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 10 | Wed | Visakan Balakumar & Jake Percival (Sheffield) | Cosmology, Relativity and Gravitation |
15:00 | J11, Hicks | Report from QFT Energy Inequalities conference | |
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 | Jack Morrice (Cape Town) | Cosmology, Relativity and Gravitation |
00:00 | J11, Hicks | Streams: a small, mesh-based look at large structure formation | |
Abstract: Today, cosmology's N-body paradigm looks a bit like a power monopoly. The codes (GADGET, RAMSES...) have huge computational overheads; descriptions of their underlying algorithms are old and hard to find; and the outputs of these codes are very difficult to analyze. These factors make the study of cosmic large scale structure accessible only to those with easy access to a lot of supercomputer cores and a familiarity with old imperative programming languages like C and Fortran. In this talk, we will look at Streams, a modest attempt to address these issues. Streams is a small package written for the Julia programming language that uses Lagrangian perturbation theory to significantly reduce overheads, and is built from a computer geometry (mesh) perspective which, together, make it very well suited to studying the formation of folds and caustics in the dark matter fluid on a personal computer. |
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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 | Elizabeth Winstanley (Sheffield) | Cosmology, Relativity and Gravitation |
15:00 | J11, Hicks | Quantum expectation values on black hole space-times | |
Abstract: The renormalized expectation value of the stress energy tensor (RSET) is an object of central importance in quantum field theory in curved space-time, but calculating this on black hole space-times is far from trivial. The standard methodology was developed in the 1980s and 1990s and successfully applied to a range of quantum fields on Schwarzschild black holes. The subject received an impetus in the last few years with to the development of two novel approaches to computing the RSET and renormalized vacuum polarization (VP). These advances have enabled calculations on a wider range of black hole space-times to be performed. In this talk we will review both the standard and novel methodologies and some results for the RSET and VP on asymptotically flat, de Sitter and anti-de Sitter black holes. |
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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 7 | Wed | Nicola Rendell (York) | Cosmology, Relativity and Gravitation |
15:00 | J11, Hicks | Infrared divergences in cosmological spacetimes | |
Abstract: We study the infrared divergences of the graviton propagator in FLRW spacetime. We show that, through the use of a 'large' gauge transformation, this divergence is a gauge effect. |
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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 | Eleni Kontou (York) | Cosmology, Relativity and Gravitation |
15:00 | J11, Hicks | Strong quantum energy inequality and the Hawking singularity theorem | |
Abstract: Hawking's singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a nonnegative effective energy density (EED), thereby guaranteeing the timelike convergence property. However, for both classical and quantum fields, violations of the SEC can be observed in some of the simplest of cases, like the massive Klein-Gordon field. Therefore there is a need to develop theorems with weaker restrictions, namely energy conditions averaged over an entire geodesic and quantum inequalities, weighted local averages of energy densities. We have derived lower bounds of the EED in the presence of both classical and quantum scalar fields allowing nonzero mass and nonminimal coupling to the scalar curvature. In the quantum case these bounds take the form of a set of state-dependent quantum energy inequalities valid for the class of Hadamard states. Finally, we discuss how these lower bounds are applied to prove Hawking-type singularity theorems asserting that, along with sufficient initial contraction at a compact Cauchy surface, the spacetime is future timelike geodesically incomplete. Talk is based on: DOI:10.1007/s10714-018-2446-5, arXiv:1809.05047 and a manuscript in preparation. |
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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 | Konstantinos Dimopoulos (Lancaster) | Cosmology, Relativity and Gravitation |
15:00 | J11, Hicks | Cosmic Inflation and Dark Energy from the Electroweak Phase Transition | |
