | Mike Payne, intro by Carol Calvert (Department of Work and Pensions) | RSS Seminar Series | |
| 16:30 | Hicks LT10 | Developing the DWP's Official Statistics Release - Tabulation Tool, Visualisation, and a Glimpse into the Future | ||
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Abstract: The Department of Work and Pensions have recently used published statistics on out-of-work benefit claimants to feed into Google's Public Data Explorer, which offers rich and powerful visualisations of the vast amount of statistics we release (see how over 50,000 figures can be displayed in one, interactive chart), and have complemented this with the publication of an interactive Google map showing the proportion of out-of-work benefit claimants across the country. The talk will briefly review the current DWP Tabulation Tool, describe how DWP's data is really suited to data visualisation, and demonstrate features to come - users will be able to create multi-dimensional tabulations, with the ability to download data directly in a number of formats (including the internationally recognised Statistical Data and Metadata Exchange - SDMX - format). |
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| 2012-04-25 | Wed | Nick Monk (Sheffield) | Applied Maths Colloquium | |
| 14:00 | LT6 | Modelling decision making in multicellular tissues. | ||
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Abstract: During the development of multicellular organisms, cells need to make decisions about their fate by integrating information from their neighbours, their surroundings, and their history. I will describe mathematical models of cellular decision making that reveal how cells can adopt different strategies depending on their setting, allowing them to make either rapid coordinated decisions or more measured decisions that provide more scope for the generation of cellular diversity. |
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| 2012-04-25 | Wed | Sam Marsh (Sheffield) | Pure Maths Colloquium | |
| 16:00 | J11 | Non-standard analysis | ||
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Abstract: Do infinitesimals exist? Bearing in mind that Pete and Bernie's Philosophical Steakhouse is now closed1, I'll discuss two approaches to a non-standard system of analysis which starts from the premise that maybe they should. The original approach due to Abraham Robinson (1960s) has model theory as its basis and I'll cover this set-up from scratch. A reworking due to Edward Nelson (1970s) is based on an extension of ZF set theory and I'll discuss similar ground from this alternative viewpoint, where a possible conclusion is that infinitesimals were always knocking around, we just didn't notice them. Footnotes:1http://www.youtube.com/watch?v=6Za2WFVrvpQ#t=275s |
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| 2012-04-24 | Tue | Nadia Gheith (Sheffield) | Pure Maths Postgraduate Seminar | |
| 13:00 | Hicks Room J11 | The rough cofibration category | ||
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Abstract: Baues introduced a notion of cofibration category as a generalisation of a Quillen model category. He defined it to be a category together with two classes of morphisms called cofibrations and weak equivalences such that specific axioms are satisfied. In this talk I will introduce a notion of rough maps-these are maps between spaces preserving the large scale structure-and prove that the category of spaces and rough maps with two classes of morphisms called rough cofibrations and coarse homotopy equivalences satisfy the cofibration category axioms. This category will be called the rough cofibration category. |
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| 2012-04-02 | Mon | Dr Dipankar Banerjee (Indian Institute of Astrophysics, Koramangala, Bangalore 560034, India) | SP2RC Friday Seminars | |
| 10:00 | Lecture Theatre 9 | Propagating Disturbances in open and closed magnetic structures of the Sun | ||
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Abstract: Propagating disturbances are observed along open and closed magnetic structures of the sun. For characterizing the nature of the propagating disturbances a combination of spectroscopy and imaging is essential. In this talk I will show examples of such observations using SUMER/SoHO, EIS/Hinode with imaging sequences from AIA/SDO. We find two different groups of periodicities, short (<3 min) and long (>9 min) at different locations and circumstances. In the short range we find oscillations with periodicities as low as 50 s. Shorter periodicities show oscillations inall the three line parameters and the longer ones only show in intensity and Doppler shift butnot in line width. Often Line profiles at these locations do not show any visible blue-shiftedcomponent and can be fitted well with a single Gaussian. This allows us to conclude that the propagating disturbances represent waves and not flows. In the last part of my Talk I will also provide an update on the current status of the two large Indian solar observatory projects, namely the space coronagraph project called /Aditya/ and ground based facility from Himalayas called /NLST/. |
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| 2012-03-29 | Thu | Eleanor Stillman (University of Sheffield) | Probability and Statistics Seminar | |
| 14:00 | LT-6 | Optimal design for multiresponse experiments | ||
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Abstract: Many statistical investigations require data to be collected so that the influence of explanatory variables on responses of interest can be deduced. Once there is more than a single response variable, there are potential conflicts of interest in selecting experiments which are efficient at estimating all responses. In this talk I will begin by introducing the general ideas of optimal experimental design and then focus on extensions to multiple responses. In particular, I will introduce a new composite optimality criterion which seeks to estimate a primary continuous response efficiently particularly when a second, binary, response has a positive outcome. I will also examine the practically important case of simultaneous estimation of both mean and variance of a single response. |
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| 2012-03-29 | Thu | Ian Leary (Southampton) | Topology seminar | |
| 15:00 | Hicks Room J11 | Platonic polygonal complexes II | ||
