20200220  Thu  John Armstrong (University of Glasgow)  SP2RC seminar 
10:00  K14  ESPOS: Learning to Invert Solar Flares with RADYN Physics  
Abstract: During a solar flare, it is believed that reconnection takes place in the corona followed by fast energy transport to the chromosphere. The resulting intense heating strongly disturbs the chromospheric structure and induces complex radiation hydrodynamic effects. Interpreting the physics of the flaring solar atmosphere is one of the most challenging tasks in solar physics. We present a novel deep learning approach, an invertible neural network, to understanding the chromospheric physics of a flaring solar atmosphere via the inversion of observed solar line profiles in Hα and Ca II λ8542. The network is trained using flare simulations from the 1D radiation hydrodynamic code RADYN as the expected atmosphere and line profile. This model is then applied to whole images from an observation of an M1.1 solar flare taken with the Swedish 1 m Solar Telescope/CRisp Imaging SpectroPolarimeter instrument. The inverted atmospheres obtained from observations provide physical information on the electron number density, temperature and bulk velocity flow of the plasma throughout the solar atmosphere ranging in height from 0 to 10 Mm. Our method can invert a 1k x 1k fieldofview in approximately 30 minutes and we show results from the whole image inversions and error calculations on the inversions. Furthermore, we delve into the mammoth task of analysing the wealth of data we have accumulated through these inversions. 

20200220  Thu  Niall Taggart (Queen's University Belfast)  Topology seminar 
16:00  J11  Comparing functor calculi  
Abstract: Functor calculus is a categorification of Taylor's Theorem from differential calculus. Given a functor, one can assign a sequence of polynomial approximations, which assemble into a Taylor tower, similar to the Taylor series from differential calculus. In this talk, I will introduce several variants of functor calculus together with their associated model categories, and demonstrate how one may compare these calculi both on a pointset and model categorical level. 

20200219  Wed  Jon Keating (Univerisities of Bristol and Oxford)  Pure Maths Colloquium 
14:00  J11  Primes and Polynomials in Short Intervals  
Abstract: I will discuss a classical problem in Number Theory concerning the distribution of primes in short intervals and explain how an analogue of this problem involving polynomials can be solved by evaluating certain matrix integrals. I will also explain a generalisation to other arithmetic questions with a similar flavour. 

20200219  Wed  Mitchell Berger (Exeter)  Applied Mathematics Colloquium 
14:00  Hicks, LT 9  Localized measures of magnetic helicity and helicity flux  
Abstract: Magnetic helicity is an ideal MHD invariant; it measures geometric and topological properties of a magnetic field. The talk will begin by reviewing helicity and its mathematical properties. It can be decomposed in several ways (for example, self and mutual helicity, Fourier spectra, field line helicity, linking, twist, and writhe). The talk will also review methods of measuring the helicity flux. Applications in solar and stellar astrophysics will be reviewed. I will then discuss some new developments in measuring localized concentrations of helicity in a welldefined, gauge invariant manner. One method involves absolute measures of helicity (rather than relative to a vacuum field), based on generalizations of the ToroidalPoloidal decomposition in spherical geometries. A second method involves employing wavelets and multiresolution analysis 

20200219  Wed  Leong Khim Wong (Cambridge)  Cosmology, Relativity and Gravitation 
15:00  J11, Hicks  Dynamics of black holes with induced scalar charges  
Abstract: While stringent nohair theorems forbid isolated black holes from possessing permanent moments beyond their mass, spin and electric charge, the presence of an external scalar field can endow a black hole with additional multipole moments even when the field is minimally coupled to gravity. Recent advancements in effective field theory (EFT) techniques make it possible to study how these induced scalar multipoles affect the dynamics of black holes in binary systems. I will present an overview of the EFT approach and will discuss some interesting phenomena that arise due to this effect, including a novel guise of superradiance. 

20200219  Wed  Robin Stephenson (Sheffield)  Probability 
15:30  LT7  
20200219  Wed  Sadiah Zahoor (Sheffield)  ShEAF: postgraduate pure maths seminar 
16:00  J11 Hicks  Modular forms and their congruences  
Abstract: Starting with a unit disc embedded inside a complex plane, we act on it by a group of symmetries. Our primary interest lies in holomorphic functions defined over this disc which are invariant under this action. These functions are called modular forms. Modular forms show bizarre symmetries due to the remarkable way they transform. I shall begin with an informal introduction to modular forms building up an insight to my current research project dealing with congruences between modular forms and similar objects. 