Abstract: Cosmic inflation is a period of accelerated expansion in the Early Universe. Inflation is the most compelling proposal for the formation of of the observed structures in the Universe like galaxies and galactic clusters. It also makes the Universe uniform and spatially flat in agreement with observations. To drive inflation an exotic substance is needed, with pressure negative enough to cause the expansion of the Universe to accelerate, when this substance is dominant. Observations suggest that the late Universe is also undergoing accelerated expansion, which is assumed to be due to another exotic substance called dark energy. Can this be the one and the same with the substance behind inflation? In this talk I present a novel idea, in which inflation leaves behind a minute potential density, which can become the dark energy observed today. The field responsible for inflation (scalaron), is trapped in a local minimum of its scalar potential until the electroweak phase transition. The transition releases the field and allows it to vary slowly down a shallow potential tail, becoming dark energy. This behaviour is facilitated by a suitable coupling between the scalaron field and the electroweak Higgs field. The model is successful without fine-tuning, because it makes use of the curious fact that the electroweak energy scale is roughly the geometric mean of the Planck scale and the dark energy scale. |
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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. | |
Abstract: In this talk I will attempt to draws comparisons between my experience of mathematics education as both an undergraduate and a postgraduate student in SoMaS with my experience of mathematics education in my current role at Sheffield Hallam. I will talk about some of the high points from my time in SoMaS that helped me become a lecturer, and in doing so I hope to highlight some of the examples of good practice in what the department does/did. Then, in the spirit of collaboration, I will share some of the things I think we do well at Hallam that SoMaS could maybe learn from. |
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Nov 22 | Thu | Istvan Ballai (Sheffield) | Plasma Dynamics Group |
15:00 | Lecture Theatre 2 (Hicks Building) | Introduction to multiple scaling methods to solve differential equations with applications to plasma physics. Part II: Nonlinear partial differential equations | |
Abstract: In the second part of my seminar I will focus on nonlinear partial differential equations that can be obtained from the MHD equations. Using the multiple scale technique I will present a method to obtain the Korteweg-de Vries-Burgers equation in a non-ideal plasma in the presence of Hall currents. Using simple methods, I will find solutions to the limiting cases of shock waves and solutions. |
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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 | Stability conditions of the Kronecker quiver | |
Abstract: To a quiver $Q$, we can associate a sequence of Calabi--Yau-$n$ triangulated categories. The spaces of stability conditions of these categories can then be computed. I will give a description of these stability manifolds, and discuss the relationship between them and the Frobenius structure of the quantum cohomology of the projective line. |
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Nov 27 | Tue | Colin Angus (ScHARR, Sheffield) | RSS Seminar Series |
16:30 | Hicks LT6 | What is a 'safe' level of alcohol? Developing the UK low-risk drinking guidleines | |
Abstract: At the beginning of 2016, the UK Chief Medical Officers announced new 'low-risk' drinking guidelines. The development of these guidelines was informed by statistical modelling work to estimate the risks associated with drinking at different levels. In this presentation, Colin Angus, who led this work, will present how these risks were estimated and the ways in which they were used to define 'low-risk' drinking. He will also discuss the limitations of this approach and the challenges in communicating the risks associated with drinking to the public. Finally the presentation will address recent work from the Global Burden of Disease study which argues that there is 'no safe level' of alcohol consumption. |
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Nov 28 | Wed | Paul McFadden (Newcastle) | Cosmology, Relativity and Gravitation |
00:00 | J11, Hicks | Conformal field theory in momentum space | |
Abstract: Conformal symmetry places strong constraints on the properties of a quantum field theory, fixing the form of all 2- and 3-point functions up to constants. The resulting expressions are well-known in position space, yet surprisingly their counterparts in momentum space have only recently been identified. We review these developments, introducing an elementary method for solving the momentum-space conformal Ward identities. In special cases, divergences arise and we must renormalise giving rise to beta functions and anomalies. Our results have interesting new applications ranging from condensed matter physics to holographic cosmology. |
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Nov 28 | Wed | Yanki Lekili (King's College London) | Pure Maths Colloquium |
