Jul 23 | Fri | Bodan Arsovski (Sheffield) | Number Theory seminar |

Jul 2 | Fri | Manolis K. Georgoulis (RCAAM of the Academy of Athens ) | SP2RC seminar |

Abstract:As an encompassing overview of the European Union FLARECAST project will be published shortly, I will attempt a critical description of the project’s key science results, involving the motivation, the methodology, the metadata and the performance verification tasks performed in its framework. The science of FLARECAST pointed to three objectives, all falling under its main goal to better understand the drivers of solar flare forecasting and to improve prediction. These objectives were, first, to find out which preflare properties of solar active regions, treated as flare predictors, work best for forecasting purposes; second, to identify promising new predictors; and third, to perform an explorative research on flare and eruption prediction that utilized numerical simulations and investigated the physical and statistical connection between flares and coronal mass ejections. Interesting, and potentially important, leads were found, that may well help spearhead future efforts. Given the project’s limited duration, some further desired tasks were ultimately left for the future. On a top level, we concluded that the stochastic nature of solar flares’ occurrence is so deeply rooted in the Sun’s fundamental magnetic activity that even a massive Big Data and machine learning effort such as FLARECAST could not decisively lift this barrier of stochasticity. Furthermore, FLARECAST adhered to the European Union’s open access policy and consistently planned to help avoid effort duplication in future forecast attempts by making openly available all data, codes, and infrastructure it created. Detailed guidance in retrieving these resources will also be presented. |
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Jun 25 | Fri | Dr Marco Stangalini (Italian Space Agency (ASI,Italy)) | SP2RC seminar |

Abstract:MHD waves in the lower solar atmosphere were generally investigated through intensity and Doppler velocity data. However, modern high spatial and temporal resolution spectropolarimetry gives access to additional diagnostics, which can be helpful in the identification and the correct interpretation of the wave modes. Very recently, thanks to high-resolution spectropolarimetric observations in the lower solar atmosphere it was possible to detect for the first time anti-phase incompressible torsional oscillations in a magnetic pore. These waves have proven to be important in a range of physical systems due to their ability to transport non-thermal energy over long distances in a magnetised plasma. This property is of specific interest in solar physics where the extreme heating of the atmosphere of the Sun remains unexplained. Despite evidences in the upper atmosphere, they were not directly observed in the photosphere. The excitation of torsional waves in photospheric magnetic structures can significantly contribute to the energy transport in the solar atmosphere and the acceleration of the solar wind, especially if such signatures will be ubiquitously detected in even smaller structures with the forthcoming next generation of solar telescopes, like DKIST, EST and Solar Orbiter, which will significantly improve the spectropolarimetric accuracy and sensitivity. In this seminar, I will show and discuss these recent results and the new interesting possibilities enabled by high-resolution spectropolarimetry in the detection and identification of wave modes in solar magnetic structures. |
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Jun 24 | Thu | Prof. Lucie Green (UCL, Mullard Space Science Laboratory) | SP2RC seminar |

Abstract:Understanding the physical processes that underly the occurrence of coronal mass ejections is a key area of research, whilst being able to forecast an ejection beforehand would provide significant benefits to space weather forecasting lead-times. In this talk, these two aims will be discussed in the context of a quantity known as magnetic helicity, in particular the so-called helicity proxy that can be determined from modelled active region magnetic field and which has shown potential in being able to indicate when an active region will produce eruptive activity. Results will be presented for NOAA active region 11158, that builds on the helicity proxy analysis already presented by Thalmann et al. (2019) to incorporate the observed evolution of the coronal field and the physical processes taking place in the time leading up to an eruption. |
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Jun 17 | Thu | Deborah Baker (Mullard Space Science Laboratory, University College London (UK)) | SP2RC/ESPOS |

Abstract:Element abundance signatures have long been used as tracers of physical processes throughout astrophysics. Understanding the spatial and temporal variations in the composition of the solar corona provides insight into how matter and energy flow from the solar chromosphere out into the heliosphere as well as from the chromospheres of solar-type stars into their astrospheres. In this work, we investigate the spatial distribution of highly varying plasma composition around one of the largest sunspots of solar cycle 24. Observations of the photosphere, chromosphere, and corona are brought together with magnetic field modeling of the sunspot in order to probe the conditions that regulate the degree of plasma fractionation within loop populations of differing connectivities. We find that, in the coronalmagnetic field above the sunspot, variation in plasma composition is highly structured, with extremes in the level of fractionation among the distinct loop populations. Loops above the umbra contain unfractionated plasma, i.e. photospheric composition, while coronal loops rooted in the penumbra contain fractionated plasma, with the highest levels observed in the loops that connect within the active region. The distribution of the highly fractionated plasma appears to be correlated with the spatial locations at which intrinsic magnetic perturbations are identified in high spatial resolution spectropolarimetric observations of the solar chromosphere. Tracing field lines from regions of highly fractionated plasma in the corona to locations of magnetic perturbations detected in the chromosphere shows that they are magnetically linked. These results indicate a direct connection between sunspot chromospheric activity and observable changes in coronal plasma composition. We interpret our findings in the wider context of coronal heating and the ponderomotive force model of elemental fractionation. |
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Jun 17 | Thu | Abdulrahman Albidah (Sheffield) | Plasma Dynamics Group |

Abstract:Modal decomposition, like POD and DMD, are incredible methodologies with a vast range of applicability. In our group, we have an open code for that in matlab. In today's talk, Abdulrahman will explain how those codes work. |
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Jun 9 | Wed | Noemi Frusciante (Lisbon) | Cosmology, Relativity and Gravitation |

Abstract:The late time cosmic acceleration is one of the most puzzling phenomena in modern cosmology. Its modeling within General Relativity (GR) through the cosmological constant (L) results in the LCDM scenario. Although the latter gives a precise description of the Universe, it is known that it still contains a number of unresolved problems. These lead researchers to look for modified gravity models, for example by including additional degrees of freedom. In this talk I will present the phenomenology and the cosmological bounds of theories consistent with the gravitational-wave event GW170817. In particular I will discuss models which solve the Hubble tension between Planck and local measurements and for which data show a statistically significant preference over LCDM. |
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Jun 3 | Thu | Azaymi Litzi Siu-Tapia (Instituto de Astrofísica de Andalucía, IAA (ES)) | SP2RC/ESPOS |

Abstract:The Mg I b2 line at 5173 Å forms over a large range of heights but its core, which forms under conditions of non-local thermodynamic equilibrium, is most sensitive to heights near the temperature minimum, a region of the solar atmosphere that has not been sufficiently explored. The next-generation solar observatories will have access to this spectral line and will allow for multi-line observations to study the different layers of the solar atmosphere simultaneously and with unprecedented polarimetric sensitivity. We will present a morphological classification of the intensity and circular polarization profiles of this spectral line at high-spatial-resolution, using observations from the Swedish 1-m Solar Telescope. We will also discuss the results of the weak field approximation applied to the Mg I b2 line, and their comparison with inversion results of the Fe I 6173 Å line to understand how the magnetic field changes with height in the solar atmosphere. |
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May 28 | Fri | Fionnlagh Dover (SP2RC (UoS)) | SP2RC seminar |

Abstract:Solar spicules are one of the dominant dynamic phenomena of the lower solar atmosphere. Here, we show our results on modelling the propagation of such localised jets driven by a momentum pulse as the exciting force near photospheric heights. Using the MPI-AMRVAC code to perform 2D MHD simulations in an idealised stratified solar atmosphere, we investigate how key parameters (e.g., driver time, equilibrium magnetic field strength, velocity amplitude of driver and tilt with respect to the magnetic field) determine the morphology of these small-scale solar jets. A parametric study is carried out and using jet tracking software we analyse the jet properties (e.g., widths, apex heights, etc). We find that jet boundary deformation occurs naturally due to speeds involved in driving these jets within the range of spicule heights that could be then a possible alternative explanation for the appearance of transverse motions (both axisymmetric and non-axisymmetric deformations). By resolving structures up to 10 km, we also find unforeseen substructures inside the spicular jet beam. We propose observers to confirm this latter finding that may be challenging due to current spatial resolution limits. |
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May 27 | Thu | Bradley W. Hindman (University of Colorado, Boulder (USA)) | Plasma Dynamics Group |