20200219  Wed  Carina Geldhauser (Sheffield)  Probability 
16:15  LT7  
20200218  Tue  William Elbaek Mistegaard (IST Vienna)  Algebra / Algebraic Geometry seminar 
12:00  F24  Quantum modularity  
Abstract: Lawrence and Zagier have shown that for a Brieskorn homology sphere there exists a power series with integer coefficients and convergent inside the unit disc, such that the ReshetikhinTuraev invariant of this threemanifold is the radial limit of that power series, as the parameter tends to a certain root of unity. This power series have interesting modularity properties. Subsequent work by Gukov, Putrov, Pei and Vafa aimed at generalizing this phenomena to other threemanifolds, leading them to the invention of a power series invariants of threemanifolds, which is now known as the socalled Zedhat invariant. These invariants are conjectured to be examples of (higher depth) quantum modular forms, and this is known to be true for some families of threemanifolds. In this talk we present the following result, which is joint with Jørgen E. Andersen: For a Seifert fibered homology sphere, the zedhat invariant can be computed via BorelLaplace resummation of the ReshetikhinTuraev invariant, as proposed (and proven in examples with three singular fibers) by Gukov, Marino and Putrov. 

20200213  Thu  Ines Krissaane (Sheffield)  Statistics Seminar 
14:00  LT 6  Robustness of Variational Inference under Model Misspecification  
Abstract: In many complex scientific problems, we deal with a model that is misspecified relative to the data generating process, in the sense that there is no parameter setting that allows the model to perfectly replicate the data. We will review the recent paper Generalized Variational Inference (https://arxiv.org/pdf/1904.02063.pdf) and expose arguments for using VI under model misspecification. As an application, we will focus on the Hodgkin Huxley model of action potentials, and infer parameters from uncertain experimental measurements using a variational auto encoder method. 

20200213  Thu  Severin Bunk (Hamburg University)  Topology seminar 
16:00  J11  Smooth OpenClosed Functorial Field Theories from BFields and DBranes  
Abstract: Bundle gerbes are a categorification of line bundles, and their connections model the Bfield in string theory. In this talk we show how bundle gerbes with connection and their Dbranes give rise to smooth openclosed field theories (OCFFTs) on a manifold M in a functorial manner. The key ingredients for this construction are the 2categorical structure of bundle gerbes, the transgression of gerbes and Dbranes to spaces of loops and paths in M, as well as a formalisation of the WessZumino amplitude on surfaces with corners. After giving an overview of these concepts, we will explain how they combine to yield the desired smooth OCFFTs on M. This is based on an ongoing collaboration with Konrad Waldorf. 

20200213  Thu  Shahin Jafarzadeh (Rosseland Centre for Solar Physics, University of Oslo)  Plasma Dynamics Group 
16:00  Room F28 (Hicks Building)  Magnetoacoustic Waves in the Lower Solar Atmosphere at High Resolution  
Abstract: Fibrillar structures of different appearances and/or properties have ubiquitously been observed throughout the Sun's chromosphere. They are often thought to map the magnetic fields, and are likely rooted in smallscale magnetic elements in the solar photosphere. Here, we present properties of magnetohydrodynamicwave dynamics in various fibrillar structures as well as in small magnetic elements in the low solar atmosphere, at highspatial resolution, from the SUNRISE balloonborne observatory as well as the Swedish Solar Telescope. Our analysis reveals the prevalence of kink and sausage waves in both types of magnetic structures, propagating at similar high frequencies. The estimated energy flux carried by the observed waves is marginally enough to heat the chromosphere (and perhaps the corona). Furthermore, such waves are compared with temperature fluctuations in the fibrils from hightemporal resolution observations with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Interface Region Imaging Spectrograph (IRIS) explorer, simultaneously observed at several millimetre and ultraviolet bands of, e.g., ALMA 1.3 mm as well as IRIS Mg II h & k, Si IV, and C II spectral lines, from which, physical properties of the fibrillar structures are also discussed. 

