Seminars this semester
| Jan 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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| Feb 2 | 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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| Feb 2 | 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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| Feb 8 | 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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| Feb 8 | 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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| Feb 9 | 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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| Feb 9 | 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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| Feb 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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| Feb 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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| Feb 15 | 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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| Feb 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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| Feb 16 | Thu | Emma Jones (University of Sheffield) | Probability and Statistics Seminar |
| 14:00 | LT-6 | ||
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| Feb 16 | Thu | Seungjin Han (University of Sheffield) | Probability and Statistics Seminar |
| 14:30 | LT-6 | ||
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| Feb 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. |
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| Feb 22 | Wed | No seminar (Exam boards) | Pure Maths Colloquium |
| 16:00 | J11 | ||
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| Feb 23 | Thu | Jim Griffin (University of Kent) | Probability and Statistics Seminar |
| 14:00 | LT-6 | ||
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| Feb 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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| Feb 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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| Feb 24 | Fri | Richard Morton (Sheffield) | SP2RC Friday Seminars |
| 13:05 | Lecture Theatre 9 | ||
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| Feb 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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| Feb 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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| Mar 1 | Thu | Chris Sherlock (University of Lancaster) | Probability and Statistics Seminar |
| 14:00 | LT-6 | ||
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| Mar 1 | Thu | Ieke Moerdijk (Sheffield) | Topology seminar |
| 15:00 | Hicks Room J11 | ||
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| Mar 7 | Wed | John Hinch (Cambridge) | Applied Maths Colloquium |
| 14:00 | |||
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| Mar 7 | Wed | Christopher Douglas (Oxford) | Pure Maths Colloquium |
| 16:00 | J11 | ||
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| Mar 8 | 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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| Mar 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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| Mar 14 | Wed | Michael Bate (York) | Pure Maths Colloquium |
| 16:00 | J11 | ||
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| Mar 15 | Thu | Eleanor Stillman (University of Sheffield) | Probability and Statistics Seminar |
| 14:00 | LT-6 | ||
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| Mar 15 | Thu | Simona Paoli (Leicester) | Topology seminar |
| 15:00 | Hicks Room J11 | ||
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| Mar 21 | Wed | Alex Best (Sheffield) | Applied Maths Colloquium |
| 14:00 | LT6 | ||
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| Mar 21 | Wed | Marco Streng (Warwick) | Pure Maths Colloquium |
| 16:00 | J11 | ||
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| Mar 22 | Thu | Ronnie Loeffen (University of Manchester) | Probability and Statistics Seminar |
| 14:00 | LT-6 | ||
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| Mar 28 | Wed | Ian Leary (Southampton) | Pure Maths Colloquium |
| 16:00 | J11 | ||
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| Mar 29 | Thu | Ian Leary (Southampton) | Topology seminar |
| 14:00 | Hicks Room J11 | ||
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Abstract: [Time to be confirmed.] |
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| Apr 2 | 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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| May 3 | Thu | Simon Wood (University of Bath) | Probability and Statistics Seminar |
| 14:00 | LT-6 | ||
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| May 17 | Thu | Lee Fawcett (University of Newcastle) | Probability and Statistics Seminar |
| 14:00 | LT-6 | ||
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