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Abstract: A flag in a polygonal complex is a triple consisting of a mutually incident vertex, edge and polygon. A polygonal complex is said to be platonic if it admits a flag transitive group of symmetries. In this talk I shall go into more detail concerning the classification of some families of platonic polygonal complexes, focusing especially on the (rather degenerate) cases when the polygons have 3, 4 or 5 sides. (The original parts of this talk are joint work with T Januszkiewicz, R Valle and R Vogeler.) Cake will be provided by Sarah |
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| 2012-03-28 | Wed | Ian Leary (Southampton) | Pure Maths Colloquium | |
| 16:00 | J11 | Platonic polygonal complexes and curvature | ||
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Abstract: Examples of platonic polygonal complexes include the five regular solids, and the tesselations of the Euclidean and hyperbolic planes by regular polygons. There appear to be too many of them to hope to classify them all, but there are good results for some subfamilies. I shall state some of these results, and explain why the case when the polygons have at least six sides is the simplest case. [This is a self-contained talk, but if you enjoy this then you might be interested in the topology seminar on Thursday which will follow on from it.] |
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| 2012-03-27 | Tue | Robin Allan (Sheffield) | Pure Maths Postgraduate Seminar | |
| 13:00 | Hicks Room J11 | An introduction to Morse Theory | ||
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Abstract: Topological manifolds are spaces that are locally homeomorphic to Euclidean space. It is known that every 1-, 2- and 3-dimensional manifold has a unique smooth structure; however in higher dimensions there exist non-smoothable manifolds. This suggests that the existence of a smooth structure should impose restrictions on the topological invariants of the manifold, or in other words, we should should be able to study its topology using calculus. In this talk I will present some ideas and results from Morse Theory. The basic idea is to use the properties of smooth functions to deduce topological facts about smooth manifolds. This is mostly achieved by looking at the behaviour of functions near critical points, which will allow us to deduce facts about the homotopy type of a manifold and even calculate its Euler characteristic and homology groups. Since the general theory is quite technical, the talk will be focussed on demonstrating some of the main results through interesting examples. |
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| 2012-03-23 | Fri | Nabil Freji (University of Sheffield) | SP2RC Friday Seminars | |
| 13:05 | Lecture Theatre 9 | MHD Sausage Oscillations in Magnetic Wave guides in the lower Solar Atmosphere | ||
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Abstract: The lower solar atmosphere is host to a wide range of magnetic wave guides. From sunspots to inter-granular bright points, they are constantly buffeted by the surrounding photosphere from granulation, p-modes or by coherent sub-photospheric drivers. Here, we present the results of an observational study of MHD sausage waves in magnetic wave guides (pores and sunspots). By studying the temporal variations in area and intensity of these magnetic wave guides, it allows the observation and identification of MHD sausage waves. Using series of high-resolution intensity images with a small cadence and employing wavelet analysis in conjunction with empirical mode decomposition allows us to have a robust method for searching for and identifying characteristic periods hidden in the area and intensity data series. We found that the magnetic pore in Active Region 10968 displays three strong periods, 2-3, 8 and 13-14 minutes. The most plausible conclusion is that both the 2-3 and 8 minute periods detected are a harmonic of the fundamental 13-14 minute period. Due to the sharp gradients in the background equilibrium plasma parameters that exist at the boundaries of the photosphere and the transition region sets up a cavity that can support standing waves. This is the first observation of concurrent higher harmonics in a solar magnetic wave-guide in the lower solar atmosphere while the third reported observation of sausage modes in solar pores. |
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| 2012-03-22 | Thu | Philipp Wruck (Sheffield) | Topology seminar | |
| 15:00 | Hicks Room J11 | Equivariant Transversality: Overview and Recent Developments | ||
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Abstract: The notion of transversality allows us to successfully describe generic behaviour of smooth maps and has important impacts in various branches of topology. A simple adaption in the equivariant context is not possible, but using techniques from real algebraic geometry and the theory of stratified spaces, a natural concept of equivariant transversality has been developed. We sketch the basic ideas and give some applications of equivariant transversality. Then we show how these ideas can be adapted to define a notion of equivariant non-degeneracy, which is important for the investigation of fixed orbits of equivariant maps and their relation to equivariant homotopy invariants. Cake will be provided by Thomas |
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| 2012-03-21 | Wed | Alex Best (Sheffield) | Applied Maths Colloquium | |
| 14:00 | LT6 | Modelling the coevolution of parasites and their hosts | ||
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Abstract: Understanding the dynamics of infectious diseases in human, animal and plant hosts is one of the biggest challenges for modern science, with considerable health, social and financial implications. Mathematical models of these host-parasite interactions can allow us to understand and predict the behaviour of many disease systems. Here I shall focus on the evolutionary dynamics of parasites and hosts, applying the evolutionary framework of adaptive dynamics to a classic model of host-parasite interactions. I shall show how parasite infectivity and host defence may be expected to evolve, both in isolation and when they coevolve with one another. Throughout I shall highlight the important role of the evolutionary trade-offs on the eventual outcome, particularly focussing on the potential for variation to arise through evolutionary branching. |
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| 2012-03-21 | Wed | Marco Streng (Warwick) | Pure Maths Colloquium | |
| 16:00 | J11 | Smaller class invariants for quartic CM-fields | ||
