# Seminars this semester

Series:

Sep 24 Thu Abhishek Rajhans (Inter-University Center for Astronomy and Astrophysics (IUCAA), Pune, India) European Solar Physics Online Seminars (ESPOS)
10:00 Zoom Forward modelling and energetics of Hi-C brightenings

Abstract:
The Solar coronal heating problem remains a persistent challenge in astrophysics. Parker postulated back in 1988 that the heating of corona should be dominated by small energy dissipation events, referred to as nanoflares. However, there have not yet been any confirmed observations of individual nanoflares. Hi-C reported unique bright points with energies ranging between log[E(ergs)] = 24-25. Those brightenings were also identified in AIA passbands. Here, I will describe 0-D hydrodynamical simulations to forward model these tiny brightenings, study their energetics, and discuss possible implications for coronal heating.

Sep 24 Thu Abhishek Rajhans (Inter-University Centre for Astronomy and Astrophysics, IUCAA (IN)) SP2RC/ESPOS
11:00 Zoom Forward modelling and energetics of Hi-C brightenings

Abstract:
The Solar coronal heating problem remains a persistent challenge in astrophysics. Parker postulated back in 1988 that the heating of corona should be dominated by small energy dissipation events, referred to as nanoflares. However, there have not yet been any confirmed observations of individual nanoflares. Hi-C reported unique bright points with energies ranging between log[E(ergs)] = 24-25. Those brightenings were also identified in AIA passbands. Here, I will describe 0-D hydrodynamical simulations to forward model these tiny brightenings, study their energetics, and discuss possible implications for coronal heating.

Sep 30 Wed Evgeny Shinder (Sheffield) Algebraic Geometry Learning Seminar
02:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 1/12: Basic invariants and examples

Sep 30 Wed Visakan Balakumar (Sheffield) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate Quantum superradiance on static black hole space-times

Abstract:
We study the quantum analogue of the classical process of superradiance for a massless charged scalar field on a charged black hole space-time. We show that an “in” vacuum state, which is devoid of particles at past null infinity, contains an outgoing flux of particles at future null infinity. This radiation is emitted in the superradiant modes only, and is nonthermal in nature.

Oct 1 Thu Rekha Jain (Sheffield) Plasma Dynamics Group
16:00 Meet Frequency power spectra of Alfvén waves in a solar coronal arcade: Discrete or Continuous?

Abstract:
In this talk I will present theoretically computed frequency power spectra for shear Alfvén waves excited in a solar coronal arcade. I investigate two separate perturbations, a cosine-modulated Gaussian perturbation and an impulsive driver. The arcade is assumed to consist of potential magnetic field lines embedded in stratified plasma. In principle, the nature of the frequency power spectra can constrain the size and the type of driver.

Oct 2 Fri Teimuraz Zaqarashvili (University of Graz, Austria) SP2RC seminar
13:00 Meet Rossby waves and solar activity variations

Abstract:
Recent progress in observations of Rossby-type waves on the Sun revived the interests towards the waves. Though the hydrodynamic Rossby waves are well studied in the Earth context, the ubiquitous existence of magnetic fields in the atmosphere/interior of the Sun requires to study the waves in magnetohydrodynamics. The talk will cover the recent direct observations of Rossby waves on the Sun, theoretical development of magneto-Rossby wave theory and the possible connection of the waves to observed long and short term variations in solar magnetic activity.

Oct 7 Wed Reinder Meinsma Algebraic Geometry Learning Seminar
02:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 2/12: Curves on surfaces, rational and algebraic equivalence of divisors

Oct 7 Wed Katy Clough (Oxford) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate Initial conditions for inflation

Abstract:
Inflation solves a number of problems in early universe cosmology but potentially introduces some new ones regarding how it was able to get started in the first place. In this talk I will explain these issues in the context of single field slow roll inflationary models, and discuss how they might restrict the phase space of initial conditions and early universe models that we consider valid. I will describe work I have done using numerical relativity to investigate the problem in the non-linear regime.

Oct 8 Thu Lucia Kleint (Leibniz Institute for Solar Physics (KIS), Germany)) European Solar Physics Online Seminars (ESPOS)
10:00 Zoom GREGOR - Optics Redesign, Updates, and First Images

Abstract:
GREGOR is Europe’s largest solar telescope. It has undergone significant upgrades and changes from 2018-2020 to improve the image quality, instrumentation, and operation. Particularly, a complete redesign of the optics laboratory was performed by KIS to obtain diffraction-limited images from the blue to the infrared. The new optics setup was completed while “trapped” on the mountain during the lockdown and we obtained first light images in July 2020. In this talk, I will summarize the most important updates, explain the new optics setup, and show the improved images.

Oct 8 Thu Lucia Kleint (Leibniz Institute for Solar Physics (KIS), Germany) SP2RC/ESPOS
10:00 Zoom GREGOR - Optics Redesign, Updates, and First Images

Abstract:
GREGOR is Europe’s largest solar telescope. It has undergone significant upgrades and changes from 2018-2020 to improve the image quality, instrumentation, and operation. Particularly, a complete redesign of the optics laboratory was performed by KIS to obtain diffraction-limited images from the blue to the infrared. The new optics setup was completed while “trapped” on the mountain during the lockdown and we obtained first light images in July 2020. In this talk, I will summarize the most important updates, explain the new optics setup, and show the improved images.

Oct 14 Wed Alberto Cobos Rabano (Sheffield) Algebraic Geometry Learning Seminar
02:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 3/12: Intersection theory on surfaces, adjunction formula

Oct 14 Wed Indira Chatterji (University of Nice) Pure Maths Colloquium
14:00 Meet Group ring conjectures and relative hyperbolicity

Abstract:
The idempotent conjecture is that there should be no idempotent in the group ring of a torsion-free group. I will discuss this conjecture, as well as associated conjectures in some geometric context, and will use them as an excuse to discuss hyperbolicity and introduce relative hyperbolicity, a context in which some of these conjectures are still open.

Oct 14 Wed Jose Cembranos (Complutense, Madrid) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate Disformal dark matter from brane-worlds

Abstract:
Scalar particles coupled to the Standard Model fields through a disformal coupling arise in different theories, such as massive gravity or brane-world models. We will review the main phenomenology associated with such particles. Distinctive disformal signatures could be measured at colliders and with astrophysical observations. The phenomenological relevance of the disformal coupling demands the introduction of a set of symmetries, which may ensure the stability of these new degrees of freedom. In such a case, they constitute natural dark matter candidates since they are generally massive and weakly coupled. We will illustrate these ideas by paying particular attention to the branon case, since these questions arise naturally in brane-world models with low tension, where they were first discussed.

Oct 15 Thu Prof. Robertus Erdelyi (University of Sheffield) SP2RC seminar
10:00 Zoom (Meeting ID: 953 3817 1418) UK-SOSS: Waves and oscillations in the solar atmosphere

Abstract:
Satellite and ground-based observations from e.g. SOHO, TRACE, STEREO, Hinode, SDO and IRIS to DST/ROSA, IBIS, CoMP, STT/CRISP have all provided a wealth of evidence of waves and oscillations present in a wide range of spatial and temporal scales of the magnetised solar atmosphere. Our understanding about localised solar structures has been considerably changed in light of these superb spatial and temporal resolution observations. However, MHD waves not only enable us to perform sub-resolution solar magneto-seismology (SMS) but are also potential candidates to carry and damp the observed non-thermal energy in localised MHD waveguides. First, we will briefly outline the basic recent developments in MHD wave theory focussing on linear MHD waves both in symmetric and asymmetric waveguides. This latter may be an important aspect for the fantastic kitty: DKIST. Next, we will concentrate on the role of the most frequently studied wave classes, including the mysterious Alfven, and magneto-acoustic sub-classes of kink and sausage waves. Finally, we will address how solar MHD waves, swirls and solar jet formation may be related. We will argue to unite MHD wave and jet theories and make efforts to develop a common modelling platform with solar applications. An example will be shown where prevalent swirls, in the form of Alfven pulses, propagate upwards through the solar atmosphere dragging with them jets and reach the chromospheric layers. We will argue why this maybe seen as an important step towards understanding better the heating problem of the solar atmosphere.