Abstract:One of the most prominent features seen in images of the solar corona by EUV telescopes are the elegant arches of glowing plasma that trace magnetic field lines through the corona. Typically, these loops are preferentially illuminated segments of a larger structure comprised of an arcade of arched field lines. Such loops are often observed to undulate in response to nearby solar flares. A flurry of observational and theoretical effort has been devoted to the explanation and exploitation of these oscillations. The grand hope is that seismic techniques can be used as probes of the strength and structure of the corona’s magnetic field. The commonly accepted viewpoint is that each visible loop oscillates as an independent entity and acts as a separate wave cavity for MHD kink waves. Thus, the seismic analysis is conveniently reduced to a 1D wave problem with boundary conditions at the foot points of the loop in the photosphere. I will argue that for many events, this generally accepted model for the nature of the wave cavity is fundamentally wrong. In particular, the entire 3D magnetic arcade in which the bright loops reside participates in the oscillation. Thus, the true wave cavity is much larger than the individual loop and inherently multidimensional. I will present theoretical arguments to support this 3D viewpoint and discuss the implications and opportunities for seismology of the solar corona. |
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May 26 | Wed | Du Pei (University of Harvard) | Pure Maths Colloquium |

Abstract:The existence of quantum field theories in higher dimensions predicts many hidden algebraic structures in geometry and topology. In this talk, I will survey some recent developments where such algebraic structures lead to new insights into 1) the quantization of moduli spaces of Higgs bundles, 2) the categorification of quantum invariants of 3-manifolds, and 3) novel types of TQFTs in four dimensions. |
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May 26 | Wed | Bruno Barros (Lisbon) | Cosmology, Relativity and Gravitation |

Abstract:In this talk, I will thoroughly explore the phenomenology of dark energy couplings, by exposing two distinct models where dark energy interacts with dark matter. We will journey through three different cosmological phases, so as to study the main influence of the coupling on formation of structure processes. The background cosmology is analysed by resorting to numerical and dynamical system techniques. We will follow closely the linear behaviour of the matter perturbations and test their growth against redshift space distortions data. We also shed some light on the sensitivity of future missions to constrain the dark coupling. Finally, we are going to witness the collapse of matter overdensities by inspecting the physics of the spherical collapse, tracking the evolution of perturbations along the first stages of their nonlinear regime, and compute the number of bound structures formed. |
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May 20 | Thu | Kristopher Cooper (University of Glasgow, School of Physics & Astronomy (UK)) | SP2RC/ESPOS |

Abstract:Small, highly frequent flares are thought to contribute to heating the Sun’s atmosphere, particularly in active regions. This impulsive energy release would heat plasma >5 MK and accelerate electrons, producing weak thermal and non-thermal signatures that could be observed by a very sensitive X-ray telescope. No such solar telescope exists currently so we use the Nuclear Spectroscopic Telescope Array (NuSTAR), an astrophysical X-ray telescope, with focusing optics imaging spectroscopy providing a unique sensitivity for observing the Sun above 2.5 keV. In this seminar, I will present an overview of the discoveries from NuSTAR solar observations where decreasing solar activity between cycle 24 and 25 has allowed GOES sub-A class microflares to be observed regularly within, and small brightenings outside, active regions. In particular, I will describe several X-ray microflares from a recently emerged active region, AR12721, that were observed on 2018 September 9-10 with NuSTAR. In combination with SDO/AIA, I will discuss the temporal, spatial, and spectral evolution of these sub-A class microflares and show that temperatures up to 10 MK are reached. Using SDO/HMI, I also present evidence of photospheric magnetic flux cancellation/emergence at the footpoints in 8 NuSTAR microflares. |
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May 20 | Thu | Vigeesh Gangadharan (Leibniz Institute for Solar Physics, Germany) | Plasma Dynamics Group |

Abstract:Internal gravity waves (IGWs) are buoyancy-driven waves common in the Earth’s atmosphere and oceans. IGWs have also been observed in the Sun’s atmosphere and are thought to play an important role in the overall dynamics of the solar atmosphere. They supply bulk of the wave energy for the lower solar atmosphere, but their existence and role in the energy balance of the upper layer remains unclear. Using radiation-magnetohydrodynamic (R-MHD) simulations, we study naturally excited IGWs in realistic models of the solar atmosphere. In this talk, we discuss some of our recent results on the influence of the Sun's magnetic field on the propagation of IGWs and their energy transport. Our analysis suggests that the IGWs are generated independent of the mean magnetic property of the atmosphere. However, their propagation into higher layers is strongly affected by the presence and the topology of the magnetic field. We discuss how IGWs may play a significant role in the heating of the chromospheric layers in regions where horizontal fields are thought to be prevalent, like the internetwork region. |
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May 19 | Wed | Birgit Richter (University of Hamburg) | Pure Maths Colloquium |

Abstract:This is a report on joint work with Eva Höning. For rings of integers in an extension of number fields there are classical methods for detecting ramification and for identifying ramification as being tame or wild. Noether's theorem characterizes tame ramification in terms of a normal basis and tame ramification can also be detected via the surjectivity of the norm map. We take the latter fact and use the Tate cohomology spectrum to detect wild ramification in the context of commutative ring spectra. I will discuss several examples in the context of topological K-theory and modular forms. |
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May 19 | Wed | Alberto Cobos | Algebraic Geometry Learning Seminar: Toric varieties |

May 18 | Tue | Srilakshmi Krishnamoorthy (I.I.S.E.R. Thiruvanthapuram) | Number Theory seminar |

Abstract:We present the explicit expression of the Eisenstein elements inside the space of modular symbols for Eisenstein series with integer coefficients for the congruence subgroups Γ0(N) of square- free level N. This answers a question of Merel. Our results are explicit versions of the Manin-Drinfeld theorem. |
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May 18 | Tue | Joseph Martin and Callum Reader (Sheffield) | MiaowMiaow (2d category theory) |

Abstract:The seminar will run for 90 mins. |
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May 13 | Thu | Dr Hugh Hudson (University of Glasgow and UC Berkeley) | SP2RC seminar |

Abstract:We often cite the Carrington flare (SOL1859-09-01) as an extreme flare/CME/geostorm event and a prototype "superflare." I discuss the original observations in the context of what we now know about solar and stellar flares. Although not an extreme event in the sense of being truly exceptional, it has become clear that the Carrington flare turned into a milestone in what we now call "multimessenger astronomy." |
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May 12 | Wed | Isha Kotecha (Okinawa Institute for Science and Technology) | Cosmology, Relativity and Gravitation |

Abstract:Thermal states are absolutely important for statistical descriptions of physical systems; likewise also in discrete quantum gravity, where classical continuum spacetime is thought to emerge from the collective physics of some underlying quantum structure. But what equilibrium even means in a background independent context is a foundational open issue. In this talk, I will discuss a generalisation of Gibbs states for use in such contexts, while emphasising on the maximum entropy principle characterisation. The resulting setup is then applied in quantum gravity, by modelling a quantum spacetime as a many-body system of candidate quanta of geometry, and utilising their field theoretic formulation of group field theory (GFT). This leads to concrete examples of quantum gravitational generalised Gibbs states. I will then present non-perturbative thermofield double vacua, and their inequivalent thermal representations, as induced by these Gibbs states. An interesting class of thermal condensates are defined, which encode fluctuations in the underlying quantum geometry. These are subsequently applied in GFT cosmology to extract an effective FLRW universe at late times, with a bounce and accelerated expansion at early times. |
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May 12 | Wed | Ana Lecuona (University of Glasgow) | Pure Maths Colloquium |

Abstract:In this talk we will mainly focus on rational homology balls: their history, interest and prominence in nowadays low dimensional topology. We will start with the basic definitions and we will spend some time trying to understand the importance of these balls and how they relate to seemingly disjoint problems. We will end by discussing some recent results which will hopefully give a picture of the current state of the art. No prior knowledge of the topic will be assumed. |
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May 12 | Wed | Kevin Wilson and Cameron Williams (Newcastle) | Statistics Seminar |