14:00 | J11 | Homological mirror symmetry made concrete | |
Abstract: Mirror symmetry is a broad correspondence between algebraic and symplectic geometry. It is a bit scary in the beginning as a true understanding of it requires some knowledge of both of these rather deep fields. In this talk, I will not give you a true understanding, rather I will provide examples of how fascinating this correspondence is. My intention is to get you "hooked" - it's up to you to decide whether you want to pursue this for a true understanding. |
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Nov 28 | Wed | Daniel Graves (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | Homology theories for algebras | |
Abstract: Since the 40s people have been developing homology and cohomology theories to try to encode information about algebras over commutative rings. In this talk I will discuss three such: Hochschild homology, Cyclic homology and Symmetric homology. The first two are classical theories that have found applications in many diverse areas. Symmetric homology is a related theory that is less well studied and slightly mysterious in comparison. |
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Nov 29 | Thu | Hope Thackray (Sheffield) | Plasma Dynamics Group |
15:00 | Lecture Theatre D (Hicks Building) | Fast MHD modes of a two (and three) shell semi-cylindrical waveguide | |
Abstract: The modelling of coronal loop structures has long been pursued as a means of determining physical properties of the Sun's corona. Here, a 3D semi-cylindrical waveguide is proposed, representing a coronal loop arcade anchored in the photosphere. By considering the eigenfunctions formed at the interface of a sharp density discontinuity (represented by "two-shell" and subsequently "three-shell" density structures), we show that waves are elliptically polarised, and that small changes in density contrast between shells can drastically affect the presence of eigenmodes. Since observational information has restrictions on resolution, the implication is that two similarly determined density structures may produce vastly different estimations of potential eigenmodes. |
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Dec 4 | Tue | Ciaran Schembri (Sheffield) | Number Theory seminar |
14:00 | J11 | Modularity of abelian surfaces over imaginary quadratic fields | |
Abstract: In this talk I will discuss the modularity of abelian surfaces with quaternionic endomorphisms. This includes a discussion of how they correspond to Bianchi newforms and how to prove this for individual cases using the Faltings-Serre method. Furthermore, we give explicit examples which do not arise as the base-change of a GL(2)-type surface, which settles a question posed by J. Cremona in 1992. |
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Dec 4 | Tue | Cristina Manolache (Imperial) | Algebra / Algebraic Geometry seminar |
15:00 | J11 | The enumerative content of Gromov-Witten theory | |
Abstract: I will discuss old and new ways of answering questions in enumerative geometry. New methods have many advantages and one major drawback. In this talk I will discuss this drawback. I will introduce Gromov--Witten invariants and I will give evidence that they do not give correct curve counts. I will introduce new enumerative invariants from curves with cusps and I will argue that cuspidal invariants have a better enumerative meaning. In the end, I will highlight one application. This is based on work in collaboration with L Battistella, F Carocci and T Coates. |
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Dec 4 | Tue | Andrea Brini (Birmingham) | Algebra / Algebraic Geometry seminar |
16:00 | J11 | Structures in Gromov-Witten theory | |
Abstract: I will survey the existence of hidden recursive structures in the Gromov--Witten (GW) theory of a complex projective variety. I will discuss a characterisation of recursions for genus zero invariants in terms of associative deformations of the cup product in cohomology, and some alternative presentations of the deformed cup product motivated by singularity theory (the celebrated "mirror symmetry"). In some happy (and central) instances mirror symmetry is often a tool powerful enough to determine recursively all GW invariants starting from minimal input data. I will consider one application of these ideas to low-dimensional topology, which is partly joint work with Gaetan Borot, relating a class of smooth invariants of 3-manifolds to recursions for GW invariants. |
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Dec 5 | Wed | Elisa Posthingel (Loughborough) | Pure Maths Colloquium |
14:00 | J11 | Newton polytopes: from the origin to their modern use | |
