Seminars this semester
Sep 26 | Wed | Yang Zhang (Sheffield (Mech Eng)) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 9 | Imaging based flame diagnostics and its quantitative analysis | |
Abstract: In this talk, a brief history of photography and their application in combustion studies will be given, which actually goes back to the 19th century. Then case studies will be shown on digital flame imaging, especially high speed imaging for the tracking of the fast flame dynamics. It will demonstrate that selective digital imaging enhancement is essential in observing the drastically different flame light intensities of the soot and chemical species. Through digital image processing, quantitative and useful information can be extracted from the flame image database. The simultaneous imaging of visible and infrared light emissions from the ignition of a flame using a single high speed colour digital camera will also be demonstrated which also poses a challenge in spectroscopic study on how to identify this infrared only emissions. |
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Oct 1 | Mon | Rachel Bearon (Liverpool) | Mathematical Biology Seminar Series |
14:00 | Hicks F41 | Revisiting Jeffery orbits; the importance of shape for micro-organism transport | |
Oct 3 | Wed | Priya Subramanian (Leeds) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 9 | Pattern formation in systems with multiple scales | |
Oct 9 | Tue | Angelo Rendina (Sheffield) | Number Theory seminar |
14:00 | J11 | Nearly holomorphic Siegel modular forms and applications | |
Abstract: Nearly holomorphic modular forms were introduced by Shimura as a generalization of modular forms to study a more general class of Eisenstein series. I will introduce some of the tools that we use to work with them, such as the Shimura-Maass differential operator and holomorphic projection, and present some applications: some formulae for the sum of divisor $s_r$ and Ramanujan $\tau$ functions and then congruences of critical $L$-values attached to Siegel modular forms, the latter being part of my research project. |
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Oct 15 | Mon | Helen Kettle (BIOSS) | Mathematical Biology Seminar Series |
14:00 | Hicks F41 | ||
Oct 16 | Tue | Kohei Kikuta (Osaka) | Algebra / Algebraic Geometry seminar |
16:00 | J11 | On categorical entropy | |
Abstract: The categorical entropy of triangulated endofunctors was defined by Dimitrov-Haiden-Katzarkov-Kontsevich motivated by classical dynamical theory. In this talk, I'll explain relations to classical entropy theory, basics on categorical entropy, many examples and future directions. |
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Oct 17 | Wed | Kevin Buzzard (Imperial) | Pure Maths Colloquium |
14:00 | Hicks Lecture Theatre C | Pure mathematics in crisis? | |
Abstract: I argue that pure mathematics is walking inexorably towards a cliff edge, and that anyone who believes that current pure mathematics is rigorous, or a science, needs to wake up and look at the facts, which there will be plenty of in this talk, and they are not pretty. Are our results reproducible? Does it matter? What *is* mathematics? Can computer scientists save us? Can *undergraduates* save us? I hope so. This talk is about pure mathematics but will be accessible to undergraduates, mathematicians both pure and applied/applicable and computer scientists. |
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Oct 18 | Thu | Gary Verth (Sheffield) | Plasma Dynamics Group |
15:00 | Room K14 (Hicks Building) | Introduction to the Sun | |
Abstract: This talk will be an introduction to the science required to understand the Sun and its atmosphere. It is primarily intended for students starting their postgraduate research in plasma, solar, or magnetospheric physics. Due to the introductory nature of the talk, it would also be suitable for any interested non-specialists. |
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Oct 18 | Thu | Simon Willerton (Sheffield) | Topology seminar |
16:00 | J11 | The Legendre-Fenchel transform from a category theoretic perspective | |
Abstract: The Legendre-Fenchel transform is a classical piece of mathematics with many applications. In this talk I'll show how it arises in the context of category theory using categories enriched over the extended real numbers $\overline{ \mathbb{R}}:=[-\infty,+\infty]$. It turns out that it arises out of nothing more than the pairing between a vector space and its dual in the same way that the many classical dualities (eg. in Galois theory or algebraic geometry) arise from a relation between sets. I will assume no knowledge of the Legendre-Fenchel transform and no knowledge of enriched categories. |