Abstract:When eliciting prior distributions from experts, it may be desirable to combine them into a single group prior. There are many methods of expert-elicited prior aggregation, which can roughly be categorised into two types. Mathematical aggregation methods combine prior distributions using a mathematical rule, while behavioural aggregation methods assist the group of experts to come to a consensus prior through discussion. As many commonly used aggregation methods have different requirements in the elicitation stage, there are few, if any, comparisons between them. Using a clinical trial into a novel diagnostic test for Motor Neuron Disease as a case study, we elicited a number of prior distributions from a group of experts. We then aggregated these prior distributions using a range of mathematical aggregation methods, including Equal Weights linear pooling, the Classical Method, and a Bayesian aggregation method. We also undertook an in-person behavioural aggregation with the experts, using the Sheffield Elicitation Framework, or SHELF. Using expert answers to seed questions, for which the elicitors know the true values, we compare and contrast the different aggregation methods and their performance. We also demonstrate how all considered aggregation methods outperform the individual experts. |
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May 12 | Wed | George Moulantzikos | Algebraic Geometry Learning Seminar: Toric varieties |

May 11 | Tue | Lassina Dembele (University of Luxembourg) | Number Theory seminar |

Abstract:There is an isogeny class of semistable abelian surfaces A with good reduction outside 277 and $End_Q(A) = Z$. The modularity (or paramodularity) of this class was proved by a team of six people: Armand Brumer, Ariel Pacetti, Cris Poor, Gonzalo Tornaria, John Voight and David Yuen. They did so by using the so-called Faltings-Serre method. This was the first known case of the paramodularity conjecture. In this work in progress, I will discuss how to (re-)prove the modularity of these surfaces by directly applying deformation theory. This could be seen as an explicit approach to deformation theory. |
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May 11 | Tue | Emily Roff (Edinburgh) | MiaowMiaow (2d category theory) |

Abstract:Seminar will run for 90 mins. |
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May 6 | Thu | Matheus Aguiar-Kriginsky Silva (University of the Balearic Islands, UIB (ES)) | SP2RC/ESPOS |

Abstract:In this seminar, we aim to present the results of two recent works centred at the use of spectropolarimetric data obtained with the CRISP instrument at the SST in the Ca II 845.2 nm line. With these observations, we obtain information about the magnetic field present in chromospheric spicules and coronal rain clumps. For this purpose, we have used the Weak-field approximation (WFA), which albeit being computationally simple to implement, needs careful assessment of the conditions of the plasma to be correctly applied. Magnetic fields of the order of hundreds of Gauss are inferred. We also combine the Ca II 845.2 nm observations with simultaneous Hα observations to estimate the temperature and non-thermal velocity of the plasma in coronal rain and spicules using the observed Doppler amplitude. |
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May 5 | Wed | Reinder Meinsma / Yirui Xiong | Algebraic Geometry Learning Seminar: Toric varieties |

May 4 | Tue | Andrea Conti (University of Luxembourg) | Number Theory seminar |

Abstract:When interpolating p-adically Galois representations attached to automorphic forms, one obtains many new representations that are not de Rham locally at p. It is expected that such representations are characterized by the condition of being trianguline at p. We study how this notion behaves under functoriality: it is easy to show that if S: GL_m -> GL_n is an algebraic representation and rho is an m-dimensional trianguline Galois representation, the composition S(rho) is again trianguline. We prove that under reasonable assumptions the reverse implication is true, with the goal of applying the result to the study of congruence loci on eigenvarieties. |
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Apr 30 | Fri | Indrani Roy (University College London) | SP2RC seminar |

Abstract:This study investigates the role of the eleven-year solar cycle on the Arctic climate during 1979–2016. It reveals that during those years, when the winter solar sunspot number (SSN) falls below 1.35 standard deviations (or mean value), the Arctic warming extends from the lower troposphere to high up in the upper stratosphere and vice versa when SSN is above. The warming in the atmospheric column reflects an easterly zonal wind anomaly consistent with warm air and positive geopotential height anomalies for years with minimum SSN and vice versa for the maximum. Despite the inherent limitations of statistical techniques, three different methods – Compositing, Multiple Linear Regression and Correlation – all point to a similar modulating influence of the sun on winter Arctic climate via the pathway of Arctic Oscillation. Presenting schematics, it discusses the mechanisms of how solar cycle variability influences the Arctic climate involving the stratospheric route. Compositing also detects an opposite solar signature on Eurasian snow-cover, which is cooling during Minimum years, while warming in maximum. It is hypothesized that the reduction of ice in the Arctic and a growth in Eurasia, in recent winters, may in part, be a result of the current weaker solar cycle. |
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Apr 28 | Wed | Tom Bridgeland (University of Sheffield) | Pure Maths Colloquium |

Abstract:I'm planning to talk about some quite old joint work with Ivan Smith which realises moduli spaces of quadratic differentials on Riemann surfaces as spaces of stability conditions on a certain class of three-dimensional Calabi-Yau triangulated categories. I expect to spend the whole talk explaining what all those words mean, and why such a result might be interesting! |
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Apr 28 | Wed | Eleni Kontou (Amsterdam) | Cosmology, Relativity and Gravitation |

Abstract:The classical singularity theorems of General Relativity rely on energy conditions that are easily violated by quantum fields. In this talk I will provide motivation for an energy condition obeyed by semiclassical gravity: the smeared null energy condition (SNEC), a proposed bound on the weighted average of the null energy along a finite portion of a null geodesic. I will then then present the proof of a semiclassical singularity theorem using SNEC as an assumption. This theorem extends the Penrose theorem to semiclassical gravity and has interesting applications to evaporating black holes. Based on: arXiv: 2012.11569 |
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Apr 28 | Wed | Ananyo Dan | Algebraic Geometry Learning Seminar: Toric varieties |

Apr 27 | Tue | Tobias Berger (University of Sheffield) | Number Theory seminar |

Abstract:This is a report on joint work in progress with Adel Betina (Vienna) to prove congruences between Eisenstein and cuspidal cohomology classes for imaginary quadratic fields. I plan to discuss applications to R=T theorems and congruences for classical CM modular forms. |
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Apr 27 | Tue | Dan Graves | MiaowMiaow (2d category theory) |

Apr 22 | Thu | Alex Prokopyszyn (University of St Andrews) | SP2RC/ESPOS |

Abstract:In this seminar, we aim to show why Fast/Alfvén waves couple at the solar surface. We will also show that the polarisation of the waves changes upon reflection at the solar surface. Finally, we will test the validity of line-tied boundary conditions for highly phase-mixed Alfvén waves. For most parameters, line-tied boundary conditions provide a good approximation. However, for highly phase-mixed waves, the coronal transverse length scales can be shorter than the corresponding parallel length scales in the chromosphere. In that case, we find that the line-tied model produces unphysically large boundary layers. Hence, we have the counter-intuitive result that the length scales parallel to the solar surface play a key role in determining the validity of line-tied boundary conditions. |
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Apr 21 | Wed | Cihan Okay (Bilkent University) | Pure Maths Colloquium |

Abstract:A central question in quantum information theory is to determine physical resources required for quantum computational speedup. Such resources are characterized in terms of intrinsic features of quantum states and include various notions such as quantum contextuality, quasiprobability representations, and topological phases. Each of these notions correspond to a different perspective taken on the question of where the computational power is hidden. We take a topological approach based on the recently established connection between classifying spaces from algebraic topology and the study of quantum contextuality from quantum foundations in joint work with Robert Raussendorf. In this talk I will explain this connection and discuss possible ways of extending the role of topology to study other kinds of quantum resources. |
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Apr 21 | Wed | Peter Clarkson (University of Kent) | Applied Mathematics Colloquium |

Abstract:In this talk I shall discuss rational solutions of the Boussinesq equation, the focusing nonlinear Schrodinger (NLS) equation and the Kadomtsev-Petviashvili I (KPI) equation, which are all soliton equations solvable by the inverse scattering. The Boussinesq equation was introduced by Boussinesq in 1871 to describe the propagation of long waves in shallow water. Rational solutions of the Boussinesq equation, which are algebraically decaying and depend on two arbitrary parameters, are expressed in terms of special polynomials that are derived through a bilinear equation, have a similar appearance to rogue-wave solutions of the focusing NLS equation and have an interesting structure. Conservation laws and integral relations associated with rational solutions of the Boussinesq equation will also be discussed. Rational solutions of the KPI equation will be derived in three ways: from rational solutions of the NLS equation; from rational solutions of the Boussinesq equation; and from the spectral problem for the KPI equation. It'll be shown that these three families of rational solutions are fundamentally different. |
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Apr 21 | Wed | Bianca Dittrich (Perimeter Institute, Waterloo) | Cosmology, Relativity and Gravitation |

