Sep 28 | Wed | Steffen Gielen (Sheffield) | Cosmology, Relativity and Gravitation |

Abstract:General relativity gives us the freedom to choose different time coordinates to describe evolution, but also says that only relational notions of evolution (such as "what is the value of quantity A when quantity B takes the value $b_0$"?) are meaningful, i.e., possibly related to observation. When we quantise, this leads to various basic technical and conceptual questions known under the heading of the "problem of time": depending on the viewpoint we seem to have either no dynamics at all or too many, potentially inequivalent, ways of defining time evolution in quantum theory. The standard quantum-mechanical demand of unitary time evolution becomes ambiguous in the general-relativistic context, as it may refer to different notions of time. Here I will discuss some of these issues in a simple cosmological model, where three inequivalent quantum theories can be defined. Demanding unitarity in these simple theories leads to quite radically different "predictions" for the resulting cosmology, illustrating the problem of time. |
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Sep 22 | Thu | Andres A. Ramos (Instituto de Astrofisica de Canarias (IAC), Spain) | Plasma Dynamics Group |

Abstract:Solar spectropolarimetry is entering the realm of big data. Current and future telescopes will produce data at a rate that will make it hard to store in a single machine and even harder to operate on the data. Thankfully, in the last decade, machine learning has experienced an enormous advance, thanks to the open possibility of training very deep and complex neural networks. In this contribution I show options to explore to deal with the big data problem and also how deep learning can be used to efficiently solve difficult problems in Solar Physics. I will focus on how differentiable programming (aka deep learning) is helping us to have access to velocity fields in the solar atmosphere, correct for the atmospheric degradation of spectropolarimetric data and carry out fast 3D inversions of the Stokes parameters to get physical information of the solar atmosphere. |
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Sep 13 | Tue | Solomon Friedberg (Boston College) | Number Theory seminar |

Abstract:The classical Shimura correspondence lifts automorphic representations on the double cover of $SL_2$ (corresponding to classical half-integral weight forms) to automorphic representations on $PGL_2$. Though efforts have been made for many years to generalize this map to higher rank groups and higher degree covers, our knowledge is limited. In this talk I present joint work with Omer Offen that points to a new Shimura lift for automorphic representations on the triple cover of $SL_3$ -- we establish the Fundamental Lemma for a relative trace formula. Moreover, this project will characterize the image of the lift by means of a period involving a theta function on $SO_8$, confirming a 2001 conjecture of Bump, Friedberg and Ginzburg. |
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Aug 29 | Mon | Paulo Godolphim (Universidad de Chile) | Mathematical Biology Seminar Series |

Abstract:The vertex model is one of the most used physical models to describe confluent tissues. Many works show the vertex model gives excellent qualitative and quantitative descriptions of different in vitro and in vivo experiments. Nevertheless, systematic validation of the model is yet barely explored. Our initial assumption is that only finding the optimal parameters that correctly describe/mimic the evolution of an (experimental) tissue is necessary but not sufficient to consider a model as an accurate description. We propose that a more restrictive condition must be matched. If a model is a good description, then the same set of parameters must be able to describe at the same time the whole tissue and also any sub-part of the tissue. We call this stricter approach Micromechanics, where one executes vertex-by-vertex independent simulations to find the optimal parameters for each vertex. If the optimal parameters are homogeneous, then the model is considered valid. If not, this indicates we need to modify the model to ensure homogeneity in the parameters alongside the tissue. We are working with experimental in vivo data of the EVL cell layer in the epiboly process (time ~11h to 22h) of an Annual Killifish embryo, where simulated vertices' positions are compared with those obtained using fluorescent microscopy. Our results show that the model tested has inhomogeneous parameters, indicating that it is not a valid description for our data. Our conclusions are still preliminary, however, we believe that this characteristic can be corrected by introducing a non-homogeneous viscosity term in the tissue energy functional. |
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Aug 26 | Fri | Pasupulati Sunil Kumar (IISER Thiruvananthapuram) | Number Theory seminar |

Abstract:Abstract. In 1979, Lenstra introduced the definition of the Euclidean ideal which is a generalization of Euclidean domain. Definition 1. Let R be a Dedekind domain and I be the set of non zero integral ideals of R. If C is an ideal of R, then it is called Euclidean if there exists a function Ψ : I → N, such that for every I ∈ I and x ∈ I^−1C - C there exist a y ∈ C such that Ψ ((x − y)IC^−1) < Ψ(I). Lenstra established that for a number field K with rank(O^x K ) ≥ 1, the number ring OK contains a Euclidean ideal if and only if the class group ClK is cyclic, provided GRH holds. Several authors worked towards removing the assumption of GRH. In this talk, I prove the existence of the Euclidean ideal class in abelian quartic fields. As a corollary, I will prove that a certain class biquadratic field with class number two has a Euclidean ideal class. I also discuss the existence of a Euclidean ideal class in certain cubic and quadratic extensions. This is joint work with Srilakshmi Krishnamoorthy. |
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Aug 25 | Thu | Rodrigo Miranda (Brasilia, Brazil) | Plasma Dynamics Group |

Abstract:We apply the Jensen-Shannon (J-S) complexity-entropy index to magnetic field data of four reconnection exhausts detected in the solar wind at 1 AU. Three events are related to the passage of an interplanetary coronal mass ejection, and one event is related to a rope-rope magnetic reconnection event. The interplanetary magnetic field is projected into the LMN coordinates by applying the hybrid minimum variance analysis. The J-S index indicates that the three components of the magnetic field display entropy and complexity values similar to stochastic fluctuations. However, we show that a high degree of intermittency within the inertial subrange is related to a lower degree of entropy and a higher degree of complexity. We also show that, for all four events, the L component of the magnetic field displays lower entropy and higher complexity than the M and N components. These results suggest that coherent structures can be responsible for decreasing entropy and increasing complexity within reconnection exhausts in the interplanetary magnetic-field turbulence. |
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Jul 28 | Thu | Roberta Duarte (São Paulo (USP)) | Plasma Dynamics Group |