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Abstract: The theory of complex multiplication allows one to construct elliptic curves with a given number of points. The idea is to construct a curve over a finite field by starting with a special curve E in characteristic 0, and taking the reduction of E modulo a prime number. Instead of writing down equations for the curve E, one only needs the minimal polynomial of its j-invariant, called a Hilbert class polynomial. The coefficients of these polynomials tend to be very large, so in practice, one replaces the j-invariant by alternative 'class invariants'. Such smaller class invariants can be found and studied using an explicit version of Shimura's reciprocity law. The theory of complex multiplication has been generalized to curves of higher genus, but up to now, no class invariants were known in this higher-dimensional setting. I will show how to find smaller class invariants using a higher-dimensional version of Shimura's reciprocity law. |
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| 2012-03-16 | Fri | Ondrej Rypacek (Sheffield Computer Science) | ||
| 13:00 | G22 Regent Court | A syntactical approach to weak ω-groupoids | ||
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Abstract: When moving to a Type Theory without proof irrelevance the notion of a setoid has to be generalized to the notion of a weak ω-groupoid. As a first step in this direction we study the formalisation of weak ω-groupoids in Type Theory. This is motivated by Voevodsky's proposal of univalent type theory which is incompatible with proof-irrelevance and the results by Lumsdaine and Garner/van de Berg showing that the standard eliminator for equality gives rise to a weak ω-groupoid. |
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| 2012-03-16 | Fri | Khalil Al-Ghafri (Sheffield) | SP2RC Friday Seminars | |
| 13:05 | Lecture Theatre 9 | The effect of variable background on oscillating hot coronal loop due to thermal conduction | ||
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Abstract: We investigate the effect of a variable, i.e. time-dependent, background on the standing acoustic (i.e. longitudinal) modes generated in a hot coronal loop. A theoretical model of 1D geometry describing the coronal loop is applied. The background temperature is allowed to change as a function of time and undergoes an exponential decay with characteristic cooling times typical for coronal loops. The magnetic field is assumed to be uniform. Thermal conduction is the dominant mechanism of cooling the hot background plasma in the presence of an unspecified thermodynamic source that maintains the initial equilibrium. The influence of the rapidly cooling background plasma on the behaviour of standing acoustic (longitudinal) waves is investigated analytically. The temporally evolving dispersion relation and wave amplitude are derived by using the WKB theory. An analytic solution for the time-dependent amplitude that describes the influence of thermal conduction on the standing longitudinal (acoustic) wave is obtained by exploiting the properties of Sturm-Liouville problems. Next, numerical evaluations further illustrate the behaviour of the standing acoustic waves in a system with variable, time dependent background. The results are applied to a number of detected loop oscillations. We find a remarkable agreement between the theoretical predictions and the observations. The cooling of the background plasma due to thermal conduction is found to cause a strong damping for the slow standing magneto-acoustic waves in hot coronal loops in general. Further to this, the increase in the value of thermal conductivity leads to a strong decay in the amplitude of the longitudinal standing slow MHD waves. |
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| 2012-03-15 | Thu | Simona Paoli (Leicester) | Topology seminar | |
| 15:00 | Hicks Room J11 | |||
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Abstract: Cake will be provided by Vikki |
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| 2012-03-15 | Thu | James Fotheringham, Richard Jacques; Andy Sutherland, Alyson Whitmarsh, Simone Chung (Sheffield; Dept of Health Information Centre, Leeds) | RSS Seminar Series | |
| 15:00 | LT10 | The Summary Hospital Mortality Index (SHMI) | ||
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Abstract: Background and Derivation of the New SHMI (James Fotheringham, Richard Jacques - Sheffield) Development and Issues in the Production of the SHMI (Andy Sutherland, Alyson Whitmarsh, Simone Chung - DoH Information Centre) The SHMI is now in use by the NHS to monitor hospital performance in England, to complement or replace other ratings such as Dr Foster's Hospital Standardised Mortality Ratio. Uniquely, it links mortality data from ONS to hospital episode statistics to examine deaths either in hospital or 30 days after discharge from hospital. In a series of linked talks, speakers from Sheffield will describe how they developed the model for computing the expected deaths, and speakers from the DoH will discuss issues in the production and use of the SHMI. The meeting will last until 17:30 and there will be a break at 16:00. |
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| 2012-03-14 | Wed | Joab Winkler (Sheffield) | Applied Maths Colloquium | |
| 14:00 | LT6 | The computation of multiple roots of polynomials whose coefficients are inexact | ||
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Abstract: This lecture will show by example some of the problems that occur when the roots of a polynomial are computed using a standard polynomial root solver. In particular, polynomials of high degree with a large number of multiple roots will be considered, and it will be shown that even roundoff error due to floating point arithmetic, in the absence of data errors, is sufficient to cause totally incorrect results to be obtained. Since data errors are usually larger than roundoff errors (and fundamentally different in character), the errors encountered with real world data are significant and emphasise the need for a computationally robust polynomial root solver. The inability of commonly used polynomial root solvers to compute high degree multiple roots correctly requires investigation. A method developed by Gauss for computing the roots of a polynomial will be discussed, and it will be shown that it has an elegant geometric interpretation in terms of pejorative manifolds, which were introduced by William Kahan (Berkeley). Polynomials defined by points on these manifolds satisfy