Abstract:General relativity taught us that spacetime geometry is dynamical and quantum theory posits that dynamical objects are quantum. In this talk I will sketch the notion of quantum geometry, which arises in loop quantum gravity. Somewhat surprisingly, this quantum geometry, although it arises from a quantization of a torsion-free theory, does include torsion degrees of freedom. I will then introduce an effective dynamics for such quantum geometries and sketch how to derive corrections that arise due to the inclusion of torsion degrees of freedom. |
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Apr 21 | Wed | Yannik Schüler | Algebraic Geometry Learning Seminar: Toric varieties |

Apr 20 | Tue | Petru Constantinescu (University College London) | Number Theory seminar |

Abstract:Motivated by a series of conjectures of Mazur, Rubin and Stein, the study of the arithmetic statistics of modular symbols has received a lot of attention in recent years. In this talk, I will highlight several results about the distribution of modular symbols, including their Gaussian distribution and the residual equidistribution modulo p. I will also talk about generalisations to quadratic imaginary fields and higher dimensions. |
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Apr 20 | Tue | James Cranch (Sheffield) | MiaowMiaow (2d category theory) |

Abstract:Notes: 14:00-15:30. Contact Joseph Martin for meeting link. |
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Apr 16 | Fri | Daria Y Shukhobodskaia (SP2RC (UoS)) | SP2RC seminar |

Abstract:The investigation of magnetohydrodynamic (MHD) wave propagation in different equilibrium configurations is important for the development of solar magneto-seismology (SMS). The applicable models of solar atmospheric waveguides are studied in the framework of Cartesian and cylindrical geometries. First, a magnetised plasma slab sandwiched between an arbitrary number of non-magnetic/ magnetic layers are considered and an analytical approach is used for the derivation of its dispersion relation. The amplitudes of the eigenmodes depend on the equilibrium structuring and the model parameters; this motivates an application as a solar magneto-seismology tool. Specific cases of two- and three-layered slabs are studied in detail and their potential applicability to magnetic bright points is discussed. Furthermore, the resonant damping of propagating kink waves is studied in a straight magnetic flux tube with the density varying along the tube taking into account the magnetic loop expansion. Also non-stationary magnetic tubes to model, for example, cooling coronal loops is considered. In particular, it was found that cooling enhances the wave amplitude and the loop expansion makes this effect more pronounced. After, we analyse $10$ driven kink oscillations in coronal loops to further investigate the ability of expansion and cooling to explain complex damping profiles. The used approach could allow to infer some important diagnostic information (such as, for example, the density ratio at the loop foot-points) from the oscillation profile alone, without detailed measurements of the loop and without complex numerical methods. The current study indicates that thermal evolution should be included in kink-mode oscillation models in the future to help us to better understand oscillations that are not purely Gaussian or exponential. Finally, fluting oscillations in a thin straight expanding magnetic flux tube in the presence of background flow are considered. The method of multiple scales is used for the derivation of the system of governing equations. We have found that the amplitude increases due to cooling and is higher for a higher expansion factor. Higher values of the wave number lead to localisation of the oscillation closer to the boundary. We show that the higher the value of the ratio of internal and external plasma densities, the higher the amplification of oscillation due to cooling. So, not only the wave number plays an important role in the evolution of the cooling system, but also the density ratio and the variation of tube expansion are relevant parameters in the cooling process of an oscillating flux tube. |
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Apr 15 | Thu | Prof Richard A Harrison (RAL Space) | SP2RC seminar |

Abstract:This presentation will take stock of where we are with Coronal Mass Ejection (CME) research, taking a brief look at the history of CME observations and the early interpretations of the phenomenon, through to the present day where we have multi-spacecraft observations with coronagraphs and heliospheric imagers and a wide range of modelling techniques, many of which are now geared towards space weather impacts. This is a research area that has matured dramatically, since the launch of the SOHO spacecraft in particular, but especially with the increased interest in space weather and missions such as STEREO and Lagrange. It is a good time to take stock and in doing so to revisit some basic issues, including the flare-CME relationship, stealth CMEs, coronal dimming and CME-CME interactions, as well as lessons learnt from imaging and tracking CMEs in the corona and in the heliosphere. Perhaps it is also a useful time to pause and ask the questions, what else do we want to know about CMEs, and how are we going to satisfy that desire? |
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Apr 15 | Thu | Juie Shetye (New Mexico State University) | Plasma Dynamics Group |

Abstract:The solar chromosphere serves as a bridging layer between the photosphere and the corona. This dynamic layer is filled with a plethora of features that vary in time and space. With the advent of high-resolution ground-based observations we can discover new features. We use some of the World’s biggest solar telescopes to zoom into this layer and it reveals never seen before dynamics. Here I present detailed observations of two science topics that are guided by observations. I show a statistical study of spicules, which are long-thin grass-like features observed on the sun. These events wiggle-jiggle and sway around their axes or along a common centre of mass to create wave-like motions on the Sun. These waves can travel with speeds on 100s of km per second to energise the solar chromosphere. The second example I show are swirling-whirling events, that look like Tornadoes on the Earth. These churn the matter from the Lowe photosphere to the chromosphere. Studying the behaviour of such events is vital in understanding a decade long question in the solar physics, that tells us how the Sun’s atmosphere is heated. In addition, the current work presented already tests the limits of current telescopes in terms of the temporal and spatial resolution. The answer to exploring the depth of chromosphere lies in building next-generation solar physics observatories such as DKIST that have 3 times more spatial resolution than CRISP and much higher temporal resolution. |
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Apr 8 | Thu | Mayukh Panja (Max Planck Institute for Solar System Research, MPS (DE)) | SP2RC/ESPOS |

Abstract:Penumbral filaments do not form naturally in MHD simulations of sunspots. This is typically circumvented by modifying the top boundary: the field is made 2-3 times more horizontal than a potential field configuration. In this talk, I will explore the possibility that penumbral filament formation is governed by the subsurface structure of sunspots. We conducted a series of numerical experiments where we used flux tubes with different initial curvatures to study the effect of the fluting instability on the subsurface structure of spots using the MURaM code. We find that the curvature of a flux tube indeed determines the degree of fluting the flux tube will undergo—the more curved a flux tube is, the more fluted it becomes. In addition, sunspots with strong curvature have strong horizontal fields at the surface and therefore readily form penumbral filaments. The fluted sunspots eventually break up from below, with lightbridges appearing at the surface several hours after fluting commences. We also propose that intruding lightbridges can be used as tracers of the subsurface magnetic field. |
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Apr 2 | Fri | Michael Griffiths (Research IT, University of Sheffield) | SP2RC seminar |

Abstract:Parallel magnetohydrodynamic (MHD) algorithms are important for numerical modelling of highly inhomogeneous solar, astrophysical and geophysical plasmas. Parallelisation techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPUs) possessing hundreds of processor cores. The opportunity has been recognised by the computational sciences and engineering communities who have recently harnessed successfully the numerical performance of GPUs. Here, we introduce the implementation of SMAUG, the Sheffield Magnetohydrodynamics Algorithm Using GPUs. SMAUG is a 1-3D MHD code capable of modelling magnetised and gravitationally stratified plasmas. We illustrate an application of SMAUG with a discussion of the results of a study of the atmospheric motions generated by the solar global resonant oscillations. Utilising a spatially structured driver across the base of the computational model, we embark on how the ensemble of performed simulations, that provide insight into the energy supplied by various wave modes, is redistributed in the atmosphere. The results shed light on the mechanisms leading to ubiquitous intensity oscillations in the stratified solar atmosphere and establish a link between signals at photospheric levels and the solar coronal response. In the final section of the talk we describe how to access the different resources which are available for running computational MHD codes with GPU’s. |
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Apr 1 | Thu | Iulia Chifu (University of Goettingen) | Plasma Dynamics Group |