Abstract:In this pilot study, we investigate the use of a deep learning (DL) model to temporally evolve the dynamics of gas accreting onto a black hole in the form of a radiatively inefficient accretion flow (RIAF). We have trained a machine to forecast such a spatiotemporally chaotic system -- i.e. black hole weather forecasting -- using a convolutional neural network (CNN) and a training dataset which consists of numerical solutions of the hydrodynamical equations, for a range of initial conditions. We find that deep neural networks seem to learn well black hole accretion physics and evolve the accretion flow orders of magnitude faster than traditional numerical solvers, while maintaining a reasonable accuracy for a long time. For instance, CNNs predict well the temporal evolution of a RIAF over a long duration of 8e4 GM/c³ which corresponds to 80 dynamical times at r = 100 GM/c². The DL model is able to evolve flows from initial conditions not present in the training dataset with good accuracy. Our approach thus seems to generalize well. Once trained, the DL model evolves a turbulent RIAF on a single GPU four orders of magnitude faster than usual fluid dynamics integrators running in parallel on 200 CPU cores. We speculate that a data-driven machine learning approach should be very promising for accelerating not only fluid dynamics simulations, but also general relativistic magnetohydrodynamic ones. |
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Jul 8 | Fri | Steven A. Wrathmall (Durham University) | SP2RC seminar |

Abstract:Major solar flare events pose a serious risk to our critical infrastructures (power networks telecommunications, navigation etc) if they interact with Earth's magnetosphere and cause geomagnetic storms. The Quantum Light and Matter group at Durham University is a part of the SAMNET network [1] to develop early warning systems for such events. At the heart of the solar telescopes are atomic line filters. Our group has worked extensively on the modelling and construction of these narrow band filters [2,3,4]. The aim of this talk is to present our recent work on developing filters to support improved space weather forecasting. 1. R. Erdélyi, M. B. Korsós, X. Huang et al., “The Solar Activity Monitor Network - SAMNet,” J. Space Weather. Space Clim. 12, 2 (2022). 2. James Keaveney, Charles S. Adams, Ifan G. Hughes, ElecSus: Extension to arbitrary geometry magneto-optics, Computer Physics Communications, Volume 224, 2018, Pages 311-324, 3. James Keaveney, Steven A. Wrathmall, Charles S. Adams, and Ifan G. Hughes, "Optimized ultra-narrow atomic bandpass filters via magneto-optic rotation in an unconstrained geometry," Opt. Lett. 43, 4272-4275 (2018) 4. Fraser D. Logue, Jack D. Briscoe, Danielle Pizzey, Steven A. Wrathmall, and Ifan G. Hughes, "Better magneto-optical filters with cascaded vapor cells," Opt. Lett. 47, 2975-2978 (2022) |
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Jul 7 | Thu | Lakshmi Pradeep Chitta (Max Planck Institute for Solar System Research (MPS), Germany) | SP2RC/ESPOS |

Abstract:Relaxation of braided coronal magnetic fields through reconnection is thought to be a source of energy to heat plasma in active region coronal loops. However, observations of active region coronal heating associated with untangling of magnetic braids remain sparse. One reason for this paucity could be the lack of coronal observations with sufficiently high spatial and temporal resolution to capture this process in action. Using new high spatial resolution (250–270 km on the Sun) and high cadence (3–10 s) observations from the Extreme Ultraviolet Imager (EUI) on board Solar Orbiter we observed untangling of small-scale coronal braids in different active regions. The untangling is associated with impulsive heating of the gas in these braided loops. We assess that coronal magnetic braids overlying cooler chromospheric filamentary structures are perhaps more common. Furthermore, our observations show signatures of both spatially coherent and intermittent coronal heating during relaxation of magnetic braids. Our study reveals the operation of both more gentle and explosive modes of magnetic reconnection in the solar corona. In this talk, we present these new EUI observations and discuss the implications for magnetic braiding associated coronal heating. |
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Jul 1 | Fri | Belucz Bernadett (SP2RC (UoS)) | SP2RC seminar |

Abstract:The wings of sunspot butterfly diagram, combined observations of EUV brightpoints, faculae, filaments, ephemeral active regions or coronal green line emissions demonstrate extended wings to much higher latitudes up to 60 degrees, which is known as the Extended Solar Cycle (ESC). This pattern shows a strong overlap between cycles. We represent these extended and overlapped wings by oppositely-directed double magnetic bands. We compute the unstable eigenmodes for MHD Rossby waves, study the interaction between the low-latitude bands and the high-latitude bands and properties of these energetically active Rossby waves as these band-pairs migrate to the equator. |
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Jun 30 | Thu | Hanneke Wiersema (Cambridge) | Number Theory seminar |

Abstract:The strong form of Serre's conjecture states that a two-dimensional mod p representation of the absolute Galois group of Q arises from a modular form of a specific weight, level and character. Serre considered modular forms of weight at least 2, but in 1992 Edixhoven refined this conjecture to include weight one modular forms. In this talk we explore analogues of Edixhoven's refinement for Galois representations of totally real fields, extending recent work of Diamond–Sasaki. In particular, we show how modularity of partial weight one Hilbert modular forms can be related to modularity of Hilbert modular forms with regular weights, and vice versa. |
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Jun 30 | Thu | Tzu-Jan Li (Paris) | Number Theory seminar |

Abstract:Helm and Moss have recently studied a problem on "local Langlands correspondence in families" for the p-adic general linear groups, through which they have also obtained an invariant-theoretical description of integral endomorphism algebras of Gelfand--Graev representations of finite general linear groups. In this talk, we shall generalise Helm--Moss's result on endomorphism algebras of Gelfand--Graev representations to the case of any reductive groups having connected center. Instead of using Helm--Moss's p-adic approach, we will use the Brauer theory of modular representations to relate the endomorphism algebra in question with the desired invariant-theoretical description. This talk is mainly based on the work [1] in collaboration with Jack Shotton. |
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Jun 30 | Thu | Chris Williams (Nottingham) | Number Theory seminar |