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Oct 23 | Tue | Kim Klinger-Logan (Minnesota) | Number Theory seminar |
14:00 | J11 | The Riemann Hypothesis and periods of Eisenstein series | |
Abstract: This summer at Perspectives on the Riemann Hypothesis, Bombieri and Garrett discussed modifications to the invariant Laplacian $\Delta=y^2(\partial_x^2+\partial_y^2)$ on $SL_2(\mathbb{Z})\backslash\mathfrak{H}$ possibly relevant to RH. We will present a $GL(2)$ $L$-function as a period of Eisenstein series which can, in turn, be thought of as a linear functional on an Eisenstein series and we will discuss how such functionals may be use to analyze the zeros of the $L$-function. This idea is an extension of recent work of Bombieri and Garrett and uses techniques from functional analysis and spectral theory of automorphic forms. |
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Oct 23 | Tue | Nebojsa Pavic (Sheffield) | Algebra / Algebraic Geometry seminar |
16:00 | J11 | Grothendieck groups and singularity categories of quotient singularities | |
Abstract: We study the K-theory of the Buchweitz-Orlov singularity category for quasi-projective algebraic schemes. Particularly, we show for isolated quotient singularities with abelian isotropy groups that the Grothendieck group of the singularity category is finite torsion and that rational Poincare duality is satisfied on the level of Grothendieck groups. We consider also consequences for the resolution of singularities of such quotient singularities and study dual properties in this setting, more concretely we prove a conjecture of Bondal and Orlov in the case of quotient singularities. |
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Oct 24 | Wed | Christian Voigt (Glasgow) | Pure Maths Colloquium |
14:00 | J11 | $C^*$-algebras, the Baum-Connes conjecture and quantum groups | |
Abstract: A central theme of research in operator algebras is the Baum-Connes conjecture, which predicts the K-theory of group $C^*$-algebras and crossed products. In this talk I will give a leisurely introduction to this conjecture, explain what it is good for, and discuss some recent connections with the theory of quantum groups. |
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Oct 24 | Wed | Istvan Cziegler (York) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 11 | Turbulence and phase transitions in tokamak plasmas | |
Abstract: The transition from the low- to the high-confinement operation is one of the most important phenomena in magnetic confinement fusion. The high-confinement regime, known as H-mode, leads to a vastly increased plasma density and temperature, which equates to a significant gain in fusion power. Since the dominant transport across the confining magnetic field is due to turbulence, the L-H transition can be thought of as a phase transition to suppressed turbulence. It is known that both the quality of global confinement and the threshold of the transition depend on macroscopic parameters, such as plasma density, magnetic topology and geometry near particle exhaust areas called divertors. The talk will connect the various scales of dynamics with this phenomenology and some broader context in physics. |
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Oct 24 | Wed | James Brotherston, Callum Reader, Sadiah Zahoor | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | ||
Abstract: What is Forcing? (Reader) I will give an introduction to the main themes behind Cohen's forcing method in ZFC, as framed by Scott through the lens of Boolean algebras. Given time there will also be some discussion of why, contrary to Godel's belief, forcing shows that the inclusion of large cardinal axioms does not solve the continuum hypothesis A Calculation of Some Group Cohomology (Brotherston) I will give a very brief introduction to group cohomology and why we care in relation to algebraic K-theory. I will then move on to outline a mostly geometric calculation of the former in the case where $G = GL_n(\mathbb{F}_q)$ with coefficients in $\mathbb{Z}/l$ for $l$ coprime to the characteristic of the field $\mathbb{F}_q$. There will hopefully be a little of number theory, algebraic topology and algebraic geometry mentioned. Tate Shafarevich Groups - The mysterious objects attached to Elliptic Curves (Zahoor) One of the main unsolved mystery about elliptic curves is the size of the Tate Shafarevich Group (Sha), that is conjectured to be finite. The lack of proof of this particular fact is one of the main barriers in giving an algorithm to compute rank of an elliptic curve. Intuitively, Sha measures the obstruction to the Hasse (local-global) principle. This talk aims at understanding Tate Shafarevich Groups using torsors of elliptic curves and is deigned for anyone having a first look at the Sha. |