Abstract:The magnetic field plays an essential role in the initiation and evolution of different solar phenomena in the corona. The structure and evolution of the 3D coronal magnetic field are still not very well known. A way to ascertain the 3D structure of the coronal magnetic field is by performing magnetic field extrapolations from the photosphere to the corona. In previous work, it was shown that by prescribing the 3D-reconstructed loops’ geometry, the magnetic field extrapolation produces a solution with a better agreement between the modeled field and the reconstructed loops. This also improves the quality of the field extrapolation. Stereoscopy, which uses at least two view directions, is the traditional method for performing 3D coronal loop reconstruction. When only one vantage point of the coronal loops is available, other 3D reconstruction methods must be applied. Within this work, we present a method for the 3D loop reconstruction based on machine learning. Our purpose for developing this method is to use as many observed coronal loops in space and time for the modeling of the coronal magnetic field. Our results show that we can build machine-learning models that can retrieve 3D loops based only on their projection information. Ultimately, the neural network model will be able to use only 2D information of the coronal loops, identified, traced, and extracted from the extreme-ultraviolet images, for the calculation of their 3D geometry. |
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Mar 25 | Thu | Valeriia Liakh (INAF-OAR National Institute for Astrophysics (IT)) | SP2RC/ESPOS |

Abstract:We report 2D MHD simulations of the large-amplitude oscillations (LAOs) in the solar prominences performed with MHD code Mancha. We aim to study the properties of LAOs using high-resolution simulations in a simple 2D magnetic configuration that contains a dipped part. We loaded the dense prominence plasma in the dips region. In order to excite oscillations, we used a perturbation directed along the magnetic field. For the same numerical model, the four spatial resolutions were considered: 240, 120, 60, and 30 km. The longitudinal LAOs (LALOs) are strongly damped even in the high-resolution simulation in the region of the weaker and more curved magnetic field (at the center and bottom of the prominence). At the prominence top, the oscillations have relatively longer damping times. Furthermore, during the first 100 minutes, the longitudinal velocity shows growing with respect to its initial amplitude. The amplification becomes even more significant in the experiments with high-resolution. The damping and amplification mechanisms involved in our experiments can be important for explaining the observed amplification and attenuation of the LALOs. |
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Mar 24 | Wed | Magnus Goffeng (Lund University) | Pure Maths Colloquium |

Abstract:An invariant that has attracted quite some attention in the last decade is the magnitude of a compact metric space. Magnitude gives a way of encoding the size of a metric space, resembling both the Euler characteristic and the capacity. In this colloquium I will give a short introduction to magnitude and present some recent results for compact metric spaces of geometric origin (i.e. domains in Euclidean space or manifolds). One of the results states that the magnitude recovers geometric invariants such as volume and certain integrals of curvatures. Based on joint work with Heiko Gimperlein and Nikoletta Louca. |
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Mar 24 | Wed | George Moulantzikos | Algebraic Geometry Learning Seminar: Toric varieties |

Mar 18 | Thu | Dr Helen Mason (University of Cambridge) | SP2RC seminar |

Abstract:Spectroscopic diagnostics have enabled us to determine the physical parameters of plasma for different solar features (active regions, jets, flares etc). Helen started her career studying the visible coronal lines from the 1952 eclipse observations. She then studied the UV and X-ray spectrum of the Sun, working on many joint UK, NASA, ESA and Japanese solar space projects including Skylab, the SMM (Solar Maximum Mission), Yohkoh, SoHO (Solar and Heliospheric Observatory), Hinode, SDO (Solar Dynamics Observatory) and IRIS (Interface Region Imaging Spectrograph). She was a founder member of the CHIANTI team, an atomic database which has been extensively used for solar data analysis. In this talk, she will pick out a few key results as examples of the value of spectroscopic diagnostics (in the transition region and corona). She will also look towards the current opportunities for research in this field and the future prospects for spectrometers. For a recent review, see: Del Zanna and Mason, 2018, Solar UV and X-ray spectral diagnostics’, Sol. Phys. Liv. Reviews. |
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Mar 18 | Thu | Kostas Tziotziou (National Observatory of Athens) | Plasma Dynamics Group |

Abstract:Small-scale vortex motions are detected at various spatial and temporal scales in the solar atmosphere, from the photosphere to the low corona. They often exhibit complex structure and dynamics and, as largely magnetic structures, can foster a variety of oscillations and wave modes. Despite, however, recent advancements in observational and theoretical studies, as well as in simulations and modelling, their proper detection, especially in chromospheric lines such as Hα and Ca II 8542 Å is still an open issue, and their structure and dynamics remain poorly understood. We present a novel automated method of chromospheric swirl detection based on their morphological characteristics that nicely complements previous LCT-related approaches. We further discuss in detail the intricate dynamics of a persistent small-scale vortex flow with significant substructure, observed with the CRisp Imaging SpectroPolarimeter (CRISP) at the Swedish Solar Telescope (SST), as well as oscillations and observational signatures of different types of waves within it and their propagation characteristics. Both discussed aspects, better detection leading to a more precise estimation of their occurrence rate and wave identification and their properties, are key elements for accurately assessing the role of vortex structures in the energy budget of the solar atmosphere. |
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Mar 17 | Wed | Ulrich Bunke (University of Regensburg) | Pure Maths Colloquium |

Abstract:Coarse geometry studies the large-scale properties of metric spaces, groups and other mathematical objects. Interesting invariants are constructed using coarse homology theories. In this exposition I will explain an axiomatic approach to coarse homology theories. A motivic statement is a statement of the form: For every coarse homology theory E assertion P(E) holds. For example, one can turn the coarse Baum-Connes conjecture into a motivic statement. I will explain how motivic statements can be captured in terms of a universal coarse homology theory. The talk is based on joint work with Alexander Engel. |
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Mar 17 | Wed | Richard Daniel (Sheffield) | Cosmology, Relativity and Gravitation |

Abstract:In this talk, I will briefly recap slow roll inflation, before demonstrating that an $f(R^2)$ theory of inflation is able to dynamically generate a Planck mass from the vacuum expectation values of the scalar fields. We see that in such models if the self interaction is non-zero, a potentially large cosmological constant will emerge. To avoid this problem we introduce another scalar field, producing a Higgs-like potential. This naturally drives the cosmological constant to zero soon after inflation. We will analyse both models in the Einstein frame, where we find a conserved Noether current simplifying the model to a N-1 scalar field model. Finally, I will discuss the non-trivial features in the power spectrum, which produce testable parameters for future cosmological experiments. |
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Mar 17 | Wed | Cristina Manolache | Algebraic Geometry Learning Seminar: Toric varieties |

Mar 11 | Thu | Sergio J. González Manrique (Astronomical Institute of Slovak Academy of Sciences (SK)) | SP2RC/ESPOS |

Abstract:We study the dynamics of plasma along the legs of an arch filament system (AFS) observed with relatively high-cadence spectropolarimetric data from the ground-based solar GREGOR telescope (Tenerife) using the GREGOR Infrared Spectrograph in the He I 10830 Å range. The temporal evolution of the plasma of an AFS was followed using the chromospheric He I 10830 Å triplet and Si I 10827 Å. Measurements of vector magnetic fields in the solar chromosphere, especially in AFS, are extremely scarce, but very important. The magnetic field configuration reveals how AFSs are sustained in the chromosphere and hints at their formation, evolution, and disappearance. The magnetic field in the AFS follows loop-like structures traced by chromospheric absorption lines. However, if magnetic field lines follow chromospheric threads as seen by filtergrams of H⍺, Ca II, or He I, is still not fully resolved. Previous studies have modeled AFS as multiple flux ropes with mixed signs of helicity consistently with the observed multiple filament bundles constituting AFS. Nevertheless, further spectropolarimetric observations are needed to address this issue. Many spectral lines are sensitive to the atmospheric parameters up to the upper chromosphere. Moreover, when combined with photospheric Zeeman sensitive spectral lines, one can infer the topology of the magnetic field from the bottom of the solar atmosphere to the chromosphere. In this talk, we are going to follow the nature of AFSs by reconstructing the magnetic field configuration of an EFR from the very beginning and follow its evolution and dynamics to support current AFS models. To that aim we used the spectropolarimetric data available at the upper photosphere (Si I) and the upper chromosphere. |
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Mar 10 | Wed | Anssi Lahtinen (University of Copenhagen) | Pure Maths Colloquium |

Abstract:Founded by Chas and Sullivan's observation that the homology of the free loop space of an oriented manifold has the structure of a Batalin--Vilkovisky algebra, string topology studies the rich algebraic structure present on the homology of the free loop spaces of certain spaces such as manifolds and classifying spaces of compact Lie groups. In this talk, I will provide a gentle and subjective introduction to the subject, and also indicate how it connects with objects such as moduli spaces of Riemann surfaces, automorphism groups of free groups, and finite groups of Lie type. |
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Mar 10 | Wed | Aaron Held (Imperial College) | Cosmology, Relativity and Gravitation |