Abstract:Let \pi be a p-ordinary cohomological cuspidal automorphic representation of GL(n,A_Q). A conjecture of Coates--Perrin-Riou predicts that the (twisted) critical values of its L-function L(\pi x\chi,s), for Dirichlet characters \chi of p-power conductor, satisfy systematic congruence properties modulo powers of p, captured in the existence of a p-adic L-function. For n = 1,2 this conjecture has been known for decades, but for n > 2 it is known only in special cases, e.g. symmetric squares of modular forms; and in all previously known cases, \pi is a functorial transfer via a proper subgroup of GL(n). In this talk, I will explain what a p-adic L-function is, state the conjecture more precisely, and then describe recent joint work with David Loeffler, in which we prove this conjecture for n=3 (without any transfer or self-duality assumptions). |
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Jun 23 | Thu | Peter Hunana (Instituto de Astrofísica de Canarias (IAC)) | SP2RC/ESPOS |

Abstract:Several generalizations of the well-known fluid model of Braginskii (Rev. of Plasma Phys., 1965) are considered. We use the Landau collisional operator and the moment method of Grad. We focus on the 21-moment model that is analogous to the Braginskii model, and we also consider a 22-moment model. Both models are formulated for general multi-species plasmas with arbitrary masses and temperatures, where all the fluid moments are described by their evolution equations. The 21-moment model contains two “heat flux vectors” (3rd and 5th-order moments) and two “viscosity-tensors” (2nd and 4th-order moments). The Braginskii model is then obtained as a particular case of a one ion-electron plasma with similar temperatures, with de-coupled heat fluxes and viscosity-tensors expressed in a quasi-static approximation. We provide all the numerical values of the Braginskii model in a fully analytic form (together with the 4th and 5th-order moments). For multi-species plasmas, the model makes calculation of transport coefficients straightforward. Formulation in fluid moments (instead of Hermite moments) is also suitable for implementation into existing numerical codes. It is emphasized that it is the quasi-static approximation which makes some Braginskii coefficients divergent in a weakly-collisional regime. Importantly, we show that the heat fluxes and viscosity-tensors are coupled even linearly and that the fully contracted (scalar) perturbations of the 4th-order moment, which are accounted for in the 22-moment model, modify the energy exchange rates. |
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Jun 22 | Wed | Andrea Calcinari (Sheffield) | Cosmology, Relativity and Gravitation |

Abstract:In cosmological group field theory models for quantum gravity coupled to a massless scalar field, the total volume follows the classical Friedmann dynamics of a flat FLRW Universe at low energies while resolving the Big Bang singularity at high energies. An open question is how to generalise these results to other homogeneous cosmologies. In this talk I will show the first steps taken towards studying Bianchi models in group field theory, based on the introduction of a new anisotropy observable analogous to the β variables in Misner’s parametrisation. In a model based on coupling three Peter-Weyl modes, we find that in an expanding Universe β initially behaves like its classical analogue before “decaying”, showing a previously studied isotropisation. I will conclude with some potential future developments about defining relational dynamics in group field theory without the need of matter, just like one can do in a classical setting thanks to the anisotropy degrees of freedom. |
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Jun 17 | Fri | Emilia Kilpua (University of Helsinki) | SP2RC seminar |

Abstract:This seminar will focus on discussing the ionised stream of plasma - the solar wind - that flows continuously from the Sun through interplanetary space. First the basic concepts and physics of the solar wind will be presented as well as of the transient coronal mass ejections (CMEs) that are regularly launched from the Sun. The seminar will continue with the outlook on recent modelling and observational efforts to study and forecast the solar wind and CMEs, with the EUropean Heliospheric FOrecasting Information Asset (EUHFORIA). |
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Jun 15 | Wed | Lisa Mickel (Sheffield) | Cosmology, Relativity and Gravitation |

Abstract:Finding a description of black holes in theories of quantum gravity is a common challenge, where one of the topics of interest is to derive the entropy of a black hole. In this talk we will work in the framework of coloured group field theories (GFTs). In previous work, coloured GFT states with a suitable topology were introduced to obtain a foliation for the Schwarzschild black hole and calculate the entanglement entropy across a (horizon) surface. We extend this construction by thermalizing the interior and exterior of the black hole using the framework of thermofield dynamics before constructing the state. The state we consider is obtained from a so-called seed state with the appropriate topology that is then consecutively refined in a topology preserving manner. Since this is work in progress, I will conclude with some final remarks on possible challenges that we might face during the computation of the entanglement entropy. |
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Jun 8 | Wed | Bachir Bekka (Université de Rennes 1) | Pure Maths Colloquium |

Abstract:A measure preserving action of a group G on a measure space X gives rise to a unitary representation of G on the Hilbert space $L^2(X)$. This action may or may not have the spectral gap property which is a very strong form of ergodicity. For instance, groups with Kazhdan's property (T) always have this property. We will survey the importance of the spectral gap property in various problems arising in graph theory, dynamical systems or operator algebras. In the case where X is a homogeneous space arising from an algebraic group, we will show that the absence of the spectral gap property is often related to amenability. |
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Jun 8 | Wed | Sivakumar Namasivayam (Sheffield) | Cosmology, Relativity and Gravitation |

Abstract:Quantum field theory in curved space-time is a theory of quantum fields propagating on a background classical curved space-time. We study a quantum scalar field, with general mass and coupling, on a background three dimensional anti-de Sitter space-time (adS3) with a view to determining the vacuum and thermal expectation values of the square of the scalar field, $\langle\Phi^2\rangle$, known as the vacuum polarisation (VP). Anti-de Sitter space-time is a maximally symmetric solution to Einstein’s field equations with a constant negative curvature which plays a pivotal role in the Ads-CFT (conformal field theory) correspondence. However the presence of a time-like boundary at spatial infinity means that information can be lost to the boundary in finite time, meaning that adS is not a globally hyperbolic space-time. Thus, we need to impose appropriate boundary conditions in order to have a well-posed quantum field theory. Applying Dirichlet, Neumann and Robin boundary conditions at the spacetime boundary, we have found that the vacuum expectation values of the VP with either Neumann or Dirichlet boundary conditions are constant and respect the maximum symmetry of the background spacetime. This is not seen with Robin boundary conditions however, which depend on the spacetime location. We have also found that both the vacuum and thermal expectation values of the VP, for all Robin parameters (except Dirichlet), converge to the Neumann value at the spacetime boundary whereas the Dirichlet expectation values have a different limit. |
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Jun 6 | Mon | Christian Böhning (Warwick) | The Sheffield Geometry and Physics Seminar |