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Oct 25 | Thu | Anna Marie Bohmann (Vanderbilt) | Topology seminar |
16:00 | J11 | Graded Tambara Functors | |
Abstract: Let G be a finite group. The coefficients of G-equivariant cohomology theories naturally form a type of structure called a Mackey functor, which incorporates data coming from each subgroup of G. When the cohomology theory is a G-ring commutative spectrum---meaning that is has an equivariant multiplication---interesting new structures arise. In particular, work of Brun and of Strickland shows that the zeroth homotopy groups have norm maps which yield the structure of a Tambara functor. In this talk, I discuss joint work with Vigleik Angeltveit on the algebraic structure induced by norm maps on the higher homotopy groups, which we call a graded Tambara functor. |
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Oct 29 | Mon | Elaine Ferguson (Glasgow) | Mathematical Biology Seminar Series |
14:00 | Hicks F41 | ||
Oct 30 | Tue | Adel Betina (Sheffield) | Number Theory seminar |
14:00 | J11 | On the p-adic periods of semi-stable modular curves | |
Abstract: I will present a joint work with E.Lecouturier in which we prove a variant of Oesterlé's conjecture about $p$-adic periods of the modular curve $X_0(p)$, with an additional $Γ(2)$-structure. We use de Shalit's techniques and $p$-adic uniformization of Mumford curves whose reduction is semi-stable. |
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Oct 31 | Wed | Miguel Teixeira (Reading) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 9 | A physically-based model for the wind-driven current in the wavy oceanic surface layer | |
Abstract: A simple analytical model is developed for the current induced by the wind and modified by surface wind-waves in the oceanic surface layer, based on a first-order turbulence closure and including the effect of a vortex force representing the Stokes drift of the waves. The shear stress is partitioned between a component due to shear in the current and a wave-induced component, which decays over a depth proportional to the wavelength. The model reproduces the apparent reduction of the friction velocity and enhancement of the roughness length estimated from current profiles, detected in a number of studies. The current profile becomes flatter for strong wave forcing owing to a smaller fraction of the total shear stress being supported by the current shear. These effects are entirely attributed to non-breaking surface waves, and predicted to increase with wave forcing. A version of the model where the shear stress decays to zero with depth is able to adequately predict the surface current speed. |
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Nov 1 | Thu | David Kuridze (Aberystwyth University) | SP2RC seminar |
10:00 | LT 10 | Spectropolarimetric Inversions of the Ca II 8542 Å Line in an M-class Solar Flare | |
Abstract: We study an M1.9-class solar flare (SOL2015-09-27T10:40 UT) using high-resolution full Stokes imaging spectropolarimetry of the Ca II 8542 Å line obtained with the CRISP imaging spectropolarimeter at the Swedish 1-m Solar Telescope. Spectropolarimetric inversions using the non-LTE code NICOLE are used to construct semi-empirical models of the flaring atmosphere to investigate the structure and evolution of the flare temperature and magnetic field. A comparison of the temperature stratification in flaring and nonflaring areas reveals strong heating of the flare ribbon during the flare peak. The polarisation signals of the ribbon in the chromosphere during the flare maximum become stronger when compared to its surroundings and to pre- and post-flare profiles. Furthermore, a comparison of the response functions to perturbations in the line-of-sight magnetic field and temperature in flaring and nonflaring atmospheres shows that during the flare, the Ca II 8542 Å line is more sensitive to the lower atmosphere where the magnetic field is expected to be stronger. The chromospheric magnetic field was also determined with the weak-field approximation, which led to results similar to those obtained with the NICOLE inversions. |
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Nov 1 | Thu | Sam Marsh and Simon Willerton (Sheffield) | Teaching Lunch |
13:00 | LT6 | Things we've tried in 115. | |