Oct 15 Thu George Haller (ETH Zurich (Switzerland)) Plasma Dynamics Group
13:00 Meet Objective material barriers to the transport of momentum and vorticity

Abstract:
I discuss a recent theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active (i.e., velocity-dependent) vector field, such as the linear momentum, the angular momentum or the vorticity, in three-dimensional unsteady flows. These diffusion barriers provide physics-based, observer-independent boundaries of dynamically active coherent structures. Instantaneous limits of these Lagrangian diffusion barriers mark objective Eulerian barriers to short-term active transport. I show how active diffusion barriers can be identified with active versions of Lagrangian coherent structure (LCS) diagnostics. In comparison to their passive counterparts, however, active LCS diagnostics require no significant fluid particle separation and hence provide substantially higher-resolved Lagrangian and Eulerian coherent structure boundaries from shorter velocity data sets. I illustrate these results on two-dimensional turbulence and three-dimensional wall-bounded turbulence.

Oct 20 Tue Haluk Sengun (Sheffield) Number Theory seminar
11:00 Google meet C*-algebras associated to locally compact groups and the Selberg trace formula

Abstract:
Given a locally compact group G, one can obtain C*-algebras by taking various completions of the convolution algebra of integrable functions on G. These C*-algebras sit in the intersection of representation theory, index theory and non-commutative geometry. In this talk, we will describe an identity, obtained in joint work with Bram Mesland (Leiden) and Hang Wang (Shanghai), that involves the K-groups of the C*-algebras of a semisimple Lie group G and of a cocompact lattice H in G. We will then argue that this identity is a K-theoretic analgoue of the celebrated Selberg trace formula. The talk is planned to be of expository nature.

Oct 20 Tue Alberto Cobos Rabano Algebraic Geometry Learning Seminar
14:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Alberaic Surfaces 4/12: Numerical equivalence, effective cone, numerical criterion for ampleness

Oct 21 Wed Atsushi Higuchi (York) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate The Hartle-Hawking vacuum state in the Schwinger-Keldysh formalism for interacting scalar field theory

Abstract:
Schwarzschild and de Sitter spacetimes are spacetimes with bifurcate Killing horizons. It is known that the preferred vacuum state (the Hartle-Hawking state) in quantum field theory in these spacetimes is a thermal state in the static patch. For example, it is the thermal state with the Hawking temperature outside the horizon in the Schwarzschild case. It is also accepted that this state is obtained by analytic continuation from the corresponding Euclidean theory. In this talk, I will make this statement more precise in the context of the Schwinger-Keldysh (or in-in) perturbation theory. (This is a joint work in progress with William C C de Lima.)

Oct 22 Thu Ricardo Gafeira (University of Coimbra, Portugal) European Solar Physics Online Seminars (ESPOS)
10:00 Zoom Modernization of the spectroheliograph of Coimbra

Abstract:
The details study of the solar activity and variability on long term data series is an important element on the understanding of the solar dynamics and evolution. In addition, their activity influences several aspects of our lives, such as climate, communications, energy, aviation, and many other fields, sustaining and threatening, simultaneously, our entire technologically-based way of life. Hence, it is paramount to secure the continuity of unbroken and self-consistent data series of solar observations and its study. The associated physical processes and structures on the Sun span over a wide range of values regarding their lifetimes, intensities, and spatial scales. Ideally, to study all these different structures in detail, we need facilities that allow us to observe the full solar disk and spectrum with very high spectral, spatial, and temporal resolutions. Unfortunately, due to technical limitations that cannot be done and there are clear trade-offs to deal with. Even today, elements like spatial resolution versus field of view (FoV), spectral coverage versus temporal resolution, observation of spectral lines in local or non-local thermodynamic equilibrium (depending on the science driver) are among the obstacles that scientists need to keep in mind as limitations for their work. State-of-the-art solar telescopes like the US American 4-meter telescope DKIST, the German GREGOR telescope, or the Solar Orbiter, plus the next generation facilities like the balloon borne SUNRISE III mission, or the future European Solar Telescope will observe the Sun with unprecedented spatial and spectral resolutions. Even though they will use the most advanced technology they do not cover all possible modes of observation. Some key aspects like small FoVs, in some cases limited number of spectral lines or the short lifetime of instruments are among those that some other types of instruments can cover. The spectroheliograph of OGAUC is one of the most durable solar instruments still operating. Having been upgraded only twice, one for new optics and another for digital image recording, it keeps daily observations since 1927. Until now this instrument has been used to study structures visible in the solar atmosphere from their intensity images at specific wavelengths, ignoring most of the visible spectral range. One of the main reasons for that is the lack of tools to extract more information from that type of observations that need to be analysed in Non-Local Thermodynamic Equilibrium (NLTE) regime. However, with the new generation of spectropolarimetric inversion codes, we are now able to invert NLTE spectral lines to extract information about the temperature, the velocity and the magnetic field vector. Such analysis is already possible with several of the aforementioned telescopes, but they do not cover all the possible observing modes. In this project, we propose to take advantage of the operating infrastructure of the OGAUC spectroheliograph and to upgrade it, improving its spectral resolution, adding other spectral regions of interest and increasing the spatial sampling and add polarimetric sensitivity. Due to its flexibility, long term run and set of observed spectral lines and polarimetric sensitivity it will be a competitive state of the art instrument competing with the other solar synoptic (full disk) ground-based spectroheliograph of its category in the. This upgrade, in combination with the new NLTE inversion codes and neural network techniques will allow us to probe at chromospheric and photospheric heights the solar temperature, velocity and magnetic field.

Oct 22 Thu Ricardo Gafeira (University of Coimbra (PT)) SP2RC/ESPOS
10:00 Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165) Modernization of the spectroheliograph of Coimbra