properties that are fundamentally different from the properties of polynomials defined by points that are not on these manifolds. The numerical interpretation of this difference provides the motivation for the method of Gauss, and the geometric properties of pejorative manifolds will therefore be emphasised and considered in detail. Furthermore, these properties explain why multiple roots are preserved in a floating point environment when the coefficients of the polynomial are corrupted by noise. This numerical interpretation leads naturally to a discussion of a structured condition number of a root of a polynomial, where structure refers to the form of the perturbations that are applied to the coefficients. It will be shown that this structured condition number, where the perturbations are such that the multi- plicities of the roots are preserved, differs significantly from the standard componentwise and normwise condition numbers, which refer to random (unstructured) perturbations of the coefficients. Several ex- amples will be given and it will be shown that the condition number of a multiple root of a polynomial due to a random perturbation in the coefficients is large, but the structured condition number of the same root is small. This large difference is typically several orders of magnitude. The computational implementation of the method of Gauss raises some non-trivial issues – the determi- nation of the rank of a matrix in a floating point environment and the quotient of two inexact polynomials – and they will be discussed because they are ill-posed operations. They must be implemented with care because simple methods will necessarily lead to incorrect results. Furthermore, problems occur when the coefficients of the polynomial span several orders of magnitude, in which case the polynomial must be processed before its roots are computed in order to guarantee computationally reliable arithmetic operations. I will finish the talk by demonstrating Matlab code that implements the method on several high degree polynomials whose coefficients have been corrupted by noise and whose theoretically exact forms have multiple roots of high degree. |
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| 2012-03-14 | Wed | Michael Bate (York) | Pure Maths Colloquium | |
| 16:00 | J11 | Fixed points in spherical buildings (and why I care about them) | ||
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Abstract: In the 1950s Jacques Tits formulated a conjecture about spherical buildings, which he had recently invented. In the intervening years, several important special cases of this conjecture have been proved, but the full conjecture is still open. In this talk I will explain what spherical buildings are, from a variety of different viewpoints, and what Tits's conjecture says about their structure. I'll illustrate the various known cases with some straightforward examples which shouldn't need more than a smattering of linear algebra and some geometric intuition. If time permits I'll also detail my small contribution to the effort to prove the full conjecture. |
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| 2012-03-13 | Tue | Matthew Gadsden (Sheffield) | Pure Maths Postgraduate Seminar | |
| 13:00 | Hicks Room J11 | An introduction to coarse geometry | ||
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Abstract: Coarse geometry is the study of large scale properties of spaces. In coarse geometry, we want to consider two spaces as being the same if they "behave the same at infinity", neglecting the fine detail. For example we consider the real numbers and the integers as being the same, as they look the same when you view them from far away. In this talk, we shall begin by introducing coarse maps and coarse equivalences, and by explaining how these definitions capture the geometry of large scale. I shall give many examples of coarsely equivalent spaces, with geometrical interpretations. One of the first key questions in coarse geometry was how do we tell metric spaces apart? To do this, we need to study coarse invariants. We will define and discuss two of them: the ends of a space and the ends of a group. Finally, we shall present a classification theorem regarding the ends of finitely-generated groups, including examples. |
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| 2012-03-08 | Thu | Ieke Moerdijk (Sheffield) | Topology seminar | |
| 15:00 | Hicks Room J11 | Two models for infinity-operads | ||
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Abstract: I will explain the Lurie model category for infinity operads based on the theory of marked simplicial sets over the nerve of Gamma, the model category for infinity operads based on dendroidal sets which I introduced with Cisinski, and a comparison between the two. Cake will be provided by Matt |
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| 2012-03-08 | Thu | Ari Laptev (Imperial) | SoMaS Colloquium | |
| 17:30 | LT7 | Spectral Inequalities for Partial Differential Equations and their Applications | ||
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Abstract: We shall discuss properties of the discrete and continuous spectrum of different classes of self-adjoint differential operators including Schrödinger operators. |
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| 2012-03-07 | Wed | John Hinch (Cambridge) | Applied Maths Colloquium | |
| 14:00 | Large drops of a power-law fluid in a thin film on a vertical fibre | |||
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Abstract: We study a thin liquid film on a vertical fibre. Without gravity, there is a Rayleigh-Plateau instability in which surface tension reduces the surface area of the initially cylindrical film. Spherical drops cannot form because of the fibre, and instead, the film forms bulges of roughly twice the initial thickness. Large bulges then grow very slowly through a ripening mechanism. A small non-dimensional gravity moves the bulges. They leave behind a thinner film than that in front of them, and so grow. As they grow into large drops, they move faster and grow faster. When gravity is stronger, the bulges grow only to finite amplitude solitary waves, with equal film thickness behind and in front. We study these solitary waves, and the effect of shear-thinning and shear-thickening of the fluid. In particular, we will be interested in solitary waves of large amplitudes, which occur near the boundary between large and small gravity. Frustratingly, the speed is only determined at the third term in an asymptotic expansion. The case of Newtonian fluids requires four term. |