20200212  Wed  Lyuba Chumakova (Edinburgh)  Applied Mathematics Colloquium 
14:00  Hicks, LT 9  Why are we not falling apart: cytoskeleton selforganization and some results on intracellular transport  
Abstract: For cells and organism to function correctly, cellular components must be robustly delivered to their biologically relevant location. This is achieved through intracellular transport, where vesicles and organelles are transported like cargo via cars (molecular motors) along highways (the microtubule cytoskeleton). Failure of this process can result in pathologies. In this talk I will present a series of studies of microtubule selforganisation and the resulting intracellular transport in epithelium, one of the four fundamental tissue types in all animals. In particular, I will address the questions of the selforganisation of the microtubule network, and how to determine the molecular motor type from the distribution of the cargo it distributes. This will be shown with stochastic simulations, in vivo experiments, and simple probabilistic models, which uncover the mathematical basis of the underlying biological phenomena 

20200212  Wed  Chris Fewster (University of York)  Cosmology, Relativity and Gravitation 
15:00  J11, Hicks  Singularity theorems with weakened energy hypotheses inspired by QFT  
Abstract: The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of these results under weakened hypotheses, by considering the Riccati inequality obtained from Raychaudhuri's equation. Here, we give a different derivation that avoids the Raychaudhuri equation but instead makes use of index form methods. We show how our results improve over existing methods and how they can be applied to hypotheses inspired by Quantum Energy Inequalities. In this last case, we make quantitative estimates of the initial conditions required for our singularity theorems to apply. The talk will be largely based on arXiv:1907.13604 (joint work with E.A. Kontou) and will introduce index form methods from the start. 

20200206  Thu  Andrés Adrover González (University of the Balearic Islands, Spain)  SP2RC seminar 
10:00  LT 11  ESPOS: Threedimensional simulations of oscillations in solar prominences  
Abstract: We numerically investigate the periodicity and damping of transverse and longitudinal oscillations in a 3D model of a curtainshaped prominence. We carried out a set of numerical simulations of vertical, transverse and longitudinal oscillations with the highorder finitedifference Pencil Code. We solved the ideal magnetohydrodynamic (MHD) equations for a wide range of parameters, including the width and density of the prominence, and the magnetic field strength (B) of the solar corona. We studied the periodicity and attenuation of the induced oscillations. We found that longitudinal oscillations can be fit with the pendulum model, whose restoring force is the field aligned component of gravity, but other mechanisms such as pressure gradients may contribute to the movement. On the other hand, transverse oscillations are subject to magnetic forces. The analysis of the parametric survey shows, in agreement with observational studies, that the oscillation period (P) increases with the prominence width. For transverse oscillations we obtained that P increases with density and decreases with B. For longitudinal oscillations we also found that P increases with density, but there are no variations with B. The attenuation of transverse oscillations was investigated by analysing the velocity distribution and computing the Alfvén continuum modes. We conclude that resonant absorption is the mean cause. Damping of longitudinal oscillations is due to some kind of shear numerical viscosity. 

20200205  Wed  Axel Polaczek (University of Sheffield)  Cosmology, Relativity and Gravitation 
15:00  J11, Hicks  Quantum Gravity and Cosmology  
Abstract: In this talk I will give an overview of quantum gravity with an emphasis on approaches that involve discretisations of spacetime. I will then focus on group field theory (GFT) which is an approach aiming to describe the dynamics of the microscopic degrees of freedom. In particular, I will discuss cosmology in the context of GFT, where one of the main results is the resolution of the big bang singularity. 

20200130  Thu  Kento Osuga (University of Sheffield)  Cosmology, Relativity and Gravitation 
15:00  J11, Hicks  Topological Recursion and Supersymmetry  
Abstract: Topological recursion is an abstract recursive formalism which was originally introduced to solve matrix models to all order in the large N expansion. Somewhat surprisingly, however, topological recursion has its own life beyond matrix models and its applications appear in both physics and mathematics such as 2d quantum gravity and GromovWitten invariants. Then an interesting question arises: does a similar story hold with supersymmetry? In this talk, I will first review the notion of topological recursion and briefly explain how it can be used to solve matrix models. I will then introduce a supersymmetric analogue of matrix models called supereigenvalue models and discuss their recursive structure. This is a joint work with Vincent Bouchard. 

20200128  Tue  Helge Ruddat (Johannes Gutenberg University Mainz)  Algebra / Algebraic Geometry seminar 
12:00  J11  Smoothing toroidal crossing varieties  
Abstract: Friedman and KawamataNamikawa studied smoothability of normal crossing varieties. I present the proof of a significantly more general smoothing result that also works for toroidal crossing spaces and relates to work on mirror symmetry by GrossSiebert and ChanLeungMa. The key technologies are the construction of log structures, a proof of a degeneration of the log Hodge to de Rham spectral sequence as well as deformation theory governed by Gerstenhaber algebras. This project is joint with Simon Felten and Matej Filip. 