Abstract:
The details study of the solar activity and variability on long term data series is an important element on the understanding of the solar dynamics and evolution. In addition, their activity influences several aspects of our lives, such as climate, communications, energy, aviation, and many other fields, sustaining and threatening, simultaneously, our entire technologically-based way of life. Hence, it is paramount to secure the continuity of unbroken and self-consistent data series of solar observations and its study. The associated physical processes and structures on the Sun span over a wide range of values regarding their lifetimes, intensities, and spatial scales. Ideally, to study all these different structures in detail, we need facilities that allow us to observe the full solar disk and spectrum with very high spectral, spatial, and temporal resolutions. Unfortunately, due to technical limitations that cannot be done and there are clear trade-offs to deal with. Even today, elements like spatial resolution versus field of view (FoV), spectral coverage versus temporal resolution, observation of spectral lines in local or non-local thermodynamic equilibrium (depending on the science driver) are among the obstacles that scientists need to keep in mind as limitations for their work. State-of-the-art solar telescopes like the US American 4-meter telescope DKIST, the German GREGOR telescope, or the Solar Orbiter, plus the next generation facilities like the balloon borne SUNRISE III mission, or the future European Solar Telescope will observe the Sun with unprecedented spatial and spectral resolutions. Even though they will use the most advanced technology they do not cover all possible modes of observation. Some key aspects like small FoVs, in some cases limited number of spectral lines or the short lifetime of instruments are among those that some other types of instruments can cover. The spectroheliograph of OGAUC is one of the most durable solar instruments still operating. Having been upgraded only twice, one for new optics and another for digital image recording, it keeps daily observations since 1927. Until now this instrument has been used to study structures visible in the solar atmosphere from their intensity images at specific wavelengths, ignoring most of the visible spectral range. One of the main reasons for that is the lack of tools to extract more information from that type of observations that need to be analysed in Non-Local Thermodynamic Equilibrium (NLTE) regime. However, with the new generation of spectropolarimetric inversion codes, we are now able to invert NLTE spectral lines to extract information about the temperature, the velocity and the magnetic field vector. Such analysis is already possible with several of the aforementioned telescopes, but they do not cover all the possible observing modes. In this project, we propose to take advantage of the operating infrastructure of the OGAUC spectroheliograph and to upgrade it, improving its spectral resolution, adding other spectral regions of interest and increasing the spatial sampling and add polarimetric sensitivity. Due to its flexibility, long term run and set of observed spectral lines and polarimetric sensitivity it will be a competitive state of the art instrument competing with the other solar synoptic (full disk) ground-based spectroheliograph of its category in the. This upgrade, in combination with the new NLTE inversion codes and neural network techniques will allow us to probe at chromospheric and photospheric heights the solar temperature, velocity and magnetic field.

Oct 26 Mon Topology Reading Group
12:00 Blackboard collaborate String Topology: Chas-Sullivan loop product

Oct 27 Tue Abhishek Saha (Queen Mary) Number Theory seminar
11:00 Google meet The Manin constant and p-adic bounds on denominators of the Fourier coefficients of newforms at cusps

Abstract:
The Manin constant $c$ of an elliptic curve $E$ over $\mathbb{Q}$ is the nonzero integer that scales the differential $\omega_f$ determined by the normalized newform $f$ associated to $E$ into the pullback of a Néron differential under a minimal modular parametrization$\phi\colon X_0(N)_{\mathbb{Q}} \twoheadrightarrow E$. Manin conjectured that $c = \pm 1$ for optimal parametrizations. I will talk about recent work that makes progress towards this conjecture by establishing an integrality property of $\omega_f$ necessary for this conjecture to hold. Our result implies in particular that $c \mid \mathrm{deg}(\phi)$ under a minor assumption at $2$ and $3$ that is not needed for cube-free $N$ or for parametrizations by $X_1(N)_{\mathbb{Q}}$. We reduce the above results to $p$-adic bounds on denominators of the Fourier expansions of $f$ at all the cusps of $X_0(N)_{\mathbb{C}}$. We succeed in proving stronger bounds in the more general setup of newforms of general weight and levels by approaching the problem representation-theoretically. These idea is to study the $p$-adic valuations of the values of the Whittaker newform of $\mathrm{GL}_2$ over a nonarchimedean local field of characteristic 0, using techniques that were originally developed by me in the context of the analytic sup-norm problem. For local fields of odd residue charactertistic, this allows us to ultimately reduce to the classical facts about $p$-adic valuations of Gauss sums. To overcome obstacles at 2, we analyze nondihedral supercuspidal representations of $\mathrm{GL}_2 (\mathbb{Q}_2)$. This is joint work with K\k{e}stutis \v{C}esnavi\v{c}ius and Michael Neururer.

Oct 27 Tue George Moulantzikos Algebraic Geometry Learning Seminar
14:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 5/12: Birational maps, blow ups, contractions of (-1)-curves

Oct 28 Wed Clara Loeh (University of Regensburg) Pure Maths Colloquium
14:00 Meet Amenable covers

Abstract:
A cover of a space by open subsets is amenable if these subsets all induce amenable images on the level of the fundamental group. In analogy with the LS-category, one can ask how small of an amenable cover one can find for a given space. By Gromov's vanishing theorem, simplicial volume is an example of an obstruction against the existence of small amenable covers. In this talk, I will put this result into context and I will briefly sketch an alternative proof for the vanishing theorem (joint work with Roman Sauer).

Oct 28 Wed Harry Desmond (Oxford) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate Fifth force searches in galaxies

Abstract:
Fifth forces generically follow from new dynamical fields, and hence are ubiquitous in extensions to the standard model. Broad classes of Lagrangian exhibit "screening mechanisms" which hide the fifth force in high-density environments such as the Milky Way, while keeping it operative on larger scales. I will describe the search for fifth forces which act differently on different components of galaxies, e.g. through screening. First, I model the gravitational environments of the local Universe to determine the screening properties of real galaxies and the strength of the fifth-force field over space. I then use this information to forward-model two signals in galaxy morphology -- displacements of stars and gas and warping of stellar disks -- and hence infer fifth-force parameters with a Bayesian likelihood framework. Taking ~16,000 HI-cross-optical detections from the ALFALFA and SDSS surveys and ~4,000 galactic disk images from the Nasa Sloan Atlas, I set the strongest constraints to date on astrophysical fifth forces. Two particularly interesting applications are to f(R) and models such as coupled quintessence in which the fifth force acts only in the dark sector: for the former I require f_R0 < 1.4x10^-8 in the Hu-Sawicki model, and for the latter a fifth-force strength <10^-4 times that of gravity.

Oct 29 Thu Inigo Arregui (Instituto de Astrofisica de Canarias (Spain)) Plasma Dynamics Group
16:00 Meet Bayesian coronal seismology

Abstract:
Coronal seismology is based on the remote diagnostics of physical conditions in the solar corona by comparison between model predictions and observations of wave activity. Our lack of direct access to the physical system of interest makes information incomplete and uncertain so our conclusions are at best probabilities. Bayesian inference is increasingly being employed in the area, following a general trend in solar and astrophysical research. In this seminar, I first justify the use of a Bayesian probabilistic approach to seismology diagnostics and explain its philosophy and methodology. Then, I report on recent results that demonstrate its feasibility and advantage in applications to coronal loops, prominences and extended regions of the corona. To finish, I suggest other areas of current interest where the use of Bayesian methods could contribute to improve our understanding on the structure, dynamics and heating of the corona.

Oct 30 Fri Norbert Gyenge (University of Sheffield) SP2RC seminar
13:00 Meet Temporal Analysis in Solar Physics

Abstract:
This talk focuses on the latest tools and techniques of temporal analysis in solar physics. Performing a temporal analysis could be challenging because all the available commonly used tools, namely, Autocorrelation, Fourier-Transformation and Wavelet Analysis, have several advantages and disadvantages. The emphasis of this talk will be on choosing the proper technique for investigation, initialising raw data, choosing a noise profile to create significance intervals and interpreting the results. All these steps will be demonstrated by active research, focusing on the oscillatory behaviour of SDO Intensity images through all the available wavelengths.