Abstract:The recent wealth of experimental data from the LIGO/Virgo as well as from the EHT collaboration is fully consistent with GR. However, the true nature of the observed compact objects must involve some new physics (quantum or classical) to ameliorate the singularities present in the interior of the respective GR description. In the spirit of local EFTs, the talk will be based on the main assumption that the new physics, whatever its origin, is tied to local curvature scales. Based on this locality principle, I construct a new class of everywhere-regular, stationary spacetimes parameterized by a mass function in horizon-penetrating coordinates. This construction allows me to identify characteristic image features of the shadows of this class of regular black holes, in particular, in distinction to other models not following the locality principle. Moving on to dynamical spacetime evolution, still following the principles of local EFT, I will present first results on a fully non-linear but well-posed numerical simulation of (quadratic) higher-derivative gravity in the spherically-symmetric sector. |
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Mar 10 | Wed | Yannik Schüler | Algebraic Geometry Learning Seminar: Toric varieties |

Mar 4 | Thu | Erico L. Rempel (Aeronautics Institute of Technology - ITA, São José dos Campos, Brazil) | Plasma Dynamics Group |

Abstract:Dynamical systems, or chaos theory, has enjoyed huge success in the analysis of systems described by ordinary differential equations, such as nonlinear oscillators, chemical reactions, electronic devices, population dynamics, etc. Usually, in the dynamical systems approach, one is concerned with the identification of the basic building blocks of the system under investigation and how they interact with each other to produce the observable dynamics, as well as how they can be manipulated to produce a desired output, in the cases where control is pursued. Examples of those building blocks are unstable equilibrium and periodic solutions, nonattracting chaotic sets and their manifolds, which are special surfaces in the phase space that basically control the dynamics, guiding solutions in preferred directions. Despite its success in those areas, many still think that the theory has limited value when applied to fully developed turbulence, like observed in solar convection, due to the infinite dimension of the phase space. In this talk, we show that this difficulty can be overcome by adopting a Lagrangian reference frame, where the phase space for each fluid particle becomes three-dimensional and the building blocks of the turbulence can be efficiently extracted by appropriate numerical tools. We reveal how finite-time Lyapunov exponents, a traditional measure of chaos, can be used to detect attracting and repelling time-dependent manifolds that divide the fluid in regions with different behavior. These manifolds are shown to accurately mark the boundaries of granules in observational data from the photosfere. In addition, stagnation points and vortices detected as elliptical Lagrangian coherent structures complete the set of building blocks of the photospheric turbulence. Such structures are crucial for the trapping and transport of mass and energy in the solar plasma. |
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Mar 3 | Wed | Jasmin Matz (University of Copenhagen) | Pure Maths Colloquium |

Abstract:Suppose M is a closed Riemannian manifold with an orthonormal basis B of $L^2(M)$ consisting of Laplace eigenfunctions. Berry's Random Wave Conjecture tells us that under suitable conditions on M, in the high energy limit (ie, large Laplace eigenvalue) elements of B should roughly behave like random waves of corresponding wave number. A classical result of Shnirelman and others that $M$ is quantum ergodic if the geodesic flow on the cotangent bundle of $M$ is ergodic, can then be viewed as a special case of this conjecture. We now want to look at a level aspect, namely, instead of taking a fixed manifold and high energy eigenfunctions, we take a sequence of Benjamini-Schramm convergent compact Riemannian manifolds together with Laplace eigenfunctions f whose eigenvalue varies in short intervals. This perspective has been recently studied in the context of graphs by Anantharaman and Le Masson, and for hyperbolic surfaces and manifolds by Abert, Bergeron, Le Masson, and Sahlsten. In my talk I want to discuss joint work with F. Brumley in which we study this question in higher rank, namely sequences of compact quotients of $SL(n,R)/SO(n)$ for $n>2$. |
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Mar 3 | Wed | Valerio Lucarini (Reading) | Applied Mathematics Colloquium |

Abstract:Extreme events provide relevant insights on the dynamics of the climate system and their understanding is key to defining useful strategies for mitigating the impact of climate variability and climate change. Here we approach the study of persistent weather extremes using the lens of large deviation theory. We first consider a simplified yet Earth-like general circulation model of the atmosphere and numerically estimate large deviation rate functions of near-surface temperature in the mid-latitudes. We find that, after a re-normalisation based on the integrated auto-correlation, the rate function one obtains at a given latitude by looking, locally in space, at long time averages agrees with what is obtained, instead, by looking, locally in time, at large spatial averages along the latitude. This is a result of scale symmetry in the spatial-temporal turbulence and of the fact that advection is primarily zonal. This agreement hints at the universality of large deviations of the temperature field. Furthermore, we discover that the obtained rate function is able to describe spatially extended and temporally persistent heat waves or cold spells, if we consider temporal averages of spatial averages over intermediate spatial scales. We then extend our analysis by looking at the output of a state-of-the-art climate model and at observational data. We show how to const ruction in a mathematically rigorous way the climatology of persistent heatwaves and cold spells in some key target regions of the planet by constructing empirically the corresponding rate functions for the surface temperature, and we assess the impact of increasing CO2 concentration on such persistent anomalies. In particular, we can better understand the increasing hazard associated to heatwaves in a warmer climate. We show that two 2010 high impact events - summer Russian heatwave and winter Dzud in Mongolia - are associated with atmospheric patterns that are exceptional compared to the typical ones, but typical compared to the climatology of extreme events. Finally, we propose an approximate formula for describing large and persistent temperature fluctuations from easily accessible statistical properties. Refs: V. Galfi, V. Lucarini, Fingerprinting Heatwaves and Cold Spells and Assessing Their Response to Climate Change using Large Deviation Theory, PRL, in review (2020) V. Galfi, V. Lucarini, J. Wouters, A Large Deviation Theory-based Analysis of Heat Waves and Cold Spells in a Simplified Model of the General Circulation of the Atmosphere, J. Stat. Mech. 033404 doi: 10.1088/1742-5468/ab02e8 (2019) |
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Mar 3 | Wed | Elsa Teixeira (Sheffield) | Cosmology, Relativity and Gravitation |

Abstract:In this talk I will give an overview of interacting dark energy, with emphasis on disformal couplings and its cosmological implications. I will then focus on the general Dark D-Brane setting, for which the interaction in the dark sector arises naturally through the induced metric on a moving brane. In particular, I will discuss the background and linear perturbation equations in this setting, together with a numerical analysis, with brief connection to observational constraints. Testing gravity in the dark sector will be an exciting topic in the upcoming decade, with next-generation cosmological data probing gravitational phenomena in finer detail. |
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Mar 3 | Wed | Karoline Van Gemst | Algebraic Geometry Learning Seminar: Toric varieties |

Feb 25 | Thu | Suzana de Souza e Almeida Silva (Sheffield) | European Solar Physics Online Seminars (ESPOS) |

Abstract:We present the state-of-art detection method of three-dimensional vortices and apply it to realistic magneto-convections simulations performed by the MURaM code. The detected vortices extend from the photosphere to the low chromosphere, presenting similar behaviour at all height levels. The vortices concentrate the magnetic field, and thereby the plasma dynamics inside the vortex is considerably influenced by the Lorentz force. Rotational motions also perturb the magnetic field lines, but they lead to only slightly bent flux tubes as the magnetic field tension is too high for the vortex flow to significantly twist the magnetic lines. We find that twisted magnetic flux tubes are created by shear motions in regions where plasma-beta>1, regardless of the existence of flow vortices. |
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Feb 25 | Thu | Suzana de Souza e Almeida Silva (University of Sheffield, Plasma Dynamics Group (UK)) | SP2RC/ESPOS |

Abstract:We present the state-of-art detection method of three-dimensional vortices and apply it to realistic magneto-convections simulations performed by the MURaM code. The detected vortices extend from the photosphere to the low chromosphere, presenting similar behaviour at all height levels. The vortices concentrate the magnetic field, and thereby the plasma dynamics inside the vortex is considerably influenced by the Lorentz force. Rotational motions also perturb the magnetic field lines, but they lead to only slightly bent flux tubes as the magnetic field tension is too high for the vortex flow to significantly twist the magnetic lines. We find that twisted magnetic flux tubes are created by shear motions in regions where plasma-beta>1, regardless of the existence of flow vortices. |
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Feb 24 | Wed | Reinder Meinsma | Algebraic Geometry Learning Seminar: Toric varieties |