Abstract:I will report on some ongoing joint work with Hans-Christian von Bothmer (Hamburg) and Lukas Buhr (Mainz). Results due to Druel and Beauville show that the blowup of the intermediate Jacobian of a smooth cubic threefold X in the Fano surface of lines can be identified with a moduli space of semistable sheaves of Chern classes c_1=0, c_2=2, c_3=0 on X. We identify this space with a space of matrix factorisations. This has the advantage that this description naturally generalises to singular and even reducible cubic threefolds. In this way, given a degeneration of X to a reducible cubic threefold X_0, we obtain an associated degeneration of the above moduli spaces of semistable sheaves. |
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Jun 6 | Mon | Navid Nabijou (Cambridge) | The Sheffield Geometry and Physics Seminar |

Abstract:Logarithmic and orbifold structures provide two independent ways to model curves in a variety tangent to a divisor. Simple examples demonstrate that the resulting systems of invariants differ, but a more structural explanation of this defect has remained elusive. I will discuss joint work with Luca Battistella and Dhruv Ranganathan, in which we identify "birational invariance" as the key property distinguishing the two theories. Our proof hinges on a technique – rank reduction – for reducing questions about normal crossings divisors to questions about smooth divisors, where the situation is much better understood. Connections to local curve counting will also be discussed. No prior knowledge of Gromov-Witten theory will be assumed. |
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Jun 1 | Wed | Dan Fretwell (University of South Wales) | Pure Maths Colloquium |

Abstract:A common theme in modern Number Theory is to find interesting discrete objects coming from very different places, but whose arithmetic properties are intimately connected. In this talk we will (hopefully) see a surprising example of this, connecting the first and third objects in the title (using the second to bridge the gap). Time permitting, we will sketch the proof, motivated by a hidden 1.5th object (Clifford algebras). (Based on joint work with E. Assaf, C. Ingalls, A. Logan, S. Secord and J. Voight) |
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May 27 | Fri | Dr Jiajia Liu (Queen's University Belfast) | SP2RC seminar |

Abstract:From geysers and atmospheric jet streams on the Earth to spicules and coronal jets in the solar atmosphere, and astronomical jets from accretion disks, elongated eruptive events exist at a tremendous range of scales in the universe. Unlike their chromospheric counterparts, spicules, which have been widely suggested to be related to the global oscillation of the Sun, solar coronal jets have been mostly studied as localised events. In this talk, I will briefly summarise a series of our work on coronal jets from the aspects of their energy partition and rotational motion, before presenting our recent adventure of exploring the potential link between solar coronal jets and the solar cycle, based on a large dataset built from more than 1200 coronal jets automatically detected from the SDO observations in the past 10 years. |
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May 26 | Thu | Samuel Grant (Queen's University Belfast, United Kingdom) | SP2RC/ESPOS |

Abstract:Solar pores have long been documented as efficient magnetic conduits for propagating magnetohydrodynamic wave energy from the photosphere into the outer regions of the solar atmosphere. Observations of pores often contain isolated and/or unconnected structures, which prevents the statistical examination of wave activity inter- play as a function of atmospheric height. Here, using high resolution observations acquired by the Dunn Solar Telescope, we examine photospheric and chromospheric wave signatures stemming from a unique collection of magnetic pores originating from the same decaying sunspot. A common driver for waves in each pore is detected, allowing for an unprecedented study of each wave guide using novel methods, to gain insight into their underlying attributes, with a view to next-gen solar observatories. |
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May 25 | Wed | Umut Varolgunes (Bogazici University) | Pure Maths Colloquium |

Abstract:In my thesis, I introduced a Floer theoretic invariant for compact subsets of symplectic manifolds called relative symplectic cohomology. This invariant has already proved to be very useful in symplectic rigidity questions and also opened the way to a fruitful reinterpretation of mirror symmetry. Most of these applications rely on an analogue of Mayer-Vietoris property from topology that holds for relative symplectic cohomology under well-understood geometric assumptions. I will briefly introduce the invariant, discuss the Mayer-Vietoris property and present some computations relevant to mirror symmetry. I will try to make the talk accessible to a more diverse audience by mainly sticking to dimension two, where a symplectic form is nothing but an area form. |
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May 25 | Wed | Dan Graves | ShEAF: postgraduate pure maths seminar |

May 23 | Mon | Francesca Carocci (EPFL) | The Sheffield Geometry and Physics Seminar |

Abstract:We consider moduli spaces M(ß,χ) of one-dimensional semistable sheaves on del Pezzo and K3 surfaces supported on ample curve classes. Working over a non-archimedean local field F, we define a natural measure on the F-points of such moduli spaces. We prove that the integral of a certain naturally defined gerbe on M(ß,χ) with respect to this measure is independent of the Euler characteristic. Analogous statements hold for (meromorphic or not) Higgs bundles. Recent results of Maulik-Shen and Kinjo-Coseki imply that these integrals compute the BPS invariants for the del Pezzo case and for Higgs bundles. This is a joint work with Giulio Orecchia and Dimitri Wyss. |
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May 23 | Mon | Lotte Hollands (Heriott-Watt University) | The Sheffield Geometry and Physics Seminar |

Abstract:Recently, there have been various exciting developments in the interplay between BPS structures, topological string partition functions and exact WKB analysis. In this talk I will report on this from the perspective of four-dimensional N=2 field theory and its lift to five dimensions. I will try to explain how the non-perturbative open and closed partition functions for these theories may be obtained from the exact WKB analysis applied to the associated differential/ difference equations, and how these partition functions encode their BPS states. This talk is based on 2109.14699, 2203.08249 and work in progress. |
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May 19 | Thu | Prof Robert Walsh (University of Central Lancashire) | SP2RC seminar |