Nov 2 Mon Topology Reading Group
12:00 Blackboard collaborate String Topology: Batalin-Vilkovisky Structure and String Bracket

Nov 3 Tue Pol van Hoften (KCL) Number Theory seminar
11:00 Google meet On the discrete part of the Hecke-orbit conjecture

Abstract:
The Hecke-orbit conjecture, proposed by Chai and Oort, gives strong restrictions on the shape of Hecke-invariant subvarieties of special fibers of Shimura varieties. It consists of a continuous part, which predicts the dimensions of Hecke orbits, and a discrete part, which predicts that certain subvarieties called central leaves are irreducible. In this talk I will give an introduction to the discrete part of the Hecke orbit conjecture, focussing mostly on explicit low-dimensional examples, and discuss a geometric proof for Shimura varieties of Hodge type. The main idea is to use the geometry of Shimura varieties with bad reduction to prove the irreducibility of "distinguished" central leaves, and to deduce the general case using the almost-product structure of Newton strata.

Nov 3 Tue Yannik Schuler Algebraic Geometry Learning Seminar
14:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 6/12: Ruled surfaces

Nov 4 Wed Ulrich Pennig (University of Cardiff) Pure Maths Colloquium
14:00 Meet Bundles of Algebras - Dixmier-Douady Theory and Beyond

Abstract:
Intuitively a bundle of algebras is a collection of algebras continuously parametrised by a topological space. In operator algebras there are (at least) two different definitions that make this intuition precise: Continuous C(X)-algebras provide a flexible analytic point of view, while locally trivial C*-algebra bundles allow a classification via homotopy theory. The section algebra of a bundle in the topological sense is a C(X)-algebra, but the converse is not true. In this talk I will compare these two notions using the classical work of Dixmier and Douady on bundles with fibres isomorphic to the compacts as a guideline. I will then explain joint work with Marius Dadarlat, in which we showed that the theorems of Dixmier and Douady can be generalized to bundles with fibers isomorphic to stabilized strongly self-absorbing C*-algebras. An important feature of the theory is the appearance of higher analogues of the Dixmier-Douady class.

Nov 4 Wed Jean-Luc Lehners (Max-Planck-Institute, Potsdam) Applied Mathematics Colloquium
14:00 Meet Path integrals, black holes and the beginning of the universe

Abstract:
Quantum gravity promises to unveil the deepest mysteries about space, time and matter. But that is for the far future. In this talk, I will review recent progress in a less ambitious setting, namely in semi-classical gravity, which may be thought of as the leading order in hbar approximation to quantum gravity. I will discuss techniques for evaluating gravitational path integrals, both in the context of black holes and regarding the implications for the Hartle-Hawking no-boundary proposal. This not only shows a close relation between black holes and the big bang, but also provides clues for an effective description of the quantum origin of the universe.

Nov 5 Thu Florian Regnault (Institut d'Astrophysique Spatiale, IAS, France) European Solar Physics Online Seminars (ESPOS)
10:00 Zoom 20 years of ACE data: how superposed epoch analysis reveal generic features in interplanetary CME profiles

Abstract:
Interplanetary Coronal Mass Ejections (ICMEs) result from the reconfiguration of magnetic fields in our star’s atmosphere. These large-scale magnetized structures propagate in the interplanetary medium where they can be probed by spacecraft. Depending on their speed, ICMEs may accumulate enough solar wind plasma to form a turbulent sheath ahead of them. They therefore consist of two main substructures : a sheath and a magnetic ejecta (ME). The magnetic ejecta is the main body of an ICME where the magnetic field is more intense and with less variance than that of the ambient solar wind. We present a statistical study using the superposed epoch analysis technique on a catalog of around 400 ICMEs where we consider the profiles of the physical parameters of the ICMEs (the magnetic field intensity, the speed, temperature, …) seen at 1 AU by the ACE spacecraft. We analyze the effects of the relative speed of ICMEs compared with the ambient solar wind to extract possible interactions between both.

Nov 5 Thu Florian Regnault (Institut d’Astrophysique Spatiale, IAS (FR)) SP2RC/ESPOS
10:00 Zoom (Meeting ID: 165 498 165) 20 years of ACE data: how superposed epoch analysis reveal generic features in interplanetary CME profiles

Nov 9 Mon Topology Reading Group
12:00 String Topology: Stable viewpoint and relation to Hochschild cohomology

Nov 10 Tue George Moulantzikos Algebraic Geometry Learning Seminar
14:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 7/12: Rational and del Pezzo surfaces

Nov 11 Wed Sira Gratz (University of Glasgow) Pure Maths Colloquium
14:00 Meet Grassmannians, Cluster Algebras and Hypersurface Singularities

Abstract:

Grassmannians are objects of great combinatorial and geometric beauty, which arise in myriad contexts. Their coordinate rings serve as a classical example of cluster algebras, as introduced by Fomin and Zelevinsky at the start of the millennium.

Jensen, King and Su construct an additive categorification of these Grassmannian cluster algebras via maximal Cohen-Macaulay modules over certain plane curve singularities. Such a Grassmannian cluster category encodes key aspects of the cluster structure on the respective coordinate ring of a Grassmannian. Notably, Plücker coordinates naturally correspond to rank 1 modules. An interesting aspect of this relation is that it affords a formal connection between two famous examples of a priori unrelated ADE classifications, providing a bridge between skew-symmetric cluster algebras of finite type and simple plane curve singularities.

In this talk, we take the above ideas to the limit: Taking colimits of Grassmannian cluster algebras gives rise to Grassmannian cluster algebras of infinite rank. We explore these structures combinatorially, and construct an infinite rank analogue of Jensen, King and Su’s Grassmannian cluster categories via maximal Cohen-Macaulay modules over certain hypersurface singularites – the Grassmannian categories of infinite rank. In particular, we investigate how Plücker coordinates are in natural correspondence with generically free modules of rank 1.

This talk is based on joint work with Grabowski, and with August, Cheung, Faber, and Schroll.

Nov 11 Wed Lisa Glaser (Vienna) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate Simulating spectral triples

Abstract:
A spectral triple consists of an algebra, a Hilbert space and a Dirac operator, the information contained in these is equivalent to that of a differential manifold. However it also offers avenues for generalization, since a general algebra can be non-commutative, which leads us to non-commutative geometry. In this talk I will introduce spectral triples and non-commutative geometry, and then from there move on to talking about my own work, using computer simulations to better understand the structure of spectral triples, and to visualize them.

Nov 12 Thu Prof. Silvia Dalla (University of Central Lancashire) SP2RC seminar
10:00 Zoom link: https://zoom.us/j/95338171418 Meeting ID: 953 3817 1418 UK-SOSS: Solar Energetic Particles: origins and propagation

Abstract:
Solar Energetic Particles (SEPs) are ions and electrons detected in interplanetary space in association with flare and coronal mass ejection events. By propagating through the solar wind’s magnetic field, these particles may reach near-Earth locations, where they pose a radiation risk to humans in space and satellite hardware. This talk will review our understanding of the origin and transport of SEPs, based on a large body of data gathered by spacecraft detectors and on theoretical models. It will focus on recent results of test particle simulations, which show that accurate modelling of SEP propagation requires a 3D approach, due to guiding centre drifts and magnetic field line meandering.

Nov 12 Thu Francisco Guzman (Universidad Michoacana de San Nicolas de Hidalgo, Mexico) Plasma Dynamics Group
16:00 Meet A code that solves the equations of MHD coupled to radiation

Abstract:
Our code is based on a finite volume discretization, uses high-resolution shock-capturing flux formulae of the HLL class. Concerning the MHD part, we use the divergence cleaning method to preserve the non-monopoles constraint. For radiation, at the moment, we use the M1 closure relation within the gray body approximation. The evolution equations for radiation become stiff for high opacities, for which we use an implicit-explicit evolution method, which allows the use of a standard integration time-step. We present our code's status and mention the solar physics scenarios where we expect to produce some applications.