Abstract: This talk aims to be a journey through the history of the Newton polygon. To any multivalued polynomial we can associate a convex polytope in Euclidean space by taking the convex hull of its exponent vectors. These polygons are named after Newton who, in the 17th century, made use of them in the setting of infinitesimal calculus. In the late 19th century they were employed by Baker to compute the genus of plane curves. An extensive study of the relation between hypersurfaces (zero loci of polynomial equations) and Newton polytopes took off in the 20th century with the advent of toric algebraic geometry. A further generalisation was introduced by Okounkov, in the last two decades, to study further properties of polarised algebraic varieties. |
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Dec 5 | Wed | Jake Shipley (SoMaS) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 11 | Strong-field gravitational lensing by black holes | |
Abstract: A key prediction of Einstein's theory of general relativity (GR) is the bending of light due to gravity, a phenomenon known as gravitational lensing. In 1919, Eddington's observation of light deflection by the Sun – weak-field gravitational lensing – played a key role in the establishment of GR as our best theory of gravitation. Almost 100 years later, we are on the verge of a new era in the field of gravitational lensing. Using the Event Horizon Telescope (EHT), an Earth-scale virtual telescope which employs very-long-baseline interferometry, astronomers will soon directly observe the supermassive black hole at the galactic centre. The high-resolution images formed by the EHT will allow us to test GR in the strong-field regime. In this talk, I will review the subject of gravitational lensing, before presenting an overview of the EHT's main aims and objectives. I will conclude with a review of some recent theoretical work on the subject of strong-field gravitational lensing by black holes. |
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Dec 5 | Wed | Thomas Morley (Sheffield) | Cosmology, Relativity and Gravitation |
15:00 | J11, Hicks | Renormalised vacuum polarisation on topological black holes | |
Abstract: Anti-de Sitter spacetime is a solution of Einstein's equations with a negative cosmological constant. This fact allows for unusual black hole solutions with non-spherical horizon topology. We calculate the renormalised vacuum polarisation for black holes with spherical, flat and hyperbolic event horizons, following the â€œextended coordinatesâ€ method, which uses a mode-sum representation for the Hadamard parametrix. Renormalisation counter terms are subtracted from the Greenâ€™s function mode-by-mode, leaving each individual term manifestly finite. |
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Dec 5 | Wed | Jake Percival (Sheffield) | Cosmology, Relativity and Gravitation |
15:30 | J11, Hicks | Semiclassical gravity for static spacetimes: Universality and structure dependence. | |
Dec 6 | Thu | Dan Heller (King Edward's School) | Teaching Lunch |
13:00 | LT3 | The New Maths A Level | |
Dec 10 | Mon | Rachel Norman (Stirling) | Mathematical Biology Seminar Series |
14:00 | Hicks LT10 | ||
Dec 11 | Tue | Dominic Joyce (Oxford) | Algebra / Algebraic Geometry seminar |
16:00 | J11 | A Ringel-Hall type construction of vertex algebras | |
Abstract: Vertex algebras are complicated algebraic structures coming from Physics, which also play an important role in Mathematics in areas such as monstrous moonshine and geometric Langlands. I will explain a new geometric construction of vertex algebras, which seems to be unknown. The construction applies in many situations in algebraic geometry, differential geometry, and representation theory, and produces vast numbers of new examples. It is also easy to generalize the construction in several ways to produce different types of vertex algebra, quantum vertex algebras, representations of vertex algebras, … It seems to be related to work by Grojnowski, Nakajima and others, which produces representations of interesting infinite-dimensional Lie algebras on the homology of moduli schemes such as Hilbert schemes. Suppose A is a nice abelian category (such as coherent sheaves coh(X) on a smooth complex projective variety X, or representations mod-CQ of a quiver Q) or T is a nice triangulated category (such as D^bcoh(X) or D^bmod-CQ) over C. Let M be the moduli stack of objects in A or T, as an Artin stack or higher stack. Consider the homology H_*(M) over some ring R. Given a little extra data on M, for which there are natural choices in our examples, I will explain how to define the structure of a graded vertex algebra on H_*(M). By a standard construction, one can then define a graded Lie algebra from the vertex algebra; roughly speaking, this is a Lie algebra structure on the homology H_*(M^{pl}) of a “projective linear” version M^{pl} of the moduli stack M. For example, if we take T = D^bmod-CQ, the vertex algebra H_*(M) is the lattice vertex algebra attached to the dimension vector lattice Z^{Q_0} of Q with the symmetrized intersection form. The degree zero part of the graded Lie algebra contains the associated Kac-Moody algebra. There is also a differential-geometric version, involving putting a vertex algebra structure on homology of moduli stacks of connections on a compact manifold X equipped with an elliptic complex E. |