Abstract:For over 40 years NASA’s Sounding Rocket Program has provided vital scientific, technical, and educational contributions to space science and is still one of the most robust, versatile, and cost-effective ways to undertake innovative space-based research. Sounding rockets carry scientific instruments into space along a parabolic trajectory. Their overall time in space is brief (typically approx. 15 minutes from launch to landing), and at lower vehicle speeds for a well-placed scientific experiment. The cost factor makes sounding rockets an attractive alternative as they do not need expensive boosters or extended telemetry and tracking coverage since they never achieve orbit. This cost effectiveness continues as the sounding rocket program takes advantage of a high degree of commonality and in many cases, only the experiment (provided by the science team) is changed. In almost all astronomy, planetary, solar, and microgravity missions, the payloads are recovered which means the costs of the experiment and sub-systems are spread out over many possible repeated missions. Of course, the limited factor of only a few minutes of true space-based data resulting such a rocket flight must also be taken into account, The solar physics community has benefited greatly over many years from sounding rocket missions for both the calibration of in-operation satellite instrumentation as well as the development of high performance imagers and spectrometers to examine the corona in remarkable ways. This talk will examine some of these missions, outlining what it is like to part of such a “ successful rocket team” (and how to act when things don’t go according to plan!). In particular, the presentation will focus on results from the unique datasets obtained by the Marshall X-ray Imaging Spectrometer and the High Resolution Coronal Imager, both of which are scheduled to fly again in 2023 and 2024 respectively. |
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May 19 | Thu | Ieke Moerdijk | Topology Reading Group |

May 18 | Wed | Ieke Moerdijk | Topology Reading Group |

May 18 | Wed | Shahn Majid (Queen Mary University of London) | Pure Maths Colloquium |

Abstract:We describe recent results in quantum or noncommutative Riemannian geometry based on bimodule connections. Here the coordinate algebra can be any unital algebra A equipped with a differential structure expressed as a bimodule Omega^1 of 1-forms as part of a differential graded algebra with A in degree 0. The simplest case is A the commutative algebra of functions on the vertices of a directed graph with Omega^1 spanned by the arrows. We show in this framework that the intrinsic quantum Riemannian geometry of the A_n graph o-o-…-o of n vertices is necessarily q-deformed with q^{2(n+1)}=1. It's q-> 1 limit is the intrinsic quantum Riemannian geometry of the natural numbers viewed as a half-line graph. We then discuss more generally how solutions of the Yang-Baxter or braid relations arise naturally from noncommutative differential geometry and relate both to quantum jet bundles and to the notion of a quantum geodesic. |
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May 18 | Wed | Francesco Sartini (ENS Lyon) | Cosmology, Relativity and Gravitation |

Abstract:The spacetime in the interior of a black hole can be described by a homogeneous line element, for which the Einstein–Hilbert action reduces to a one-dimensional mechanical model. We have shown that this model exhibits a symmetry under the (2+1)-dimensional Poincaré group. The existence of this symmetry unravels new aspects of symmetry for black holes and opens the way toward a rigorous group quantization of the interior, which in turn provides a powerful tool to discriminate between different regularization schemes. Remarkably, the physical ISO(2,1) symmetry can be seen as a broken infinite-dimensional symmetry. This is done by reinterpreting the action for the model as a geometric action for the BMS3 group, where the configuration space variables are elements of the algebra bms3 and the equations of motion transform as coadjoint vectors. |
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May 12 | Thu | Ieke Moerdijk | Topology Reading Group |

May 11 | Wed | Ieke Moerdijk | Topology Reading Group |

May 11 | Wed | Sven Raum (University of Stockholm) | Pure Maths Colloquium |

Abstract:One of the original motivations of Murray and von Neumann introducing operator algebras was to study the unitary representation theory of groups. This naturally leads to the question of studying building blocks of representation theory, that is simple operator algebras associated with groups. From a modern point of view, not only groups but also other group-like structures such as groupoids should be investigated. This talk introduces the audience to group and groupoid operator algebras and tells the story of how our point of view on their simplicity changed dramatically over the past 10 years. At the end of the talk, I will present some recent results on simple groupoid C*-algebras that were obtained in joint work with Kennedy, Kim, Li and Ursu. |
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May 11 | Wed | Sunny Vagnozzi (Cambridge) | Cosmology, Relativity and Gravitation |

Abstract:Most of the efforts in searching for dark energy (DE) have focused on its gravitational signatures, and in particular on its equation of state. However, there is a lot to be learned by getting off the beaten track. I will first focus on non-gravitational interactions of (screened) DE with visible matter, leading to the possibility of “direct detection of dark energy”, analogous to direct detection of dark matter: I will argue that such interactions can and potentially may already have been detected in experiments such as XENON1T, while discussing some of their complementary cosmological and astrophysical signatures. I will then discuss early- and late-time consistency tests of LCDM, and how these may shed light on (early and late) DE, particularly in relation to the Hubble tension, presenting two such tests based on the early ISW effect and the ages of the oldest astrophysical objects in the Universe. If time allows, I will present new ways of probing more general ultralight particles (which may be related to either dark matter or DE), using black hole shadows and planetary objects such as asteroids. |
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May 9 | Mon | Martijn Kool (Utrecht) | The Sheffield Geometry and Physics Seminar |

Abstract:I will introduce invariants for counting surfaces on Calabi-Yau fourfolds. In a family, they are deformation invariant along Hodge loci. If non-zero, the variational Hodge conjecture for the family under consideration holds. Time permitting, I will discuss DT/PT wall-crossing and relations to Nekrasov's Magnificent Four. Joint work with Y. Bae and H. Park. |
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May 9 | Mon | Balázs Szendrői (Oxford) | The Sheffield Geometry and Physics Seminar |

Abstract:Starting with an ADE singularity C^2/Gamma for Gamma a finite subgroup of SL(2,C), one can build various moduli spaces of geometric and representation-theoretic interest as Nakajima quiver varieties. These spaces depend in particular on a stability parameter; quiver varieties at both generic and non-generic stability are of geometric interest. We will explain some of these connections, focusing in particular on generating functions of Euler characteristics at different points in stability space. Based on joint papers and projects with Craw, Gammelgaard, Gyenge, and Nemethi. |
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May 5 | Thu | Ieke Moerdijk | Topology Reading Group |