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| 2012-03-07 | Wed | Christopher Douglas (Oxford) | Pure Maths Colloquium | |
| 16:00 | J11 | Fusion categories and field theories. | ||
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Abstract: I will describe a relationship between certain monoidal categories called fusion categories and 3-dimensional topological field theories, focusing on the correspondence between algebraic properties of the categories and topological properties of the associated field theories. Fusion categories are monoidal categories that have the nice properties of the category of representations of a finite group: each object has a dual, there are finitely many simple objects, and any object decomposes into a finite sum of simples. We show that any fusion category gives rise to a 3-dimensional topological field theory. A key question about the algebraic structure of a fusion category is whether the double dual operation is trivial, as it is in the representation category of a finite group. I will explain why this question corresponds to the question of whether the 3-manifold invariants of the associated field theory depend on a spin structure. This is joint work with Chris Schommer-Pries and Noah Snyder. |
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| 2012-03-06 | Tue | David O'Sullivan (Sheffield) | Pure Maths Postgraduate Seminar | |
| 13:00 | Hicks Room J11 | The Atiyah-Singer Index Theorem | ||
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Abstract: The Atiyah-Singer Index Theorem – the work of Michael Atiyah and Isadore Singer in the 1960s - has been described as “one of the deepest and most beautiful results in modern geometry”, incorporating results such as the Riemann-Roch Theorem (algebraic geometry), the Hirzebruch Signature Theorem and the Gauss-Bonnet Theorem as special cases. The theorem equates two very different quantities: The first is an analytic property of a particular type of operator that is used to model systems of differential equations. In particular, it gives information about the dimension of the solution space – and hence the number of solutions to such a system. This is easy to define, but usually impossible to calculate directly. The second quantity is a value related to the topology of the space on which the operator is defined. By contrast this is more difficult to define, but readily computable. In this talk I will introduce the concepts necessary to define the both of the above quantities and state the theorem. |
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| 2012-03-01 | Thu | Chris Sherlock (University of Lancaster) | Probability and Statistics Seminar | |
| 14:00 | LT-6 | A hidden Markov model for disease interactions | ||
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Abstract: Interactions between parasite species in a host are of great interest to ecologists but are often too complex to predict a priori. A longitudinal study of a population of field voles was undertaken with presence or absence of six different parasite species measured repeatedly. Although trapping sessions were regular, a different set of voles was caught at each session leading to incomplete profiles for all subjects. A simple analysis, which discards much of the data, has already been carried out; we offer a more powerful alternative. We use a discrete-time hidden Markov model for each disease with transition probabilities dependent on covariates via a set of logistic regressions. For each disease the hidden states for each of the other diseases at a given time point form part of the covariate set for the Markov transition probabilities from that time point to the next. This allows us to gauge the influence of each parasite species on the transition probabilities for each of the other parasite species. Inference is performed via a Gibbs sampler, one iteration of which cycles through each of the diseases, first using an adaptive Metropolis-Hastings step to sample from the conditional posterior of the covariate parameters for that particular disease given the hidden states for all other diseases and then sampling from the hidden states for that disease given the parameters using the Forward-Backward algorithm. |
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| 2012-03-01 | Thu | Ieke Moerdijk (Sheffield) | Topology seminar | |
| 15:00 | Hicks Room J11 | On categories with two objects | ||
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Abstract: In this talk we'll analyse cofibrant objects in the model category of categories on two objects enriched in a monoidal model category. As an application, we will obtain a Bergner type model structure on the category of all such enriched categories with arbitrary set of objects. Cake will be provided by Jonathon |
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| 2012-02-29 | Wed | Ati Sharma (Sheffield) | Applied Maths Colloquium | |
| 14:00 | LT6 | Predicting structure in turbulence | ||
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Abstract: How to find a simple model that predicts the important structural and statistical features of turbulence is a central unsolved problem in classical physics. Most commonly found flows are turbulent, for instance flow of air over an aeroplane wing or water past a ship's hull, flow of oil through an trans-continental pipeline, or the movement of the atmosphere. All these flows experience chaotic three-dimensional motion, but nonetheless show persistent, repeating structure. This talk will cover significant new advances, involving the application of systems-theoretic ideas to the equations governing turbulence, which predict these structures. The computationally cheap approach explains and predicts structures and velocity statistics that have previously been identified only in experiments or by direct numerical simulation. Short Biography After graduating as a physicist from UCL, Dr Sharma completed his doctoral thesis in control engineering at Imperial College, London on the modelling and control of tokamak nuclear fusion reactors. Following two years in industry, he returned to academia as a postdoc to work on fluid flow control, and was then awarded an Imperial College Junior Research Fellowship in that area. Dr Sharma joined ACSE as a lecturer in July. |
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| 2012-02-29 | Wed | Kazuma Shimomoto | Pure Maths Colloquium | |
| 16:00 | J11 | Modular forms and Galois representations; its algebraic aspect | ||