Nov 16 Mon Topology Reading Group
12:00 Blackboard collaborate String Topology: Operads (little framed discs)

Nov 17 Tue Ariel Weiss (Jerusalem) Number Theory seminar
11:00 J11 Lafforgue pseudocharacters and the construction of Galois representations

Abstract:
A key goal of the Langlands program is to attach Galois representations to automorphic representations. In general, there are two methods to construct these representations. The first, and the most effective, is to extract the Galois representation from the étale cohomology of a suitable Shimura variety. However, most Galois representations cannot be constructed in this way. The second, more general method is to construct the Galois representation, via its corresponding pseudocharacter, as a p-adic limit of Galois representations constructed using the first method. In this talk, I will demonstrate how the second construction can be refined by using V. Lafforgue’s G-pseudocharacters in place of classical pseudocharacters. As an application, I will prove that the Galois representations attached to certain irregular automorphic representations of U(a,b) are odd, generalising a result of Bellaïche-Chenevier in the regular case. This work is joint with Tobias Berger.

Nov 17 Tue Yirui Xiong (Sheffield) Algebraic Geometry Learning Seminar
14:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 8/12: Minimal models (nef K^2 or P^2 or ruled), uniqueness

Nov 18 Wed Andreagiovanni Reina (CS, Sheffield)
14:00 Meet Collective Decision Making: From Bees to Robots via Multiscale Modelling

Abstract:
I will give an overview of my studies on modelling and simulating collective decision making in distributed systems. Such systems, found in biology, sociology, and engineering, are composed of a large number of interacting individuals that coordinate in order to reach a consensus. The main phases of the collective decision making process consist of identifying the available options, estimating their quality, and selecting the best option or any of them. I will present the main results of my research in understanding and designing each of these phases. Collective systems are inherently difficult to analyse as the stochastic nonlinear interactions between individuals can give rise to complex emergent dynamics. Therefore, I employ a collection of advanced techniques, commonly defined as multiscale modelling. Relying on a set of methods, rather than a single one, gives the benefit of having complementary techniques addressing one another's limitations. In fact, through multiscale modelling, it is possible to analyse the systems at various levels of complexity and detail, from macroscopic group-level dynamics to microscopic individual-level behaviour, and from noise-free deterministic models to stochastic spatial descriptions. I finally shed a light on the recently developed opensource software for automated multiscale modelling. This software, called MuMoT, can also be a useful resource for remote teaching. For more info on MuMoT see (Marshall et al. PlosOne 2019) or MuMoT live notebook (https://mumot.readthedocs.io/). Bio: Dr Andreagiovanni Reina is a Research Fellow in Collective Robotics at the University of Sheffield, UK. He is currently working on the DiODe project (Distributed Algorithms for Optimal Decision-Making) led by Prof. James Marshall, and is the Principal Investigator of the Swarm Awareness project (https://swarmawareness.group.shef.ac.uk/). Andreagiovanni is the researcher responsible for more than 900 Kilobot robots and the related Augmented Reality for Kilobot (ARK) infrastructure at Sheffield Robotics. He holds a PhD in applied sciences from IRIDIA (Marco Dorigo's AI-Laboratory) of the Université Libre de Bruxelles, Belgium, and an M.Sc. in computer engineering from Politecnico di Milano, Italy. He has been a researcher in five European projects on distributed robotic systems since 2009. In December 2020, he plans to return to Brussels with an FNRS Fellowship on modelling heterogeneity in decentralised consensus. Full info at http://areina.staff.shef.ac.uk.

Nov 18 Wed Sara Arias de Reyna (University of Seville) Pure Maths Colloquium
14:00 Meet Modular forms and the arithmetic of fields

Abstract:

Modular forms are holomorphic functions on the upper half-plane which display some symmetry with respect to the action of a subgroup of $SL(2,\mathbb{Z})$. However, it turns out that they encode a great deal of arithmetic information about some field extensions of the rational numbers. This relationship has been fruitfully exploited to prove results in number theory, perhaps the more notorious being the proof of Fermat's Last Theorem by A. Wiles.

In this talk we want to describe the interplay between these two subjects and provide an application of field arithmetic to the existence of certain families of weight one modular forms. This is joint work with François Legrand and Gabor Wiese.

Nov 18 Wed Andreagiovanni Reina (CS, Sheffield) Applied Mathematics Colloquium
14:00 Meet Collective Decision Making: From Bees to Robots via Multiscale Modelling

Abstract:
I will give an overview of my studies on modelling and simulating collective decision making in distributed systems. Such systems, found in biology, sociology, and engineering, are composed of a large number of interacting individuals that coordinate in order to reach a consensus. The main phases of the collective decision making process consist of identifying the available options, estimating their quality, and selecting the best option or any of them. I will present the main results of my research in understanding and designing each of these phases. Collective systems are inherently difficult to analyse as the stochastic nonlinear interactions between individuals can give rise to complex emergent dynamics. Therefore, I employ a collection of advanced techniques, commonly defined as multiscale modelling. Relying on a set of methods, rather than a single one, gives the benefit of having complementary techniques addressing one another's limitations. In fact, through multiscale modelling, it is possible to analyse the systems at various levels of complexity and detail, from macroscopic group-level dynamics to microscopic individual-level behaviour, and from noise-free deterministic models to stochastic spatial descriptions. I finally shed a light on the recently developed opensource software for automated multiscale modelling. This software, called MuMoT, can also be a useful resource for remote teaching. For more info on MuMoT see (Marshall et al. PlosOne 2019) or MuMoT live notebook (https://mumot.readthedocs.io/). Bio: Dr Andreagiovanni Reina is a Research Fellow in Collective Robotics at the University of Sheffield, UK. He is currently working on the DiODe project (Distributed Algorithms for Optimal Decision-Making) led by Prof. James Marshall, and is the Principal Investigator of the Swarm Awareness project (https://swarmawareness.group.shef.ac.uk/). Andreagiovanni is the researcher responsible for more than 900 Kilobot robots and the related Augmented Reality for Kilobot (ARK) infrastructure at Sheffield Robotics. He holds a PhD in applied sciences from IRIDIA (Marco Dorigo's AI-Laboratory) of the Université Libre de Bruxelles, Belgium, and an M.Sc. in computer engineering from Politecnico di Milano, Italy. He has been a researcher in five European projects on distributed robotic systems since 2009. In December 2020, he plans to return to Brussels with an FNRS Fellowship on modelling heterogeneity in decentralised consensus. Full info at http://areina.staff.shef.ac.uk.

Nov 18 Wed Elisa Maggio (Sapienza, Rome) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate Gravitational wave signatures of exotic compact objects

Abstract:
Gravitational waves from the coalescence of compact binaries provide a unique opportunity to test gravity in strong field regime. In particular, the postmerger phase of the gravitational signal is a proxy for the nature of the remnant. This is of particular interest in view of some quantum-gravity models which predict the existence of horizonless exotic compact objects that overcome the paradoxes associated to black holes. Such exotic compact objects can emit a modified ringdown with respect to the black hole case and late-time gravitational wave echoes as characteristic fingerprints. In this talk, I develop a generic framework to the study of the ringdown of exotic compact objects and provide a gravitational-wave template for the echo signal. Finally, I assess the detectability of exotic compact objects with current and future gravitational-wave detectors.