May 4 | Wed | Ieke Moerdijk | Topology Reading Group |

May 4 | Wed | Marcel Ortgiese (Bath) | Probability |

Abstract:The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph. Moreover, we generalise the model to include a `temperature' parameter. The interplay between the temperature and the structure of the random graph leads to a very rich phase diagram, where in the different phases different parts of the underlying geometry dominate the time to consensus. Our proofs rely on the well-known duality to coalescing random walks and a detailed understanding of the structure of the random graphs in terms of a thinned Galton-Watson forest. |
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May 4 | Wed | Lissa de Souza Campos (Pavia) | Cosmology, Relativity and Gravitation |

Abstract:I will consider a free, scalar, massive quantum field theory on static spacetimes with a timelike boundary. Invoking the works of Ishibashi and Wald, Sturm-Liouville theory and concepts from algebraic quantum field theory, I will outline the steps to take for the explicit construction of physically-sensible two-point functions admitting generalized Robin boundary conditions. Each boundary condition determines an inequivalent dynamics, but they are all equivalently physically-sensible. I will comment on an ongoing investigation aimed at highlighting an extra ambiguity regarding the choice of boundary conditions at an irregular singularity: there might be not just one or a one-parametric family of, but rather infinite admissible boundary conditions to be taken into account. |
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May 3 | Tue | Domenic Germano (Melbourne) | Mathematical Biology Seminar Series |

Abstract:Simple epithelial tissues occur in various structures throughout the body, such as the endothelium, mesothelium, linings of the lungs, saliva and thyroid glands, and gastrointestinal tract. Despite the prevalence of simple epithelial tissues, the maintenance of tissue and organ structures during dynamic homeostasis is often not well understood. In order for a system to be stable, cell renewal, cell migration and cell death must be finely balanced. Moreover, a tissue’s shape must remain relatively unchanged. Furthermore, for the mathematical biologist, there is a choice to make, regarding appropriate boundaries and how they should be modelled, as not all models result in the same outcome. This talk will contain two parts. In the first part, we will present a novel 3D, multilayer, cell-centre model of simple epithelial tissues. In this model, cell movement is governed by the minimisation of a bending potential across the epithelium, cell-cell adhesion, and viscous effects. Using this model, we will show how the tissue is capable of maintaining a consistent structure while undergoing self renewal. During the second part, we will address the issue of making suitable modelling choices with relation to tissue boundaries. We will present three key models and discuss the advantages and disadvantages of each model, as well as some model applications. |
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Apr 28 | Thu | Ieke Moerdijk | Topology Reading Group |

Apr 27 | Wed | Ieke Moerdijk | Topology Reading Group |

Apr 27 | Wed | Wushi Goldring (University of Stockholm) | Pure Maths Colloquium |

Abstract:Automorphic representations are some of the richest and most mysterious mathematical objects discovered to-date. They simultaneously generalize (i) infinite-dimensional representations of real Lie groups, (ii) modular forms and (iii) the Hecke characters of class field theory. As such, automorphic representations incorporate representation theory, analysis and arithmetic. In the late 1960's, Robert Langlands laid out a program to unravel much of the seemingly hidden structure of automorphic representations. To begin to understand the Langlands program, it is useful -- at least at first -- to distinguish two kinds of conjectures: Roughly, Langlands' Functoriality Principle can be seen as intrinsic to automorphic representations -- revealing a myriad of relations between different automorphic representations of different groups. By contrast, the extrinsic Langlands correspondence explains how certain automorphic representations should be related to Galois theory and algebraic geometry. Every automorphic representation has associated numerical invariants called Hecke eigenvalues -- these are complex numbers. One of the most interesting aspects of the Langlands program is that some automorphic representations have Hecke eigenvalues which are algebraic numbers, while for others they are transcendental. At this time, we seem to lack a conceptual understanding for why this dichotomy exists. While the Langlands correspondence suggests that certain automorphic representations should have algebraic Hecke eigenvalues, it remains unclear -- even at the level of conjectures -- wherein lies the watershed line between algebraic and transcendental. I will spend most of my talk introducing automorphic representations, their Hecke eigenvalues, functoriality and the correspondence. The end goal of my talk is then to explain what can be said about the algebraicity of Hecke eigenvalues by combining (1) Previously known cases of algebraicity and (2) Langlands functoriality. On the one hand, I will explain why the algebraicity of Hecke eigenvalues does propagate from some cases to others via functoriality -- this gives new theorems and conjectures on algebraicity of Hecke eigenvalues. On the other hand, I will explain why most cases -- including Maass forms -- are not reducible to known ones via functoriality. |
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Apr 27 | Wed | Wenkai Xu (Oxford) | Probability |

Abstract:In this talk, I will introduce a novel nonparametric goodness-of-fit testing procedure for exchangeable exponential random graph models (ERGMs) when a single network realisation is observed. The test determines how likely it is that the observation is generated from a target unnormalised ERGM density. The test statistics are derived from a kernel Stein discrepancy, a divergence constructed via Stein’s method using functions in a reproducing kernel Hilbert space, combined with a discrete Stein operator for ERGMs. Theoretical properties for the testing procedure for a class of ERGMs will be discussed; simulation studies and real network applications will be presented. |
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Apr 27 | Wed | Adrián del Rio (Penn State) | Cosmology, Relativity and Gravitation |

Abstract:Since the discovery in 1969 of the anomalous non-conservation of the chiral fermion current in QED, it is known that classical symmetries of field theories may fail to survive the quantization, leading to what is known as quantum anomalies. In this talk I will introduce a new example in the context of quantum electrodynamics and gravity. I will first show that the classical electric-magnetic symmetry of Maxwell theory breaks down quantum-mechanically in curved spacetimes. Then I will show that solutions of Einstein's equations can trigger this effect if and only if they admit a flux of gravitational radiation with net circular polarization. I will argue that typical scenarios where this occurs include binary black holes that break spacetime mirror symmetries, as for instance in precessing systems. The emergence of this anomaly physically implies that some astrophysical systems can spontaneously generate a flux of photons from the quantum vacuum with net helicity. This is not predicted by the Hawking effect and could have interesting implications. |
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Apr 25 | Mon | Naoki Koseki (Edinburgh) | The Sheffield Geometry and Physics Seminar |