Abstract: In MAS115 Mathematical Investigation Skills -- where the students learn programming and LaTeX amongst other things -- we have experimented with various ideas including peer assessment, video marking, group work, students creating mathematical websites, in-class marking of homework. Usually we try to think of things which will benefit the students, but not increase our workload overly. We will present a smorgasbord of things we've tried and comment on how successful they've been, hopefully giving other people ideas along the way. |
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Nov 1 | Thu | Samuel Skirvin (Sheffield) | Plasma Dynamics Group |
15:00 | Room K14 (Hicks Building) | Properties of Alfvénic waves in the solar chromosphere | |
Abstract: In the first part of my talk I will discuss the results of investigation of the properties of transverse waves existing in spicules using the automated wave tracking code NUWT. Analysing a distance-time diagram at an altitude of 7 Mm relative to the solar limb produces the measured distribution of properties such as wave amplitude, period and velocity amplitude. In the second part of the talk I will provide an overview of the recent studies on the effect of initial flow profiles on the dynamics of solar jets and introduce the work I will be doing as part of my PhD project |
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Nov 1 | Thu | Markus Szymik (NTNU) | Topology seminar |
16:00 | J11 | Quandles, knots, and homotopical algebra | |
Abstract: Knots and their groups are a traditional topic of geometric topology. In this talk I will explain how aspects of the subject can be approached using ideas from Quillen’s homotopical algebra, rephrasing old results and leading to new ones. |
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Nov 2 | Fri | Professor Craig J. Rodger (University of Otago) | SP2RC seminar |
14:00 | Sir Henry Stephenson Building, LT01 | And then the Sun went "Bang": An Overview of Space Weather Research | |
Abstract: The Sun is the main provider of energy for the Earth; without it we would surely die. However, the Sun is not just a huge light bulb sending heat and light to us - it is a gigantic fiery ball of burning gas on which the largest explosions in our solar system take place. The highly dynamic Sun affects the Earth in multiple ways. We are only just starting to understand how the Sun drives "Space Weather" - changes in the environment on and around the Earth which affect our technological systems. In my colloquia I will give an overview of this research field, and provide some specific examples around hazards to Earth-orbiting satellites and electrical transmission networks. |
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Nov 6 | Tue | Vlad Serban (Vienna) | Number Theory seminar |
14:00 | J11 | A finiteness result for families of Bianchi modular forms | |
Abstract: We develop a p-adic "unlikely intersection” result and show how it can be used to examine which Hida families over imaginary quadratic fields interpolate a dense set of modular forms for GL2 over an imaginary quadratic field. In this way we arrive at the first proven examples where only finitely many classical automorphic forms are on a p-adic family. |
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Nov 9 | Fri | Alexander Shukhobodskiy (Sheffield) | SP2RC seminar |
14:00 | F28 | Kink Oscillations of Expanding Coronal Loops in the Presence of Bulk Flow | |
Abstract: Transverse coronal loop oscillations were first observed by TRACE in 1998 and reported by Aschwanden et al. (1999) and Nakariakov et al. (1999). One important property of transverse coronal loop oscillations is that they are usually strongly damped with the damping time being comparable with the oscillation period. However, sometimes this is not the case. At present, a generally accepted mechanism of this damping is resonant absorption. Observations show that very often oscillating coronal loops are in a highly dynamic state. In particular, they can cool quickly with a characteristic cooling time of the order of a few periods of kink oscillation. It was later showed theoretically that cooling causes amplification and may result in existence of oscillations for which amplitude does not vary in time. Although the coronal loop expansion is relatively small, the ratio of the loop cross-section radii at the apex and at the foot-points still can be about 1.5. These leads to particular interest the effect of expansion on kink oscillations. A coronal loop is modeled as a cylindrical magnetic flux tube. The tube consists of a core region and a thin transitional region at the tube boundary. The plasma density monotonically decreases from its value in the core region to the value outside the tube. Both the plasma density and velocity of background flow vary along the tube and in time. Using multiscale expansions, the system of two equations describing the kink oscillations was derived. This model is then studied both analytically and numerically. |