Nov 19 Thu Ryan Milligan (Queen’s University Belfast) European Solar Physics Online Seminars (ESPOS)
10:00 Zoom Lyman-alpha Variability During Solar Flares

Abstract:
The chromospheric hydrogen Lyman-alpha line at 1216A is the brightest emission line in the solar spectrum, and yet studies of solar flares at this wavelength have been scarce in the literature over the past 50 years. The study of Lyman-alpha is important for understanding space weather effects as changes in the Sun’s Lyman-alpha output can drive changes in the dynamics and composition of planetary atmospheres. Lyman-alpha is also a significant radiator of solar flare energy, providing an important diagnostic of energy release and transport processes. Milligan et al. (2020) published a statistical study of ~500 M- and X-class flares using GOES/EUVS data, showing that although the Lyman-alpha irradiance increases by only a few percent during large events, it can radiate up to 100 times more energy than the corresponding X-rays. Flares that occurred closer to the solar limb, however, were found to exhibit a smaller Lyman-alpha enhancement relative to those on the disk due to opacity and/or foreshortening effects. It was also shown that acoustic oscillations in the chromosphere can be detected through Lyman-alpha flare observations, and that impulsive Lyman-alpha emission, not X-rays, can induce currents in the E-layer of Earth’s ionosphere. A follow-up study now includes B- and C-class flares, which although not readily observable in disk-integrated measurements, can be investigated using a superposed epoch analysis. Despite increases of <1% above the solar background, a clear centre-to-limb variation was found in agreement with larger events. These findings should serve as a baseline for the advent of new Lyman-alpha flare observations and advanced numerical simulations that will become available during Solar Cycle 25.

Nov 19 Thu Ryan Milligan (Queen’s University Belfast, Astrophysics Research Centre (UK)) SP2RC/ESPOS
10:00 Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165) Lyman-alpha Variability During Solar Flares

Abstract:
The chromospheric hydrogen Lyman-alpha line at 1216A is the brightest emission line in the solar spectrum, and yet studies of solar flares at this wavelength have been scarce in the literature over the past 50 years. The study of Lyman-alpha is important for understanding space weather effects as changes in the Sun’s Lyman-alpha output can drive changes in the dynamics and composition of planetary atmospheres. Lyman-alpha is also a significant radiator of solar flare energy, providing an important diagnostic of energy release and transport processes. Milligan et al. (2020) published a statistical study of ~500 M- and X-class flares using GOES/EUVS data, showing that although the Lyman-alpha irradiance increases by only a few percent during large events, it can radiate up to 100 times more energy than the corresponding X-rays. Flares that occurred closer to the solar limb, however, were found to exhibit a smaller Lyman-alpha enhancement relative to those on the disk due to opacity and/or foreshortening effects. It was also shown that acoustic oscillations in the chromosphere can be detected through Lyman-alpha flare observations, and that impulsive Lyman-alpha emission, not X-rays, can induce currents in the E-layer of Earth’s ionosphere. A follow-up study now includes B- and C-class flares, which although not readily observable in disk-integrated measurements, can be investigated using a superposed epoch analysis. Despite increases of <1% above the solar background, a clear centre-to-limb variation was found in agreement with larger events. These findings should serve as a baseline for the advent of new Lyman-alpha flare observations and advanced numerical simulations that will become available during Solar Cycle 25.

Nov 23 Mon Topology Reading Group
12:00 Blackboard collaborate String Topology: Cacti operad and the action on loop spaces

Nov 24 Tue Jaclyn Lang (Oxford) Number Theory seminar
11:00 Google meet Images of two-dimensional pseudorepresentations

Abstract:
There is a general philosophy that the image of a Galois representation should be as large as possible, subject to its symmetries. This can be seen in Serre's open image theorem for non-CM elliptic curves, Ribet and Momose's work on Galois representations attached to modular forms, and recent work of the speaker and Conti-Iovita-Tilouine on Galois representations attached to p-adic families of modular forms. Recently, Bellaïche developed a way to measure the image of an arbitrary pseudorepresentations taking values in a local ring A. Under the assumptions that A is a domain and the residual representation is not too degenerate, we explain how the symmetries of such a pseudorepresentation are reflected in its image. This is joint work with Andrea Conti and Anna Medvedovsky.

Nov 24 Tue Cristina Manolache (Sheffield) Algebraic Geometry Learning Seminar
14:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 9/12: Surfaces with k = 0 (K3, Enriques, abelian, bielliptic)

Nov 25 Wed Ailsa Keating (University of Cambridge) Pure Maths Colloquium
14:00 Meet Two-variable singularities and symplectic topology

Abstract:
Start with a two-variable complex polynomial f with an isolated critical point at the origin. We will survey a range of classical structures associated to f, and explain how these can be revisited and enhanced using insights from symplectic topology. No prior knowledge of singularity theory or symplectic topology will be assumed.

Nov 25 Wed Ivonne Zavala (Swansea) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate Multifield Inflation: Fat inflatons, large turns and the η-problem

Abstract:
I will discuss multifield models of inflation where all scalar fields are heavier than the Hubble scale, thus evading the η-problem. I will show how this is achieved in multifield inflation thanks to large turns in the field space, which I will introduce. I will then illustrate this scenario in a D5-brane model in Type IIB string flux compactifications, where the brane moves along the angular and radial directions in a warped throat driving fat D-brane natural-like inflation, with interesting cosmological predictions.

Nov 26 Thu Petr Heinzel (Astronomical Institute, Czech Academy of Sciences) Plasma Dynamics Group
16:00 Meet Partial ionization of hydrogen plasma in the solar atmosphere - a non-LTE modeler's view

Abstract:
Based on our extensive experience with the non-LTE radiative-transfer modeling of different atmospheric structures (chromosphere, flares, prominences, CME-cores), I will demonstrate the importance of partial hydrogen ionization and review the most relevant atomic processes. I will also discuss the role of non-equilibrium ionization of hydrogen.

Nov 27 Fri Krisztián Vida (CSFK) SP2RC seminar
13:00 Meet Coronal mass ejections on late-type stars

Abstract:
In search of finding stellar CMEs we analyzed a large number of archive spectral observations of F-M dwarfs. While the F-K sample showed no events, M stars produced enough eruptions for statistical analysis. In this talk, I’ll summarize what we can learn from these detections and non-detections, and how this improves our knowledge on the possible habitability around these systems.

Dec 1 Tue Neil Dummigan (Sheffield) Number Theory seminar
11:00 Google meet Lifting congruences of modular forms to half-integral weight

Abstract:
In the situation where two newforms of the same level are congruent modulo some prime divisor, one can ask whether half-integral weight modular forms assigned to them by Kohnen's correspondence enjoy the same property. Under certain conditions, it is possible to prove this by proving a congruence (of Fourier coefficients, not just Hecke eigenvalues) between certain associated Siegel modular forms, the Saito-Kurokawa lifts.

Dec 1 Tue Reinder Meinsma Algebraic Geometry Learning Seminar
14:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 10/12: Elliptic surfaces

Dec 2 Wed Yemon Choi (University of Lancaster) Pure Maths Colloquium
14:00 Meet Fourier algebras and dual convolution

Abstract:

The Fourier transform provides a map between function spaces on a given abelian group G and function spaces on its dual group, which interchanges convolution and pointwise product. The functions on G that correspond to integrable functions on its dual group form a natural Banach algebra, known as the Fourier algebra of G. In the 1960s it was shown that one can extend the definition of the Fourier algebra to non-abelian groups, and the resulting Banach algebra has since been the subject of much study. In many cases there is also a corresponding version of the Fourier transform, but scalar-valued Fourier coefficients must be replaced by operator-valued Fourier coefficients.