Abstract:Recently, Maulik and Toda gave a mathematical definition of the Gopakumar-Vafa(GV) invariants, which are the virtual counts of curves inside a Calabi-Yau 3-fold. GV invariants are conjecturally equivalent to other curve counting theories such as Gromov-Witten invariants (GV=GW conjecture). One of the mysterious features of GV invariants is a chi-independence conjecture, which is expected from GV=GW conjecture. In my recent work with Tasuki Kinjo (Tokyo), we proved the chi-independence of GV invariants for a certain class of non-compact Calabi-Yau 3-dolds, called local curves. I will explain our result and other recent developments of the theory. |
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Apr 25 | Mon | Nadir Fasola (Sheffield) | The Sheffield Geometry and Physics Seminar |

Abstract:Nested Hilbert schemes of points and curves on smooth projective surfaces encode interesting information about enumerative problems and physical theories. Their virtual fundamental classes have been shown to recover both the virtual classes of Seiberg-Witten and reduced stable pair theories, while their obstruction theories can be used to obtain information about Vafa-Witten and reduced Donaldson-Thomas invariants. Motivated by a D-brane construction arising in supersymmetric String Theory, I’ll study the representation theory of an enhancement of the ADHM quiver. This, in a particular case, models nested Hilbert schemes of points on the affine plane or, more generally, flags of framed torsion-free sheaves on the projective plane. The partition function of the theory determined by such a quiver naturally computes generating functions of virtual invariants of moduli spaces of stable representations, which, in turn, are conjectured to carry some information about the cohomology of character varieties via a work of Hausel, Letellier and Rodriguez-Villegas. |
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Apr 6 | Wed | Antonio Ferreiro (Dublin City University) | Cosmology, Relativity and Gravitation |

Abstract:The spontaneous production of particles due to a gravitational field is one of the cornerstones of the theory of quantum fields in curved spacetime. This effect has an important role in our current understanding of the early phases of our Universe. I will introduce this phenomenon and point out the difficulties that arise when computing physical magnitudes, e.g. the stress-energy tensor. Finally, I will show the connection between this effect and the generation of matter during the reheating phase in the inflationary scenario. |
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Mar 31 | Thu | Susanna Parenti (Institut d'Astrophysique Spatiale (IAS), Université Paris-Saclay, CNRS, France) | SP2RC/ESPOS |

Abstract:The 3D MHD global modeling is a powerful tool to test all the possible candidate physical processes responsible for the formation and evolution of the corona and heliosphere. To fully understand the possible role of each of these mechanisms, we need a validation process where the output from the simulations is quantitatively compared to the observational data. In this work, we present the results from our validation process applied to the wave turbulence driven 3D MHD corona-wind model WindPredict-AW. At this stage of the model development, we focus the work to the coronal regime in quiescent condition. We analyze three simulations results, which differ by the boundary values. We use the 3D distributions of density and temperature, output from the simulations at the time of around the first Parker Solar Probe perihelion (during minimum of the solar activity), to synthesize both extreme ultraviolet (EUV) and white light polarized (WL pB) images to reproduce the observed solar corona. For these tests, we selected AIA 193 A, 211 A and 171 A EUV emissions, MLSO K-Cor and LASCO C2 pB images obtained the 6 and 7 November 2018. We then make quantitative comparisons of the disk and off limb corona. We show that our model is able to produce synthetic images comparable to those of the observed corona. |
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Mar 28 | Mon | Angelica Simonetti (Cambridge) | The Sheffield Geometry and Physics Seminar |

Abstract:Cusp singularities and their quotients by a suitable action of Z/2Z are among the surface singularities which appear at the boundary of the compactification of the moduli space of surfaces of general type due to Kollar, Shepherd-Barron and Alexeev. Since only those singularities that admit a smoothing family occur at the boundary of this moduli space, it is useful to find nice conditions under which they happen to be smoothable. We will describe a sufficient condition for a cusp singularity admitting a Z/2Z action to be equivariantly smoothable. In particular we will see it involves the existence of certain Looijenga (or anticanonical) pairs (Y,D) that admit an involution fixed point free away from D and that reverses the orientation of D. |
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Mar 28 | Mon | Qingyuan Jiang (Edinburgh) | The Sheffield Geometry and Physics Seminar |

Abstract:In this talk, we will discuss the counterpart of Grothendieck's projectivization construction in the realm of derived algebraic geometry. (1) We will first discuss the motivations and definitions of derived projectivizations and study their fundamental properties. (2) We will then focus on complexes of perfect-amplitude contained in [0,1]. In this case, the derived projectivizations enjoy special pleasant properties. For example, they satisfy the generalized Serre's theorem and the derived version of Beilinson's relations, and there are structural decompositions for their derived categories. (3) Finally, we will discuss some applications of this framework, including: (3-i) applications to classical situations, such as derived categories of certain reducible schemes and irreducible singular schemes. (3-ii) applications to Hecke correspondence moduli, focusing on the cases of surfaces. (3-iii) applications to moduli of pairs and moduli of extensions, focusing on the cases of curves, surfaces, and threefolds. If time allows, we might also discuss the generalizations of these results to the cases of derived Grassmannians and some other types of derived Quot schemes. |
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Mar 24 | Thu | Fatima Kahil (Max Planck Institute) | Plasma Dynamics Group |