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Abstract: In this talk, I will begin to give a brief review on the algebraic or p-adic aspect of modular forms. Then I will move on to the modern view of modular forms with its relation to Iwasawa theory. If time permits, I would like to mention some recent topics. This talk is elementary. |
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| 2012-02-28 | Tue | Timothy Eardley (Sheffield) | Pure Maths Postgraduate Seminar | |
| 13:00 | Hicks Room J11 | Representations of Galois groups | ||
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Abstract: Galois groups play an important role in algebraic number theory and an effective way of studying them is via representations. We shall motivate this study and then focus on representations over finite fields. These in turn are studied via deformations to certain more general rings. We will give hypotheses under which there is a 'universal deformation ring', which classifies these deformations. In fact, this is an application of the categorical notion of representable functors. We will end with some examples of deformation rings. |
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| 2012-02-24 | Fri | Richard Morton (Sheffield) | SP2RC Friday Seminars | |
| 13:05 | Lecture Theatre 9 | |||
| 2012-02-23 | Thu | Jim Griffin (University of Kent) | Probability and Statistics Seminar | |
| 14:00 | LT-6 | Shrinking to some purpose | ||
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Abstract: In Bayesian statistics there has recently been interested in using priors whose density has a spike at zero in regression problems. These priors can lead to adaptive shrinkage of regression effects and so can be used for sparse regression problems where many of the regression coefficients are assumed to be zero (or very close to zero). This talk will consider the Normal-Gamma prior and extensions of it to encourage more general forms of shrinkage. For example, we might want to shrink differences of regression effects, or we might want to allow the "importance" of regression effects to change over time. |
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| 2012-02-23 | Thu | Eugenia Cheng (Sheffield) | Topology seminar | |
| 15:00 | Hicks Room J11 | Multivariable adjunctions and mates | ||
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Abstract: (Joint work with Nick Gurski and Emily Riehl.) The so-called "mates correspondence" (named by Australians) arises in the presence of adjunctions. It enables us neatly to pass between natural transformations involving left adjoints and those involving right adjoints, and is used efficaciously in Emily Riehl's work on algebraic model categories. When Emily visited us last year, she was extending her work to algebraic monoidal model categories. For this, she was looking for a multivariable generalisation of the mates correspondence, and a framework in which to describe it. The ordinary mates correspondence is elegantly described using double categories, and Nick and I sat down with Emily and produced the theory of "cyclic double multicategories", which not only answers her question but is also a satisfying piece of category theory: the best of both worlds. Moreover, it is an output directly resulting from MSRC funding. |
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| 2012-02-23 | Thu | Keith Still (Bucks New University) | RSS Seminar Series | |
| 16:30 | Hicks LT2 | Crowd Modelling to Assess Risks in Crowded Spaces | ||
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Abstract: In this lecture Prof. Still will outline the background to modelling crowd flow, fill and failure using a wide range of examples of crowded spaces and how 'simple' maths could have been used to prevent mass fatalities. Drawing on over 20 years of experience in consulting around the world, his talk is illustrated with examples of modelling tools and techniques, from some of the world's largest, most dangerous and challenging, crowd modelling projects. He also illustrates how shockwaves form and how they can be predicted, and prevented, in crowded spaces. |
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| 2012-02-22 | Wed | No seminar (Exam boards) | Pure Maths Colloquium | |
| 16:00 | J11 | |||
| 2012-02-21 | Tue | Victoria Quigley (Sheffield) | Pure Maths Postgraduate Seminar | |
| 13:00 | Hicks Room J11 | Classification of AF-algebras | ||
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Abstract: C*-algebras are a type of algebra commonly studied in functional analysis. In this talk we will discuss a special class of C*-algebras called äpproximately finite-dimensional" (AF). An AF-algebra is the inductive limit of a sequence of finite-dimensional C*-algebras. Such algebras retain relatively simple structure which makes them easier to analyse than other C*-algebras, but their study has led to many results which apply to more general classes of C*-algebras. In the 1970's, George Elliott gave a classification theorem for AF-algebras using their K-theory. We will end the talk by presenting this theorem, after first covering some basic theory of AF-algebras, as well as some of the properties of analytic K-theory. |
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| 2012-02-16 | Thu | Emma Jones (University of Sheffield) | Probability and Statistics Seminar | |
| 14:00 | LT-6 | Using A Bayesian Hierarchical Model for Tree-Ring Dating | ||
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Abstract: The width of tree-rings are determined by several factors including a local climatic signal apparent in that year, and the tree's growth trend. The climatic signal influences growth such that if the summer is warm and wet, the ring tends to be wider than if the summer is cold and dry. The growth trend describes the fast growth of the tree when it is young producing wide rings, followed by narrower rings as it ages. Other factors such as the soil conditions, presence of pests and diseases and competition for light and nutrients can also effect the ring width. The impact of these latter factors are collectively known as noise. It is assumed that trees within the same geographical region are exposed to the same climatic signal in each year, but that this differs from year to year. Tree-ring dating involves matching sequences of tree-ring widths from timbers of unknown age to dated sequences known as 'master' chronologies. Before matching takes place, all data are preprocessed to remove the growth trends. The timbers of unknown age (typically from a single building or