Feb 18 | Thu | Dr Huw Morgan (Aberystwyth University) | SP2RC seminar |

Abstract:Any remote measurement of the solar corona in white light (or other) wavelength is an integration of emission along an extended line of sight. Historically, most studies necessarily assumed an axi-symmetric distribution to the density, thus derived properties contained an inherent and unquantified uncertainty. From the SOHO era onwards, space-based coronagraphs (LASCO/SOHO, and COR/STEREO) make frequent, uninterrupted, and high-quality observations of the corona which allow estimates of the true density distribution using coronal rotational tomography (CRT). A recent breakthrough in CRT is revealing a new view of the corona which is gained directly from observation. For the first time, we can view long-term trends in the coronal rotation rate, find meaningul links between coronal and interplanetary density structures, and use estimated densities at a range of heights to constrain outflow velocity and acceleration. The density distributions provide a ground truth for model extrapolations of the photospheric magnetic field, and new empirical boundary conditions for solar wind models. Tentative evidence of the Parker spiral onset can be seen close to the Sun. The next step in CRT methods is the inclusion of a time-dependent density distribution: initial results show promising correlations with Parker Solar Probe measurements, and the discovery of large variations on daily timescales not associated with mass ejections. |
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Feb 18 | Thu | Mijie Shi (KU Leuven, Belgium) | Plasma Dynamics Group |

Abstract:In the quest to solve the long-standing coronal heating problem, it has been suggested that coronal loops could be heated by waves. Despite the accumulating observational evidence of the possible importance of coronal waves, still very few 3D MHD simulations exist that show significant heating by MHD waves. In this seminar, I will present our recent 3D coronal loop model heated by transverse waves against radiative cooling. The coronal loop is driven at the footpoint by transverse oscillations and subsequently the induced Kelvin-Helmholtz instability deforms the loop cross-section to a fully turbulent state. Wave energy is transferred to smaller scales where it is dissipated, overcoming the internal energy losses by radiation. These results open up a new avenue to address the coronal heating problem. |
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Feb 17 | Wed | Kang Li (KU Leuven) | Pure Maths Colloquium |

Abstract:Roughly speaking, a ghost operator is often an infinite matrix such that its matrix entries vanish at the infinity. This notion was introduced by Guoliang Yu in the study of the so-called coarse Baum-Connes conjecture. It is a very central topic in coarse geometry and operator algebras with applications to provide counterexamples to the coarse Baum–Connes conjecture, the existence of non-exact groups and the rigidity problem for Roe-type algebras. In this talk, we will visualize a class of ghost projections in terms of expanderish graphs. |
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Feb 17 | Wed | Daniele Oriti (LMU Munich) | Cosmology, Relativity and Gravitation |

Abstract:We overview recent results on the extraction of an effective cosmological dynamics from fundamental quantum gravity formalisms in which spacetime is not fundamental, focusing on so called tensorial group field theories (strictly related to lattice quantum gravity and loop quantum gravity). This line of research is inspired by the idea of our universe as a quantum gravity condensate, and at the same time realizes it concretely. We emphasize how reaching the desired objective requires addressing several outstanding issues in quantum gravity: identifying quantum states in the fundamental theory with a good geometric interpretation, performing some form of coarse graining of the fundamental dynamics, defining diffeomorphism invariant observables to express the resulting coarse grained dynamics in physically transparent language. We also discuss what the theory says about the fate of the big bang singularity at the beginning of our universe. |
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Feb 17 | Wed | Evgeny Shinder | Algebraic Geometry Learning Seminar: Toric varieties |

Feb 11 | Thu | Vasco Henriques (Rosseland Centre for Solar Physics, Norway) | European Solar Physics Online Seminars (ESPOS) |

Abstract:The chromosphere of the umbra of sunspots is a remarkably dynamic layer featuring extremely fine sub-arcsec structure. Such structures appear dark against enveloping umbral flashes, but also bright before or after a flash, other features still are bright throughout. Only recently did we start understanding such fine features and semi-empirical modelling is converging with simulations to provide insight, not only into such fine structure, but also into the umbral flash phenomenon itself. The observational evidence weighs overwhelmingly towards a strong corrugation of the umbra where the material in short dynamic fibrils over-extends in a column of upflowing material while the adjacent areas flash. The delayed small-scale umbral brightenings at the bottom of such columns are an out-of-phase flash where the late-stage downflowing column meets the upflowing under-layers. Recent inversions using NICOLE at both umbral flashes and small-scale brightenings result in a downflow over upflow stratification perfectly bridging the transition of downflowing fibrils to upflowing fibrils as well as red-shifted absorption cores to blue-shifted absorption cores in the broader surroundings. Locally, each inverted column is remarkably similar in velocity profile to those from forward modelling, provided the formation height of the observed Ca II 8542 line is slightly lower in the Sun than in the simulations. Conspicuously, resonant cavities naturally cause the upper downflowing layers to become visible in forward modelling and the top-layer downflows to last longer than otherwise. Open questions, and how these can be addressed by future observations, are briefly discussed. |
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Feb 11 | Thu | Vasco Henriques (Rosseland Centre for Solar Physics, Norway) | SP2RC/ESPOS |

Abstract:The chromosphere of the umbra of sunspots is a remarkably dynamic layer featuring extremely fine sub-arcsec structure. Such structures appear dark against enveloping umbral flashes, but also bright before or after a flash, other features still are bright throughout. Only recently did we start understanding such fine features and semi-empirical modelling is converging with simulations to provide insight, not only into such fine structure, but also into the umbral flash phenomenon itself. The observational evidence weighs overwhelmingly towards a strong corrugation of the umbra where the material in short dynamic fibrils over-extends in a column of upflowing material while the adjacent areas flash. The delayed small-scale umbral brightenings at the bottom of such columns are an out-of-phase flash where the late-stage downflowing column meets the upflowing under-layers. Recent inversions using NICOLE at both umbral flashes and small-scale brightenings result in a downflow over upflow stratification perfectly bridging the transition of downflowing fibrils to upflowing fibrils as well as red-shifted absorption cores to blue-shifted absorption cores in the broader surroundings. Locally, each inverted column is remarkably similar in velocity profile to those from forward modelling, provided the formation height of the observed Ca II 8542 line is slightly lower in the Sun than in the simulations. Conspicuously, resonant cavities naturally cause the upper downflowing layers to become visible in forward modelling and the top-layer downflows to last longer than otherwise. Open questions, and how these can be addressed by future observations, are briefly discussed. |
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Feb 10 | Wed | Kevin Painter (Politecnico di Torino) | Applied Mathematics Colloquium |

Abstract:The formation of swarms, schools, flocks, herds, aggregates etc is a classical example of self-organisation, with the benefits of forming a high density group ranging from efficient migration to higher fecundity. Often, groups form through a mechanism of chemical signalling between population members, an evolutionary ancient communication used by both microscopic and macroscopic species. Populations in fluid environments, though, must contend with complex and turbulent flows, potentially detrimental (e.g. splitting up groups) or beneficial (e.g. coalescing individuals) to the formation and maintenance of a group. As a counter to flow, rheotaxis describes a behaviour in which individuals orient their body axis with respect to the current and is observed in both unicellular and multicellular organisms . Here we investigate the extent to which rheotaxis and flow impact on chemically-mediated aggregation, revealing these can impact both negatively and positively according to the population state and flow conditions. A hypothesised density-dependent rheotaxis appears capable of optimising group formation and maintenance, exploiting the positive benefits from each of flow and rheotaxis. The results are discussed in the context of broadcast swarming phenomena in marine invertebrates. |
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Feb 10 | Wed | Luke Hart (Manchester) | Cosmology, Relativity and Gravitation |