20200124  Fri  Fiona Turner & Maram Alossaimi (Sheffield)  Postgraduate seminars 
16:00  J11 Hicks  What can Bayesian methodology tell us about past ice sheet changes? (Fiona Turner)
Poisson algebra (Maram Alossaimi) 

Abstract: What can Bayesian methodology tell us about past ice sheet changes? Ice sheet modellers and palaeoclimatologists have been reconstructing past global ice sheets for several decades. However, despite increasingly detailed models and more proxy data, there is still a large amount of uncertainty around what the planet looked like in previous ice ages. This is especially relevant for the Last Glacial Maximum (LGM, 21Ka); as the most recent cold period in the glacial cycle, understanding how much the ice sheets have changed since then helps us to understand how they adapt to changing climates. In my talk I will present the work I have been doing on using Bayesian methods to reduce uncertainty around the Antarctic ice sheets at the LGM. Using previous reconstructions, the climate model HadCM3 and proxy data collected form ice cores, I have built a probability distribution of the ice sheet and compared it to our prior estimates. Poisson algebra The concept of Poisson algebra comes from defining a bilinear product $\{\cdot,\cdot\}$ on $\mathbb{K}$algebra in which $\mathbb{K}$ is a field, to bring a new noncommutative structure. I will give some definitions, examples and the main Lemma (Oh, 2006) in our research. In the end, if there is time I will introduce the new Poisson algebra class A. 

20200123  Thu  Sudheer K. Mishra (Department of Physics, Indian Institute of Technology (BHU), Varanasi, India)  SP2RC seminar 
10:00  LT10, Hicks Building  ESPOS: Magnetic Rayleigh–Taylor Unstable Plumes and Hybrid KHRT Instability into a Looplike Eruptive Prominence  
Abstract: The magnetic Rayleigh–Taylor instability is a fundamental MHD instability and recent observations show that this instability develops in the solar prominences. We analyze the observations from Solar Dynamic Observatory/Atmospheric Imaging Assembly of a MRT unstable looplike prominence. Initially, some smallscale perturbations are developed horizontally and vertically at the prominencecavity interface. These perturbations are associated with the hot and low dense coronal plasma as compared to the surrounding prominence. The interface supports magnetothermal convection process, which acts as a buoyancy to launch the hot and low denser plumes (P1 and P2) propagating with the speed of 35–46 km s1 in the overlying prominence. The selfsimilar plume formation initially shows the growth of a linear MRTunstable plume (P1), and thereafter the evolution of a nonlinear singlemode MRTunstable second plume (P2). A differential emission measure analysis shows that plumes are less denser and hotter than the prominence. We have estimated the observational growth rate for both the plumes as 1.32±0.29×10−3 s−1 and 1.48±0.29×10^−3 s^−1, respectively, which are comparable to the estimated theoretical growth rate (1.95×10^−3 s^−1). Later, these MRT unstable plumes get stabilize via formation of rolled (vortexlike) plasma structures at the prominencecavity interface in the downfalling plasma. These rolledplasma structures depict KelvinHelmholtz instability, which corresponds to the nonlinear phase of MRT instability. However, even after the full development of MRT instability, the overlying prominence is not erupted. Later, a RayleighTaylor unstable tangled plasma thread is evident in the rising segment of this prominence. This tangled thread is subjected to the compression between eruption site and overlying dense prominence at the interface. This compression initiates strong shear at the prominencecavity interface and causes KelvinHelmholtz vortexlike structures. Due to this shear motion, the plasma downfall is occurred at the right part of the prominence–cavity boundary. It triggers the characteristic KH unstable vortices and MRTunstable plasma bubbles propagating at different speeds and merging with each other. The shear motion and lateral plasma downfall may initiate hybrid KHRT instability there. 

20200115  Wed  Igor Sikora (Warwick)  ShEAF: postgraduate pure maths seminar 
16:00  J11 Hicks  Elmendorf's theorem  
Abstract: Elmendorf's theorem is an absolutely key result in the equivariant homotopy theory. It relates homotopy type of Gspaces with homotopy of its fixed points diagrams. During the talk I will state the theorem, discuss what actually a homotopy theory in some category is, discuss a little bit of model categories and eventually I may approach proving the theorem, but I cannot promise the latter right now. 