woodland) are, firstly, sequentially matched against one another to identify the relative offsets with the 'best' match. The sequence produced is known as a 'site'chronology. The site chronology is then further matched to a local master chronology, to attempt to produce a date estimate for the site chronology. Traditionally the quality of the matches (both within the site chronology and between the site chronology and the master chronology) are assessed via the classical statistical t-test. A match at a particular offset is only considered to be 'best' if it produces the largest t-value of all of the possible offsets and is greater than (an arbitrary value of) 3.5. The success rate of dating varies within sites and across regions; the national average being approximately 60-70 A Bayesian model for tree-ring dating allows important prior information on parameters to be drawn into the inference process; this prior information can be taken from trees and can also be elicited from expert dendrochronologists. The model assumes that each ring width is composed of an overall climatic signal and some noise, and can be further extended to include climatic signals at varying geographic scales. Probabilities for a match at each offset can be produced conditional on the data and the prior specifications. The method removes the need to identify a single 'best' match, but it does rely on careful prior specification of parameters. Consequently, we have collated ring width data from trees of known age from several woods in the UK and are using these to provide informative prior knowledge. |
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| 2012-02-16 | Thu | Seungjin Han (University of Sheffield) | Probability and Statistics Seminar | |
| 14:30 | LT-6 | Adaptive filtering for algorithmic pairs trading | ||
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Abstract: Pairs trading as a statistical arbitrage methodology has received considerable attention and popularity since its initial application in the 1980’s. It is based on the assumption that a spread of two assets is mean-reverted, and any violating fluctuations are taken advantage in order to realize profits. For real time detection of mean reversion, we employ a time-varying autoregressive model in a state-space form, online estimation of which is achieved by recursions of Kalman filtering and adaptive forgetting. Two novel algorithms for a variable forgetting factor are proposed and compared with a standard recursive least squares algorithm with adaptive memory. |
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| 2012-02-16 | Thu | Fionntan Roukema (Sheffield) | Topology seminar | |
| 15:00 | Hicks Room J11 | Dehn Fillings of Manifolds with Small Volume 2 | ||
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Abstract: In this talk we will recall some basic notions from Dehn surgery and remind ourselves about why we care about "exceptional surgeries" and "exceptional pairs". We then return to a tabulation of 3-manifolds of "small volume" and speak how it is possible to enumerate the set of exceptional slopes, pairs and fillings of "most" manifolds in this tabulation. If time permits we will speak about questions for future consideration. Cake will be provided by Eugenia |
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| 2012-02-15 | Wed | Fionntan Roukema (Sheffield) | Pure Maths Colloquium | |
| 16:00 | J11 | Dehn Fillings of Manifolds with Small Volume | ||
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Abstract: Dehn surgery is a classical area of low dimensional topology with many beautiful results connecting the subject matter to the description of 3-manifolds, the original Poincare conjecture, and the geometry of knot exteriors. In this talk we will introduce and motivate Dehn surgery with a view to speaking about "exceptional surgeries"; this will naturally bring us to a well known tabulation of 3-manifolds of "small volume". It will be our goal to discuss an unusually simple description of the "exceptional fillings" associated with this tabulation. The presentation will attempt to be intuitive and contain many pictures. |
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| 2012-02-14 | Tue | Jonathan Elliott (Sheffield) | Pure Maths Postgraduate Seminar | |
| 13:00 | Hicks Room J11 | Introduction to profunctors | ||
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Abstract: Functors provide the appropriate notion of structure-preserving map between categories, but many applications require a more general notion of relation between categories. I will begin by discussing relations between sets, and bimodules over rings or monoids. I will then explain how profunctors simultaneously generalise relations, bimodules and functors. Finally I will discuss how to compose profunctors by analogy with tensor products of bimodules, so that profunctors are the 1-cells of a bicategory. |
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| 2012-02-10 | Fri | Giuseppe Colantuono (Sheffield) | SP2RC Friday Seminars | |
| 13:05 | Lecture Theatre 9 | A simple model to evaluate photovoltaics with energy storage: initial results and ideas | ||
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Abstract: Energy storage can be a means of smoothing out the unpredictability of "green" energy sources and increase the availability of power at times of peak demand. Efforts for integrating photovoltaics (PV) with batteries are already going on, even if they still suffer from high costs. A possible metric to evaluate the impact of storage coupled to a PV array is "Loss Of Load Hours" (LOLH). LOLH represents the total amount of time, for a given period (e.g one month), during which the demand (e.g. the power usage of the home where the PV array is installed) cannot be satisfied and electricity must be drawn from the grid. An analogous measure is the total time during which the battery is fully charged, energy cannot be stored any longer and is therefore uploaded to the grid. A simple model for the computation of LOLH will be presented . The inputs of the model are given by the timeseries of the solar irradiance incident on the PV array and the timeseries of the power load. Some preliminary results and possible developments for both real-world and idealized loads will be discussed. |
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| 2012-02-09 | Thu | Vanessa Didelez (University of Bristol) | Probability and Statistics Seminar | |
| 14:00 | LT-6 | Mendelian Randomisation as an Instrumental Variable Approach to Causal Inference | ||