In this talk, which will mostly be expository, I will give a sketch of these constructions, focusing on some specific examples arising from groups such as SU(2) or the real ax+b group. I will then discuss the following natural but slightly ill-posed question: what operation on the "dual side" corresponds to pointwise product of functions in G? In particular, I will report on recent work (joint with M. Ghandehari) where we are able to describe the dual convolution explicitly for the real ax+b group. Time permitting, I will mention some applications to the study of derivations and cocycles on certain Fourier algebras.

Dec 2 Wed Andrew Krause (Oxford) Applied Mathematics Colloquium
14:00 Meet Recent Progress & Open Frontiers in Turing-Type Morphogenesis

Abstract:
Motivated by recent work with biologists, I will showcase some mathematical results on Turing instabilities in complex domains. This is scientifically related to understanding developmental tuning in the whiskers of mice, and more generally pattern formation on multiple scales and evolving domains. Such phenomena are typically modelled using reaction-diffusion systems of morphogens, and one is often interested in emergent spatial and spatiotemporal patterns resulting from instabilities of a homogeneous equilibrium, which have been well-studied. In comparison to the well-known effects of how advection or manifold structure impacts unstable modes in such systems, I will present results on instabilities in heterogeneous systems, as well as those arising in the setting of evolving manifolds. These contexts require novel formulations of classical dispersion relations, and may have applications beyond developmental biology, such as in population dynamics (e.g. understanding colony or niche formation of populations in heterogeneous environments). These approaches also help close the vast gap between the simple theory of diffusion-driven pattern formation, and the messy reality of biological development, though there is still much work to be done in validating even complex theories against the rich dynamics observed in nature.

Dec 2 Wed Andrew Gow (Sussex) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate A History of the Universe in 100 Primordial Black Holes

Abstract:
A summary of the work completed during the course of my PhD so far, centred on the hypothesised Primordial Black Holes (PBHs). The talk will begin at the curvature power spectrum, and advance forward in time through the creation of PBHs and the intricacies of their mass distribution, culminating in the possibility of the LIGO gravitational wave signals being from PBH mergers, instead of astrophysics.

Dec 3 Thu Meetu Verma (Leibniz-Institut für Astrophysik Potsdam (AIP), Germany) European Solar Physics Online Seminars (ESPOS)
10:00 Zoom Classification of High-resolution Solar Hα Spectra using t-distributed Stochastic Neighbor Embedding

Abstract:
The Hα spectral line is a well-studied absorption line revealing properties of the highly structured and dynamic solar chromosphere. The presented work is based on high-spectral resolution Hα spectra obtained with the echelle spectrograph of the Vacuum Tower Telescope (VTT) located at Observatorio del Teide (ODT), Tenerife, Spain. The number of spectra accumulated at VTT over one observing day easily reaches up to millions. Hence, we require tools to identify and classify spectra with minimal human intervention. I will present exploratory work, which provides the framework and some ideas on how to tailor a classification scheme towards specific spectral data and science questions. t-distributed Stochastic Neighbor Embedding (t-SNE) is a machine learning algorithm, which is used for nonlinear dimensionality reduction. In this application, it projects Hα spectra onto a two-dimensional map, where it becomes possible to classify the spectra according to results of Cloud Model (CM) inversions. The CM parameters optical depth, Doppler width, line-of-sight velocity, and source function describe properties of the cloud material. Initial results of t-SNE indicate its strong discriminatory power to separate quietSun and plage profiles from those that are suitable for CM inversions. Furthermore, I will discuss our choice of various t-SNE parameters, the impact of seeing on classification, the results arising from various types of input data, and the link of the identified clusters to chromospheric features. Although t-SNE proves to be efficient in clustering high-dimensional data, human inference is required at each step to interpret the results.

Dec 3 Thu Meetu Verma (Leibniz Institute for Astrophysics Potsdam (DE)) SP2RC/ESPOS
11:00 Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165) Classification of High-resolution Solar Hα Spectra using t-distributed Stochastic Neighbor Embedding

Abstract:
The Hα spectral line is a well-studied absorption line revealing properties of the highly structured and dynamic solar chromosphere. The presented work is based on high-spectral resolution Hα spectra obtained with the echelle spectrograph of the Vacuum Tower Telescope (VTT) located at Observatorio del Teide (ODT), Tenerife, Spain. The number of spectra accumulated at VTT over one observing day easily reaches up to millions. Hence, we require tools to identify and classify spectra with minimal human intervention. I will present exploratory work, which provides the framework and some ideas on how to tailor a classification scheme towards specific spectral data and science questions. t-distributed Stochastic Neighbor Embedding (t-SNE) is a machine learning algorithm, which is used for nonlinear dimensionality reduction. In this application, it projects Hα spectra onto a two-dimensional map, where it becomes possible to classify the spectra according to results of Cloud Model (CM) inversions. The CM parameters optical depth, Doppler width, line-of-sight velocity, and source function describe properties of the cloud material. Initial results of t-SNE indicate its strong discriminatory power to separate quietSun and plage profiles from those that are suitable for CM inversions. Furthermore, I will discuss our choice of various t-SNE parameters, the impact of seeing on classification, the results arising from various types of input data, and the link of the identified clusters to chromospheric features. Although t-SNE proves to be efficient in clustering high-dimensional data, human inference is required at each step to interpret the results.

Dec 8 Tue Jun Su (Cambridge) Number Theory seminar
11:00 Meet Arithmetic group cohomology with generalised coefficients

Abstract:
Cohomology of arithmetic subgroups, with algebraic representations as coefficients, has played an important role in the construction of Langlands correspondence. Traditionally the first step to access these objects is to view them as cohomology of sheaves on locally symmetric spaces and hence connect them with spaces of functions. However, sometimes infinite dimensional coeffients also naturallhy arise, e.g. when you try to attach elliptic curves to weight 2 eigenforms on GL_2/an imaginary cubic field, and the sheaf theoretic viewpoint might no longer be fruitful. In this talk we'll explain a very simple alternative understanding of the connection between arithmetic group cohomology (with finite dimensional coefficients) and function spaces, and discuss its application to infinite dimensional coefficients.

Dec 8 Tue Ananyo Dan Algebraic Geometry Learning Seminar
14:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 11/12: Surfaces of general type

Dec 9 Wed Kathryn Hess (École Polytechnique Fédérale de Lausanne) Pure Maths Colloquium
14:00 Meet Topological insights in neuroscience

Abstract:

Over the past decade, research at the interface of topology and neuroscience has grown remarkably fast. Topology has, for example, been successfully applied to objective classification and digital synthesis of neuron morphologies, to automatic detection of network dynamics, and to the construction of a powerful and parameter-free mathematical framework for relating the activity of a network of neurons or brain regions to its underlying structure, both locally and globally.

In this talk I will present a medley of recent applications of topology to neuroscience, many of which resulted from close collaboration with the Blue Brain Project.

Dec 9 Wed Gary Mirams (Nottingham) Applied Mathematics Colloquium
14:00 Meet Selecting and parameterising a model for a potassium ion channel's dynamics

Abstract:
There are a wide range of suggested models in the literature for how the hERG potassium channel opens and closes in response to changes in the voltage across cell membranes. These are typically ODE models with a handful of state variables and up to tens of parameters. Experiments can clamp voltage and measure the resulting current, but we'd like to be able to predict the current in new (unseen) situations that might occur in different cells, people and conditions. In this talk, I'll describe our efforts to choose and parameterise a model, by using novel experimental designs with rapidly fluctuating input waveforms, as well as a strict separation between training and validation of the models. The rapid experiments have allowed us to make cell-specific models and to create a parameterisation for a mutant channel which sheds light on why the mutant may increase the risk of cardiac arrhythmias. We've also used high-throughput measurements to look at cell-cell variability and to examine the temperature-dependence of channel opening. I'll discuss some of the open challenges in tying together experimental design for ion channel models with selection, parameterisation, validation and assessment of discrepancy/misspecification.