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Dec 12 | Wed | Steffen Kionke (Karlsruhe Institute for Technology) | Pure Maths Colloquium |
14:00 | J11 | Profinite properties of arithmetic groups | |
Abstract: Which properties of a group are determined by the set of its finite quotients? We give an introduction to this classical question and present examples and non-examples of such "profinite" properties. Afterwards we take a closer look at profinite properties of arithmetic groups. An arithmetic group is, roughly speaking, a group of matrices with integer entries. We present a property which is surprisingly determined by the finite quotients and we try to explain this phenomenon. In the end, we mention possible generalizations and open problems. This is based on joint work with H. Kammeyer, J. Raimbault and R. Sauer. |
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Dec 12 | Wed | Sebastian Trojanowski (Sheffield) | Cosmology, Relativity and Gravitation |
15:00 | J11, Hicks | Looking forward to new physics with FASER: ForwArd Search ExpeRiment at the LHC | |
Abstract: One of the most rapidly developing areas of research in particle physics nowadays is to look for new, light, extremely weakly-interacting particles that could have avoided detection in previous years due to the lack of luminosity. These, so-called intensity frontier searches, have also broad cosmological connections to e.g. dark matter, as well as can help to unravel the mystery of neutrino masses. In this talk, we will summarize the current status of this field with a particular emphasis on a newly proposed experiment to search for such particles produced in the far-forward region of the LHC, namely FASER, the ForwArd Search ExpeRiment. FASER has been proposed as a relatively cheap detector to supplement traditional experimental programmes searching for heavy new physics particles in the high-pT region and, therefore, to increase the whole BSM physics potential of the LHC. On top of potentially far-reaching implications to BSM particle physics and cosmology, the newly proposed detector can also be used to measure high-energy SM neutrino cross sections. |
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Dec 12 | Wed | Luca Pol | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | The spectrum of a triangulated category | |
Abstract: The spectrum of a commutative ring spec(R) is an interesting topological space that encodes lots of geometric and algebraic information. In 2004, Paul Balmer generalized this definition to any tensor triangulated category setting the scene for Tensor Triangular Geometry. One of the main achievement of the Balmer spectrum is to put in a unique framework three classification results: Devinats, Hopkins and Smith's theorem in Stable Homotopy Theory, Thomason's theorem in Algebraic Geometry and Benson, Carlson and Rickard's theorem in Modular Representation Theory. In this talk I will define the Balmer spectrum and show some concrete examples. |
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Dec 13 | Thu | Konstantina Loumou (University of Glasgow) | SP2RC seminar |
10:00 | LT 10 | The association of RHESSI flares to the Hale Sector Boundary and Active Longitudes | |
Abstract: Are some parts of the Interplanetary Magnetic Field’s (IMF) neutral line more flare energetic than others? What are Hale Sector Boundaries (HSBs) and are they connected with flares? Do they have anything to do with Active Longitudes? In this work, I will discuss how RHESSI flares are associated with structures in the solar magnetic field termed as HSBs. If you think of the large-scale domains of different polarity that the IMF is formed of, they the parts of the boundary between them, that have the same polarity change as the sunspots back at the Sun. As the polarity of sunspots follows Hale’s law, the HSB of a particular polarity change will only occur in one hemisphere per cycle, and then alternate in the next cycle. It has previously been shown that HSBs coincide with stronger magnetic fields and more frequent flare occurrence (Dittmer 1975, Svalgaard & Wilcox 1976, Svalgaard et al. 2011). I will explain how we extended this work through solar cycles 23 and 24 using RHESSI flare locations from 2002 to 2016. We compared these flares to the HSBs determined using two different methods. One uses the polarity change at the Earth to estimate when the HSB was at solar central meridian and the other uses Potential Field Source Surface (PFSS) extrapolations to identify the HSB for all times. We found that for both Cycle 23 and 24 more than 40% of non-limb flares were located near a HSB, a correlation that varies with cycle phase and hemisphere. I will describe how this evolves with time and the potential of these approaches for assisting flare forecasting. We then used the locations of HSBs calculated with the first method, using Earth-based data, to a Carrington rotation system and compared them with the migration paths of Active Longitudes as show in Gyenge et al. (2016). We found that there are times where they overlap, but that is not happening in a consistent manner. They often move at different rates relative to each other (and the Carrington solar rotation rate) and these vary over each Cycle. |