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Abstract: In epidemiology we often want to estimate the causal effect of an exposure on a health outcome based on observational data, where the possibility of unobserved confounding cannot be excluded. To deal with this problem, it has recently become popular to use a technique called Mendelian randomisation, where it is exploited that the exposure is associated with a genetic variant, which can be assumed to be unaffected by the same confounding factors and which makes it suitable as a so-called instrumental variable. In my talk, this technique is illustrated with various examples, in particular with the effect of alcohol consumption on blood pressure / hypertension. Different methods of using an instrumental variable to estimate the causal effect on a binary outcome are compared based on their theoretical properties as well as by simulation. Finally, it will be discussed if a Bayesian approach is useful in the context of Mendelian randomisation. References:Didelez and Sheehan (2007). Mendelian randomisation as an instrumental variable approach to causal inference, Statistical Methods in Medical Research, 16, 309-330. Didelez, Meng and Sheehan (2010). Assumptions of IV methods for observational epidemiology, Statistical Science, 25, 22-40. Palmer, Sterne, Harbord, Lawlor, Sheehan, Meng, Granell, Davey Smith, Didelez (2011). Instrumental variable estimation of causal risk ratios and causal odds ratios in Mendelian randomization analyses, The American Journal of Epidemiology, 173 (12). Jones, Thompson, Didelez and Sheehan (2012). On the choice of parameterisation and priors for the Bayesian analyses of Mendelian randomisation studies. To appear in Statistics in Medicine. |
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| 2012-02-09 | Thu | David Barnes (Sheffield) | Topology seminar | |
| 15:00 | Hicks Room J11 | Stable Model Categories | ||
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Abstract: A model category is a way of giving a category a notion of homotopy. Hence in a model category we can talk of maps being homotopic or objects being homotopy equivalent. The two basic examples of model categories are topological spaces and chain complexes. Hence model categories are of interest to both topologists and algebraists. One condition that a model category may satisfy is that of stability. This is where there is a shift functor or suspension functor which is an equivalence on the homotopy category. Chain complexes are such an example, however the category of topological is not a stable model category. In this talk I will define the notion of stability more carefully, and try to describe how one may alter a category to make it stable. In particular, we will see that spectra are the stabilisation of spaces. |
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| 2012-02-08 | Wed | Paul Linden (Cambridge) | Applied Maths Colloquium | |
| 14:20 | LT6 | Gravity-driven flows in stratified fluids | ||
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Abstract: This talk will describe experiments on flows driven by horizontal density gradients in fluids which are stably stratified. Examples are intrusions on density interfaces or in stratified ambient fluids, and cases where the intruding fluid is also stably stratified. Traditional approaches that have been applied to unstratified fluids have been to use ideas of energy conversion from available potential energy to kinetic energy to predict the speeds of the gravity-driven flows, which in this simple case are gravity currents. I will explore how well these approaches work in systems which can support internal waves and discuss the resulting dynamics. |
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| 2012-02-08 | Wed | Tom Bridgeland (Oxford) | Pure Maths Colloquium | |
| 16:00 | J11 | Hall algebras and quantum groups | ||
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Abstract: Quantized enveloping algebras are Hopf algebras that are q-deformations of universal enveloping algebras. Despite being defined by a bunch of peculiar looking relations, they have found applications in many parts of maths and physics. Twenty years ago Ringel showed how to give a conceptual description of the positive half of a quantized enveloping algebra using Hall algebras of quiver representations. I'll attempt to explain why introducing Z2 graded complexes into the picture leads to a similar description of the whole thing. |
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| 2012-02-02 | Thu | Mohammad Al-Boshmki (Sheffield) | Pure Maths Postgraduate Seminar | |
| 13:00 | Hicks Room J11 | Classifying spaces | ||
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Abstract: Classifying spaces have played a central role in homotopy theory over the last fifty years. The classifying space of a group G is a path-connected space with fundamental group G and no other non-trivial homotopy groups. In this talk we will give a construction of classifying spaces for any topological group G, showing that classifying spaces always exist and are unique up to homotopy. We will illustrate this with examples such as Z, Z_2 and S^1. |
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| 2012-02-02 | Thu | James Cranch (Sheffield ) | ||
| 15:00 | G22 Regent Court | Dependently Typed Programming and Proof in Agda | ||
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Abstract: James will show some more realistic examples of datatypes (including ordered list maps) and some portions of his work with categories. |
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| 2012-01-19 | Thu | Simon Foster (Sheffield Computer Science) | ||
| 15:00 | G22 Regent Court | Dependently Typed Programming and Proof in Agda | ||
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Abstract: Agda is a dependently typed programming language in the style of the functional programming language Haskell. What sets it apart from Haskell is its inclusion of dependent types which allow much finer grained constraints on data and functionality to be specified. Furthermore Agda doubles as a powerful ITP, in which properties about implemented programs can be proved. In this tutorial I will introduce the Agda interface and demonstrate the key features of the language. I will create some datatypes, functions and show how to build some proofs about them, some of which will be (semi-)automated. |
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School of Mathematics and Statistics (SoMaS)
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