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Nov 12 | Mon | George Constable (Bath) | Mathematical Biology Seminar Series |
14:00 | Hicks LT10 | ||
Nov 13 | Tue | Philip G. Judge (High Altitude Observatory ) | SP2RC seminar |
13:00 | LT 09 | Restoring the observational basis for solar physics | |
Abstract: SUMMARY: A simple near-UV polarimeter on board a spacecraft that is more than 0.1 radians away from the Earth-Sun line will, with the suite of terrestrial solar observatories, resolve all ambiguities in vector field measurements, permitting us to restore studies of solar magnetic fields to its proper, observationally-based place. I will show how the spectrum of Fe~I at UV and IR wavelengths can strengthen the foundations of solar physics with consequences for all subjects involving magnetic activity. MOTIVATION: In recent years, research in solar physics has arguably become divorced from genuinely penetrating measurements. The idea of refuting theoretical pictures with critical observations seems to be losing ground to the development and application of computer models as a prime tool, indeed some models appear to have superceded the Sun itself in terms of ``reality''. Funding agencies and peer review enable what I call "institutionalized science" which is designed from the outset to optimize the number of publications, leading to vast numbers of, at best, incremental advances. I will argue that our collective "institutions" need to reward bold new ideas that are risky. I will present one such idea that will enable us to place measurements of solar magnetism at stage center, recognizing that the variable magnetism lies at the core of essentially all problems of interest in solar physics. |
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Nov 14 | Wed | Lukasz Grabowski (Lancaster) | Pure Maths Colloquium |
14:00 | J11 | Approximation of groups with respect to the rank metric. | |
Abstract: I'll talk about an ongoing joint work with Gabor Elek about approximation of groups with respect two the rank metric. The basic question is the following variant of the Halmos problem about commuting matrices: if A and B are large matrices such that the rank of the image of the commutator is small, is it true that A and B can be perturbed with small rank matrices in such a way that the resulting matrices commute? There are interesting connections to classical notions of commutative algebra, in particular we develop what are perhaps some new (or forgotten) variants of Nullstellensatz for primary ideals. |
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Nov 14 | Wed | James McLaughlin (Northumbria) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 9 | Modelling Quasi-Periodic Pulsations in Solar and Stellar Flares | |
Abstract: Solar flare emission is detected in all EM bands and variations in flux density of solar energetic particles. Often the EM radiation generated in solar and stellar flares shows a pronounced oscillatory pattern, with characteristic periods ranging from a fraction of a second to several minutes. These oscillations are referred to as quasi-periodic pulsations (QPPs), to emphasise that they often contain apparent amplitude and period modulation. We review the current understanding of quasi-periodic pulsations in solar and stellar flares. In particular, we focus on the possible physical mechanisms, with an emphasis on the underlying physics that generates the resultant range of periodicities. These physical mechanisms include MHD oscillations, self-oscillatory mechanisms, oscillatory reconnection/reconnection reversal, wave-driven reconnection, two loop coalescence, MHD flow over-stability, the equivalent LCR-contour mechanism, and thermal-dynamical cycles. We also provide a histogram of all QPP events published in the literature at this time. The occurrence of QPPs puts additional constraints on the interpretation and understanding of the fundamental processes operating in flares, e.g. magnetic energy liberation and particle acceleration. Therefore, a full understanding of QPPs is essential in order to work towards an integrated model of solar and stellar flares. Based on McLaughlin et al., 2018, Space Science Review, 214, 45, https://doi.org/10.1007/s11214-018-0478-5 |
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Nov 14 | Wed | Jordan Williamson (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | Equivariant Topology and Commutative Algebra | |