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Dec 13 | Thu | Steffen Kionke (Karlsruhe Institute of Technology) | Number Theory seminar |
11:00 | J11 | The first Betti number of arithmetic hyperbolic 3-manifolds | |
Abstract: An arithmetic hyperbolic 3-manifold is the quotient of the 3-dimensional hyperbolic space by an action of a discrete arithmetically defined subgroup of SL(2,C). The cohomology of these manifolds contains number theoretic information and it is of interest to understand the dimension of the cohomology. We discuss some known results about the first Betti numbers of arithmetic hyperbolic 3-manifolds. In particular, we review a method to obtain lower bounds which was developed by Harder, Rohlfs and others. Finally, we explain how the representation theory of compact p-adic Lie groups can be used to obtain significantly stronger results. |
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Dec 14 | Fri | Marianna Korsos (Sheffield) | SP2RC seminar |
13:00 | K14 | Leap forward in Space Weather forecast: Novel prediction of flares | |
Abstract: In this presentation, we address newly discovered pre-flare behavioural patterns in typical sunspot groups by focusing on their evolution as a function of height above the solar surface in a 3-dimensional solar AR. Here, we further probe and apply the concept of the pre-flare behavioural patterns using a magneto-hydrodynamic (MHD) simulation generating solar-like flares. We introduce and discuss the relevant properties and the capability of pre-flare tracking of ARs to improve Space Weather forecasting by focusing on the evolution from the photosphere towards the chromosphere, Transition Region and low corona. The basis of a proxy measure of our approach is the so-called weighted horizontal gradient of magnetic field (W_GM) defined between spots of opposite polarities closer to the polarity inversion line(s) of an AR. The value and the temporal variation of W_GM is found to possess novel and potentially important diagnostic information about (i) the intensity of expected flares and (ii) the accuracy of onset time prediction. Next, we will demonstrate how, by tracking the temporal evolution of W_GM, distance between opposite polarity spots and the associated net flux at various heights in the lower solar atmosphere evolves as function of height. We show that this latter temporal behaviour across the chromosphere-low corona has fundamentally new forecast capabilities. We found, that at a certain height the converging of opposite polarities begins much earlier than at the photosphere or at other heights. Therefore we present a tool to identify the optimum height in the solar atmosphere for flare prediction that may considerably increase the capability of the time prediction . |
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Dec 17 | Mon | Alice Pozzi (UCL) | Number Theory seminar |
14:00 | J11 | The eigencurve at Eisenstein weight one points | |
Abstract: In 1973, Serre observed that the Hecke eigenvalues of Eisenstein series can be $p$-adically interpolated. In other words, Eisenstein series can be viewed as specializations of a $p$-adic family parametrized by the weight. The notion of $p$-adic variations of modular forms was later generalized by Hida to include families of ordinary cuspforms. In 1998, Coleman and Mazur defined the eigencurve, a rigid analytic space classifying much more general $p$-adic families of Hecke eigenforms parametrized by the weight. The local nature of the eigencurve is well-understood at points corresponding to cuspforms of weight $k \geq 2$, while the weight one case is far more intricate. In this talk, we discuss the geometry of the eigencurve at weight one Eisenstein points. In particular, we focus on the unusual phenomenon in which cuspidal Hida families specialize to Eisenstein series at weight one. Our approach consists in studying the deformation rings of certain (deceptively simple!) Artin representations. We discuss how this Galois-theoretic method yields some new insight on Gross’s formula relating the leading term of the $p$-adic L-function to $p$-adic logarithms of units of certain number fields. |
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Dec 18 | Tue | Alexis Virelizier (Lille) | Topology seminar |