Abstract:Cosmological recombination has been widely regarded a solid pillar of understanding the cosmic microwave background (CMB) and its anisotropies. For many years, the questions have been answered over the accuracy of these calculations due to exceptional codes as CosmoRec and HyRec as well as numerous publications on the intricate atomic processes. However, the era that dawned the formation of hydrogen and helium atoms has still given us brilliant insights into exotic physics as well as tribalistic disputes in the various pockets of modern cosmology. In this talk, we will briefly recap the physics of recombination before highlighting extensions to the standard model (parametric and non-parametric) that affect the surface of last scattering. Finally, we will look to the future probes that provide a direct, spectral handprint of the atomic transitions in hydrogen and helium: the recombination radiation. Here we will conclude with the feasibility of studying these lines with prospective missions such as SuperPIXIE, Voyage 2050 and what happens when the exotic physics modifications that we can test with the CMB anisotropies are propagated through to the SEDs from recombination. |
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Feb 10 | Wed | Paul Johnson | Algebraic Geometry Learning Seminar: Toric varieties |

Feb 5 | Fri | Dr. Sijie Yu (Center for Solar-Terrestrial Research, New Jersey Institute of Technology) | SP2RC seminar |

Abstract:Thanks to recent advances in radio interferometric instrumentation, we've entered a new era of solar radio observations---broadband dynamic imaging spectroscopy. In this talk, I will first introduce the history of solar radio observations based on either total-power (integrated over the Sun) dynamic spectral measurements or imaging at a few discrete frequencies, then review some recent progress based on dynamic imaging spectroscopy over a wide frequency range that has placed us in a strong position to make revolutionary breakthroughs in understanding high-energy processes in the solar corona. Future perspectives will also be briefly discussed. |
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Jan 28 | Thu | (University of St Andrews, Solar and Magnetospheric Theory Group (UK)) | SP2RC/ESPOS |

Jan 28 | Thu | Ben Snow (University of Exeter) | European Solar Physics Online Seminars (ESPOS) |

Abstract:Shocks are a universal feature of warm plasma environments, such as the lower solar atmosphere and molecular clouds, which consist of both ionised and neutral species. Including partial ionisation leads to the existence of a finite width for shocks, where the ionised and neutral species decouple and recouple. As such, drift velocities exist within the shock that lead to frictional heating between the two species, in addition to adiabatic temperature changes across the shock. The local temperature enhancements within the shock alter the recombination and ionisation rates and hence change the composition of the plasma. We study the role of collisional ionisation and recombination in slow-mode partially ionised shocks. In particular, we incorporate the ionisation potential energy loss and analyse the consequences of having a non-conservative energy equation. A semi-analytical approach is used to determine the possible equilibrium shock jumps for a two-fluid model with ionisation, recombination, ionisation potential, and arbitrary heating. Two-fluid numerical simulations are performed using the (PIP) code. Results are compared to the magnetohydrodynamic (MHD) model and the semi-analytic solution. Accounting for ionisation, recombination, and ionisation potential significantly alters the behaviour of shocks in both substructure and post-shock regions. In particular, for a given temperature, equilibrium can only exist for specific densities due to the radiative losses needing to be balanced by the heating function. A consequence of the ionisation potential is that a compressional shock will lead to a reduction in temperature in the post-shock region, rather than the increase seen for MHD. The numerical simulations pair well with the derived analytic model for shock velocities. |
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Jan 27 | Wed | Theo Torres Vicente (Nottingham) | Cosmology, Relativity and Gravitation |

Abstract:In this talk, we consider the electromagnetic radiation-reaction/self-force process for a charged particle orbiting a rotating black hole. We will present and complement the existing results for the scalar and gravitational cases, to give a full picture of integer spins in the Kerr spacetime. We restrict ourselves to the case of circular orbits and we will compute the dissipative and conservative components of the electromagnetic self-force numerically, by solving the inhomogeneous Teukolsky equations using the BHperturbation toolkit. The results will be compared to the scalar and gravitational cases found in the literature. |
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Jan 21 | Thu | Professor Valery M Nakariakov (Centre for Fusion, Space & Astrophysics, University of Warwick, United Kingdom) | SP2RC seminar |

Abstract:Standing transverse oscillations of the plasma loops of the solar corona have been intensively studied for the last 20 years as a tool for the diagnostics of the coronal magnetic field. Those oscillations are confidently interpreted as standing fast magnetoacoustic kink modes of the plasma non-uniformities. Statistical analysis demonstrates that, in the majority of cases, the oscillations are excited by a mechanical displacement of the loop from an equilibrium by a low coronal eruption. Standing kink oscillations are observed to operate in two regimes: rapidly decaying large amplitude oscillations and undamped small amplitude oscillations. In both these regimes, different loops oscillate with different periods that scale with the oscillating loop length. The oscillation amplitude does not show dependence on the loop length or the oscillation period. In the decayless regime the damping should be compensated by energy supply which allows the loop to perform almost monochromatic oscillations with almost constant amplitude and phase. We developed a low-dimensional model explaining the undamped kink oscillations as a self-oscillatory process caused by the effect of negative friction, which is analogous to producing a tune by moving a bow across a violin string. The period of self-oscillations is determined by the frequency of the kink mode. The ubiquity of decayless kink oscillations makes them an excellent tool for MHD seismology, in particular, for probing free magnetic energy in preflaring active regions. |
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Jan 14 | Thu | Sudheer K. Mishra (Indian Institute of Technology, BHU, India) | European Solar Physics Online Seminars (ESPOS) |

Abstract:Using multi-wavelength imaging observation obtained from the Atmospheric Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO), we study the evolution of Kelvin-Helmholtz (K-H) instability in a fan-spine magnetic topology. This fan-spine configuration is situated near the Active Region 12297 and is rooted in a nearby sunspot. The two layers of the cool plasma flows lift up from the fan plane in parallel and interact with each other at the maximum height of the elongated spine in the lower corona. The first layer of the plasma flow (F1) moving with a slow velocity (5 km/s) reflected from the spine’s field lines. Subsequently second layer of plasma flow (F2) with impulsive velocity (114-144 km/s) interacts with the first layer at the maximum height and generating the shear motion , which is responsible for the evolution of the Kelvin-Helmholtz instability inside the elongated spine. The amplitude and characteristics wavelength of the K-H unstable vortices increases, which satisfy the linear growing mode of this instability. Using linear stability theory of the K-H instability, we calculate the Alfvén velocity in the lower layer. We conjecture that the estimated shearing velocity is higher than the estimated the Alfvén velocity in the second denser layer, which also satisfies the classical criterion of K-H instability. The fan-spine configuration possesses magnetic field and sheared velocity component, we estimate the parametric constant [Λ≥1] which confirms that the velocity shear dominates and the linear phase of the K-H instability is evolved. The present observation indicate that in the presence of complex magnetic field structuring and plasma flows, the K-H instability evolve in the fan-spine configuration may evolve the rapid heating, and connectivity changes may occur due to the fragmentation via the K-H instability. It also act as a rapid mechanism to transfer the mass and energy release between two distinct regions separated by the fan-spine configuration. |
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Jan 14 | Thu | Sudheer K. Mishra (Indian Institute of Technology, BHU, India) | SP2RC/ESPOS |

Abstract:Using multi-wavelength imaging observation obtained from the Atmospheric Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO), we study the evolution of Kelvin-Helmholtz (K-H) instability in a fan-spine magnetic topology. This fan-spine configuration is situated near the Active Region 12297 and is rooted in a nearby sunspot. The two layers of the cool plasma flows lift up from the fan plane in parallel and interact with each other at the maximum height of the elongated spine in the lower corona. The first layer of the plasma flow (F1) moving with a slow velocity (5 km/s) reflected from the spine’s field lines. Subsequently second layer of plasma flow (F2) with impulsive velocity (114-144 km/s) interacts with the first layer at the maximum height and generating the shear motion , which is responsible for the evolution of the Kelvin-Helmholtz instability inside the elongated spine. The amplitude and characteristics wavelength of the K-H unstable vortices increases, which satisfy the linear growing mode of this instability. Using linear stability theory of the K-H instability, we calculate the Alfvén velocity in the lower layer. We conjecture that the estimated shearing velocity is higher than the estimated the Alfvén velocity in the second denser layer, which also satisfies the classical criterion of K-H instability. The fan-spine configuration possesses magnetic field and sheared velocity component, we estimate the parametric constant [Λ≥1] which confirms that the velocity shear dominates and the linear phase of the K-H instability is evolved. The present observation indicate that in the presence of complex magnetic field structuring and plasma flows, the K-H instability evolve in the fan-spine configuration may evolve the rapid heating, and connectivity changes may occur due to the fragmentation via the K-H instability. It also act as a rapid mechanism to transfer the mass and energy release between two distinct regions separated by the fan-spine configuration. |
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