Abstract: Equivariant topology is the study of spaces with a group action, and some invariants for studying these objects are equivariant cohomology theories. In this talk, we will explain how algebraic techniques can be used to study equivariant cohomology theories, and we will give a sketch-proof of a theorem of Greenlees-Shipley which classifies the equivariant cohomology theories on free G-spaces over the rational numbers. This will involve a discussion of Borel cohomology and its relation to representation theory, and the algebraicization theorem of Shipley, which provides a bridge between algebra and topology. |
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Nov 15 | Thu | Matt Allcock (University of Sheffield) | SP2RC seminar |
10:00 | LT 10 | Asymmetric Solar Waveguides: theory and observations | |
Abstract: Are solar MHD waveguides symmetric? It is convenient to assume that they are. The solar physics community is familiar with the traditional notion of sausage and kink waves, which propagate along waveguides in the solar atmosphere that we assume are symmetric. In this talk, we drop this assumption and motivate the study of MHD wave propagation in asymmetric waveguides from theoretical and observational viewpoints. We discuss the implications that asymmetric waveguides have for mode identification, highlighting the observational ambiguity between waves in symmetric and asymmetric waveguides, which becomes a crucial consideration when implementing magneto-seismology diagnostics. We present a novel technique for solar magneto-seismology that utilises the observed asymmetry of MHD waves to diagnose background parameters of the solar atmosphere that are difficult to measure using traditional methods. We present a preliminary application of this technique to chromospheric fibrils as a proof-of-concept and discuss the potential further application to prominences, elongated magnetic bright points, and sunspot light walls. |
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Nov 15 | Thu | Istvan Ballai (Sheffield) | Plasma Dynamics Group |
15:00 | Room K14 (Hicks Building) | Introduction to multiple scaling methods to solve differential equations with applications to plasma physics. Part I: Ordinary linear differential equations | |
Abstract: Many of the equations we encounter in our research in solar and space plasma physics dynamics contain essential physical constraints (non-linearity, singularities, complex domains of interest, complex boundary conditions, etc.) that makes difficult to find exact solutions. Therefore, in order to obtain information about solutions of governing equations, we are forced to use analytical approximate methods, numerical solutions, or both. The most important analytical approximation methods are perturbation methods, where the solutions are represented by the first few terms of an expansion. In this seminar I will review perturbation methods used to solve ordinary differential equations, highlighting their advantages and shortcomings. The presentation will revolve around simple examples of differential equations, presenting methods of finding approximate analytical solutions of differential equations applicable to plasma physics. |
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Nov 20 | Tue | Eoin Murphy (Sheffield) | Algebra / Algebraic Geometry seminar |
16:00 | J11 | Simultaneous deformations of Hall algebras | |
Abstract: In this talk, we discuss how Ringel-Hall algebras, an algebra associated to suitably finite Abelian categories, can be viewed in certain cases as simultaneously deforming two simpler algebras. One of these algebras is the universal enveloping algebra of a Lie algebra, while the other is a Poisson algebra. Time permitting we also discuss an analogous deformation picture for a generalization of Ringel-Hall algebras due to Bridgeland. |
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Nov 21 | Wed | Tobias Berger (Sheffield) | Pure Maths Colloquium |
14:00 | J11 | Paramodularity of abelian surfaces | |
Abstract: The key ingredient in Wiles' proof of Fermat's last theorem was to establish the modularity of elliptic curves. Despite many impressive advances in the Langlands programme the analogous question of modularity for abelian varieties of dimension 2 is still open. I will discuss what we know and present joint work with Kris Klosin (CUNY) on the modularity of abelian surfaces which have a rational torsion point. |
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Nov 21 | Wed | Simon Malham (Herrot-Watt) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 9 | Partial differential equations with non-local nonlinearities: Generation and solution | |