Dec 10 Thu Prof Philippa Browning (University of Manchester) SP2RC seminar
10:00 LT 11 UK-SOSS: Heating and particle acceleration in twisted flux ropes in solar and stellar flares

Abstract:
Twisted magnetic flux ropes are reservoirs of free magnetic energy. I will describe some recent advances in modelling plasma heating and non-thermal particle acceleration in twisted magnetic flux ropes in the context of solar flares. After an overview of twisted magnetic flux ropes in the corona, I will show how magnetic reconnection in fragmented current structures in kink-unstable twisted loops can both heat plasma and efficiently accelerate both electrons and ions. Forward modelling of the observational signatures of this process in EUV, hard X-rays and microwaves will be described, and the potential for observational identification of twisted magnetic fields in the solar corona discussed. Furthermore, the reconnection activity can drive oscillations which may be observable as oscillations in the microwave emission. Then, coronal loops with multiple twisted threads will be considered, showing how instability in a single unstable twisted thread may trigger reconnection with stable neighbours, releasing their stored energy and causing an “avalanche” of heating events, with important implications for solar coronal heating. This avalanche can also accelerate charged particles throughout the structure. Many other stars exhibit flares, and I will briefly describe recent work on modelling radio emission in flares in young stars (T Tauri stars). In particular, the enhanced radio luminosity of these stars relative to scaling laws for the Sun and other Main Sequence stars will be discussed.

Dec 10 Thu Richard Morton (University of Northumbria) Plasma Dynamics Group
16:00 Meet A new seismology of the corona

Abstract:
The Coronal Multi-channel Polarimeter (CoMP) instrument has proved itself invaluable for the study of propagating kink waves in the corona. After making the initial discovery back in 2007, CoMP has been able to provide a number of insights into the properties of the kink waves. The kink mode is found to be present throughout the corona and appears to be continuous. The widespread and reliable presence means that the propagating kink mode can make a fantastic tool for magneto-seismology. While CoMP shows a persistent Doppler velocity signal related to the propagating kink mode, the continuous transverse motions of the coronal structures can also be detected with Solar Dynamics Observatory (SDO/AIA). However the scale of the displacements are at the edge of the SDO's capabilities, requiring careful measurements to be able to study them and exploit them for seismology. In this talk I discuss the new possibilities for coronal seismology using the propagating kink mode, demonstrating how we’ve used both CoMP and SDO/AIA to measure the young solar wind, the density structure in a coronal hole and provide the first estimates for the global coronal magnetic field.

Dec 15 Tue Evgeny Shinder (Sheffield) Algebraic Geometry Learning Seminar
14:00 online in Blackboard collaborate (please e-mail Evgeny for the link) Algebraic Surfaces 12/12: Final overview of the classification of surfaces

Dec 16 Wed Marina Iliopoulou (University of Kent) Pure Maths Colloquium
14:00 Meet A discrete Kakeya-type inequality

Abstract:
The Kakeya conjectures of harmonic analysis claim that congruent tubes that point in different directions rarely meet. In this talk we discuss the resolution of an analogous problem in a discrete setting (where the tubes are replaced by lines), and provide some structural information on quasi-extremal configurations. This is joint work with A. Carbery.

Dec 16 Wed Konstantinos Zygalakis (Edunburgh) Applied Mathematics Colloquium
14:00 Meet Hybrid modeling for the stochastic simulation of multi-scale chemical kinetics

Abstract:
It is well known that stochasticity can play a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be adequately modeled by Markov processes and, for such systems, methods such as Gillespie’s algorithm are typically employed. While such schemes are easy to implement and are exact, the computational cost of simulating such systems can become prohibitive as the frequency of the reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation for systems where all reactants are present in large concentrations, the approximation breaks down when the fast chemical species exist in small concentrations, giving rise to significant errors in the simulation. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as computing observables of cell cycle models. In this talk, we present a hybrid scheme for simulating well-mixed stochastic kinetics, using Gillespie–type dynamics to simulate the network in regions of low reactant concentration, and chemical Langevin dynamics when the concentrations of all species are large. These two regimes are coupled via an intermediate region in which a “blended” jump-diffusion model is introduced. Examples of gene regulatory networks involving reactions occurring at multiple scales, as well as a cell-cycle model are simulated, using the exact and hybrid scheme, and compared, both in terms of weak error, as well as computational cost. If there is time, we will also discuss the extension of these methods for simulating spatial reaction kinetics models, blending together partial differential equation with compartment based approaches, as well as compartment based approaches with individual particle models.

Dec 16 Wed Antonia Micol Frassino (ICC, Barcelona) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate Exotic and quantum BTZ black holes

Abstract:
In this talk, I will discuss some black hole solutions in three-dimensional gravity that manifest interesting properties. In particular, I will consider the three-dimensional Einstein-AdS action in the presence of a gravitational Chern-Simons term and focus on a family of geometries that goes from the BTZ black hole to its 'exotic' counterpart. Then, in the context of braneworld holography, I will describe the holographic construction of the quantum rotating BTZ black hole (quBTZ) using an exact four-dimensional bulk solution. I will present some of the thermodynamic properties of these black holes, focus on the generalized first law and discuss possible further developments.

Dec 17 Thu Fionnlagh Mackenzie Dover (Sheffield) European Solar Physics Online Seminars (ESPOS)
10:00 Zoom MHD simulations and the morphology of spicular solar jets

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.

Dec 17 Thu Fionnlagh Mackenzie Dover (University of Sheffield, Solar Physics and Space Plasma Research Centre (UK)) SP2RC/ESPOS
10:00 Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165) MHD simulations and the morphology of spicular solar jets

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.

Jan 14 Thu Sudheer K. Mishra (Indian Institute of Technology, BHU, India) European Solar Physics Online Seminars (ESPOS)
10:00 Zoom The Kelvin-Helmholtz Instability in the Fan-spine Magnetic Topology in the Solar Corona

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.

Jan 14 Thu Sudheer K. Mishra (Indian Institute of Technology, BHU, India) SP2RC/ESPOS
10:00 Zoom link: https://zoom.us/j/165498165 The Kelvin-Helmholtz Instability in the Fan-spine Magnetic Topology in the Solar Corona

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.

Jan 21 Thu Professor Valery M Nakariakov (Centre for Fusion, Space & Astrophysics, University of Warwick, United Kingdom) SP2RC seminar
10:00 Zoom link: https://zoom.us/j/95338171418 UK-SOSS: Magnetohydrodynamic Seismology of the Solar Coronal Plasma with Kink Oscillations

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.

Jan 27 Wed Theo Torres Vicente (Nottingham) Cosmology, Relativity and Gravitation
15:00 Blackboard Collaborate Electromagnetic self-force on a charged particle on Kerr spacetime

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.

Jan 28 Thu (University of St Andrews, Solar and Magnetospheric Theory Group (UK)) SP2RC/ESPOS
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Feb 5 Fri Dr. Sijie Yu (Center for Solar-Terrestrial Research, New Jersey Institute of Technology) SP2RC seminar
13:00 Meet Dynamic imaging spectroscopy at radio wavelength: new insight into energetic processes on the Sun

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.