16:00 | J11 | Generalized Kuperberg invariants of 3-manifolds | |
Abstract: In the 90s, Kuperberg defined a scalar invariant of 3-manifolds from each finite-dimensional involutory Hopf algebra over a field. The construction is based on the presentation of 3-manifolds by Heegaard diagrams and involves tensor products of the structure tensors of the Hopf algebra. These tensor products are then contracted using integrals of the Hopf algebra to obtain the scalar invariant. We generalize this construction by contracting the tensor products with other morphisms. Examples of such morphisms are derived from involutory Hopf algebras in symmetric monoidal categories. This is a joint work with R. Kashaev. |
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Jan 8 | Tue | Josep Alvarez-Montaner (Universitat Politecnica de Catalunya) | Algebra / Algebraic Geometry seminar |
14:00 | J11 | Local cohomology of binomial edge ideals and their generic initial ideals | |
Abstract: The aim of this talk is to give a detailed study of local cohomology modules of binomial edge ideals. Our main result is a Hochster type decomposition formula for these modules. As a consequence, we obtain a simple criterion for the Cohen-Macaulayness of these ideals and we describe their Castelnuovo-Mumford regularity and their Hilbert series. We also prove a conjecture of Conca, De Negri and Gorla relating the graded components of the local cohomology modules of binomial edge ideals and their generic initial ideals. |
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Jan 16 | Wed | Atsushi Takahashi (Osaka) | Algebra / Algebraic Geometry seminar |
16:00 | J11 | On a full exceptional collection in the category of maximally graded matrix factorizations of an invertible polynomial of chain type | |
Abstract: In ’77 Orlik-Randell asked about the existence of a certain distinguished basis of vanishing cycles in the Milnor fiber associated to an invertible polynomial of chain type. With my student, Daisuke Aramaki we transport their conjecture to the category of matrix factorizations by the (conjectural) homological mirror symmetry equivalence and then prove the resulting statement. |
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Jan 17 | Thu | Ricardo Gaferia (Instituto de Astrofísica de Andalucía - CSIC ) | SP2RC seminar |
10:00 | LT 10 | Machine learning assisted parallel inversions | |
Abstract: With the increase of data volume and the need of more complex inversion codes to interpret and analyze solar observations, it is necessary to develop new tools to boost inversions and reduce computation times and costs. In this presentation, I discuss the possibilities and limitations of using machine learning as a tool to estimate optimum initial physical atmospheric models necessary for initializing spectral line inversions. Tests have been carried out for the SIR and DeSIRer inversion codes. This approach allows firstly to reduce the number of cycles in the inversion and increase the number of nodes and secondly to automatically cluster pixels which is an important step to invert maps where completely different regimes are present. Finally, I also present a warp for SIR and DeSIRer inversion codes that allows the user to easily set up parallel inversions. |
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Jan 18 | Fri | Norbert Gyenge (Sheffield) | SP2RC seminar |
13:00 | LT 10 | The Nonaxisymmetric Behaviour Of Solar Eruptive Events | |
Abstract: This thesis investigates new approaches for predicting the occurrence of solar eruptive events based on coronal mass ejection (CME), solar flare and sunspot group observations. The scope of the present work is to study the spatio-temporal properties of the above-mentioned solar features. The analysis may also provide a deeper understanding of the subject of solar magnetic field reorganisation. Furthermore, the applied approaches may open opportunities for connecting these local phenomena with the global physical processes that generate the magnetic field of the Sun, called the solar dynamo. The investigation utilises large solar flare statistical populations and advanced computational tools, such as clustering techniques, wavelet analysis, autoregressive moving average (ARIMA) forecast, kernel density estimations (KDEs) and so on. This work does not attempt to make actual predictions because it is out of the scope of the recent investigation. However, the thesis introduces new possible approaches in the subject of flare and CME forecasting. The future aim is to construct a real-time database with the ability to forecast eruptive events based on the findings of this thesis. This potential forecasting model may be crucial for protecting a wide range of satellite systems around the Earth or predicting space weather based on the obtained results may also assist to plan safe space exploration in the future. |
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