Abstract: We present a programme for generating the solutions of large classes of nonlinear partial differential equations, by pulling the equations back to a linear system of equations. The idea underlying this programme is to lift the standard relation between Riccati equations and linear systems to the infinite dimensional setting. This generalisation is well-known in optimal control theory where the off-line Riccati solution mediates the optimal current state feedback. The solution procedure can be presented at an elementary level and many examples will be included. Such example applications are partial differential equations with nonlocal nonlinearities, for example the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation and Smoluchowski's coagulation equation and, by association, the inviscid and viscous Burgers equations with local advective nonlinearities. |
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Nov 21 | Wed | Igor Sikora (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | Eilenberg-Zilber map and Acyclic Models | |
Abstract: When we are thinking about homology of a product of topological spaces, the first answer coming into mind is the Kunneth Theorem. Actually, it is only part of the truth. During the talk I will focus on the other part, which is chain level relation between singular complex of a product and a product of complexes - or more generally, between chain complexes associated to the simplicial abelian group and a product of complexes. This is done by very nice technique, called acyclic models. I assume basic knowledge of singular homology, i.e. definition of a chain complex and of a singular complex of a space. |
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Nov 22 | Thu | David O' Sullivan (Sheffield Hallam University) | Teaching Lunch |
13:00 | LT5 | A reflection on Higher Education across Sheffield. | |
Nov 22 | Thu | Robert Bruner (Wayne State) | Topology seminar |
16:00 | J11 | The mod 2 Adams Spectral Sequence for Topological Modular Forms | |
Abstract: In joint work with John Rognes, we have computed the 2-local homotopy of tmf, with full details. We first compute the cohomology of A(2) by a method of general interest. Grobner bases play a key role in allowing us to give a useful description it. I will briefly describe this. We then show that all the Adams spectral sequence differentials follow from general properties together with three key relations in the homotopy of spheres. We then compute the hidden extensions and the relations in homotopy using the cofibers of 2, eta and nu. This allows us to give a clear and memorable description of tmf_*. I will end with a brief description of the duality present in tmf_* coming from the Anderson duality for tmf. |
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Nov 26 | Mon | Elaine Crooks (Swansea) | Mathematical Biology Seminar Series |
14:00 | Hicks LT10 | ||
Nov 27 | Tue | Jack Shotton (Durham) | Number Theory seminar |
14:00 | J11 | Shimura curves and Ihara's lemma | |
Abstract: Ihara's lemma is a statement about the structure of the mod l cohomology of modular curves that was the key ingredient in Ribet's results on level raising. I will motivate and explain its statement, and then describe joint work with Jeffrey Manning on its extension to Shimura curves. |
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Nov 27 | Tue | Caitlin McAuley (Sheffield) | Algebra / Algebraic Geometry seminar |
16:00 | J11 | ||
Nov 27 | Tue | Colin Angus (ScHARR, Sheffield) | RSS Seminar Series |
16:30 | Hicks LT6 | What is a 'safe' level of alcohol? | |
Abstract: Colin will discuss the development of the UK low-risk drinking guidelines. |
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Nov 28 | Wed | Yanki Lekili (King's College London) | Pure Maths Colloquium |
14:00 | J11 | ||
Dec 4 | Tue | Ciaran Schembri (Sheffield) | Number Theory seminar |
14:00 | J11 | TBA | |
Dec 4 | Tue | Cristina Manolache (Imperial) | Algebra / Algebraic Geometry seminar |
16:00 | J11 | ||
Dec 5 | Wed | Elisa Posthingel (Loughborough) | Pure Maths Colloquium |
14:00 | J11 | ||
Dec 5 | Wed | Jake Shipley (SoMaS) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 11 | ||
Dec 10 | Mon | Rachel Norman (Stirling) | Mathematical Biology Seminar Series |
14:00 | Hicks LT10 | ||
Dec 11 | Tue | TBA | Number Theory seminar |
14:00 | J11 | ||
Dec 11 | Tue | Dominic Joyce (Oxford) | Algebra / Algebraic Geometry seminar |
16:00 | J11 | ||
Dec 12 | Wed | Steffen Kionke (Karlsruhe Institute for Technology) | Pure Maths Colloquium |
14:00 | J11 | ||
Dec 12 | Wed | Ciaran Schembri (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | ||
Dec 13 | Thu | Alice Pozzi (UCL) | Number Theory seminar |
14:00 | J11 | TBA | |