Abstract:The Polarimetric and Helioseismic Imager (PHI) is one of the six remote sensing instruments on board the Solar Orbiter Satellite (SO). It is a spectropolarimetric imager which provides maps of the photospheric magnetic field with a spatial resolution of 200 km at perihelion (0.3 AU). In this talk, I will introduce the SO/PHI instrument and show its proven capabilities tested during the commissioning and cruise phase of the Solar Orbiter. Cross-calibration of the SO/PHI data products with other NEO satellites like SDO will be presented as well. Intercalibration of the SO/PHI high resolution magnetograms with the EUV images of the Extreme Ultraviolet Imager (EUI) on-board SO allowed for studying the magnetic component of the small-scale EUV brightenings detected by EUI and termed campfires. I will present the results of this study and show how the next higher resolution SO/PHI data taken near perihelion at 0.3 AU from the Sun will help improve our understanding of the magnetic origin of these campfires |
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Mar 23 | Wed | Nikita Nikolaev (University of Sheffield) | Pure Maths Colloquium |

Abstract:Complex singular differential equations play a major role far beyond pure mathematics: classical equations like Airy, Bessel, and Schrödinger equations are just some famous examples that appear in physics and engineering. As geometers, we prefer to study their geometric generalisations called meromorphic connections on holomorphic vector bundles over Riemann surfaces (a.k.a. "differential equations on steroids"). There are many excellent reasons to do this: one is that their moduli spaces (i.e., spaces of equivalence classes) have an incredibly rich geometry that links with a vast variety of subjects from (to name just a few) integrable systems and Poisson geometry, to quantum algebras and representation theory, to Gromov-Witten theory and quantum field theory. Moduli spaces of connections are exceptionally captivating objects, "a gift to geometry that keeps on giving" as some of us would say. In broad and as accessible terms as possible, I will present a little bit of this really fascinating story to give you a sense or a glimpse of the subject’s richness. At the end, I will mention a word or two about a new geometric method (called abelianisation) to analyse higher-rank connections (i.e., higher-order differential equations) by placing them in correspondence with much simpler objects: rank-one connections (i.e., first-order differential equations) but over a geometrically more complicated Riemann surface. |
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Mar 23 | Wed | Antonella Palmese (UC Berkeley) | Cosmology, Relativity and Gravitation |

Abstract:The synergy between gravitational wave (GW) experiments, such as LIGO/Virgo, and optical surveys, such as the Dark Energy Survey (DES), is most prominent in the discovery of electromagnetic counterparts to GW events and the application of the standard siren method, which has already enabled several measurements of the Hubble Constant. Our DES follow-up observations of the first binary neutron star merger detected by LIGO/Virgo enabled the discovery of the first optical counterpart to a GW event and the first standard siren measuement, while also providing information about the origin of the binary. We have later extended the standard siren analysis to compact object binary merger events without electromagnetic counterparts using galaxy catalogs, for which I will present the latest results. These measurements are a promising tool to shed light on the Hubble constant tension in the coming years. In the last part of the talk, I will present some interesting possibilities for the formation of the most massive binary black hole mergers detected so far which are related to galaxies’ central black holes, in particular those in dwarf galaxies and Active Galactic Nuclei. |
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Mar 18 | Fri | Dr Mausumi Dikpati (NCAR, Boulder, Colorado) | SP2RC seminar |

Abstract:Abstract: Rossby waves are a class of inertial waves, occurring in thin layers within fluid regions of stars and planets due to the variation in Coriolis forces with latitude.The discovery of Rossby waves (Rossby, 1939) in the Earth's atmosphere led to great advances in the ability to forecast our planet's weather patterns. It is the combination of mean west to east atmospheric flow and (finite amplitude) Rossby waves in the atmosphere that create “jet streams” at midlatitudes. Understanding their interaction and the resulting longitudinal structure allows for accurate prediction of how synoptic weather patterns evolve and propagate to the east. In effect the “jet stream” steers our Earth's weather from location to location in midlatitudes. In the past several years observational evidence has indicated that there are also Rossby waves in the Sun. Although Rossby waves have been detected in the Sun's photosphere and corona, they most likely originate in layers where the vertical extent and radial motions are much less than the horizontal extent and motions. Solar tachocline is such a layer where Rossby waves can be generated in the Sun, and because of predominantly horizontal motions of supergranules in the sub-photospheric layer, that layer can also be a generation layer for solar Rossby waves. Rossby waves differ from their Earth's counterparts by being strongly modified by the magnetic fields in the Sun. After discussing the basics of solar Rossby waves, we will present a few recent simulations of nonlinear interactions between Rossby waves and magnetic fields in solar tachocline. We will show that “tachocline nonlinear oscillations” (TNOs) occur, very much like nonlinear Orr mechanism in fluid dynamics. TNOs have periods similar to those observed in the solar atmosphere— enhanced periods of solar activity, or “seasons”—occurring at intervals between six months and two years. These seasonal/subseasonal activity bursts produce the strongest eruptive space weather events. Thus, a key to forecasting the timing, amplitude, and location of future activity bursts, and hence space weather events, could lie in our ability to simulate the longitudinal patterns produced by the interactions of Rossby waves and magnetic fields. |
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Mar 17 | Thu | Juan Camilo Guevara Gomez (Rosseland Centre for Solar Physics, University of Oslo, Norway) | SP2RC/ESPOS |

Abstract:Magnetohydrodynamic (MHD) waves are thought to be one of the key mechanisms for transferring energy and momentum through the Sun’s atmosphere, hence maintaining the temperature profile of the outer atmospheric layers. Here, we have studied small-scale chromospheric bright features, exhibiting oscillations in brightness temperature, size, and horizontal velocity, in Bands 3 (∼3 mm) and 6 (∼1.2 mm) of 2 seconds cadence solar observations with ALMA, as well as in associated synthetic lines from a Bifrost simulation, degraded to match the ALMA’s spatial and temporal resolutions. In total, 486 and 235 features were analysed in the observations and simulations, respectively. Periods of the oscillations and phase angles between the perturbations in any of the two parameters were characterised by means of wavelet analysis. As a result, median periods were obtained for the oscillations on the order of 90 s (Band 3) and 64 s (Band 6) for brightness temperature, 82 s (Band 3) and 56 s (Band 6) for size and, 65 s (Band 3) and 52 s (Band 6) for horizontal velocity. Phase relations between the high-frequency oscillations in brightness temperature and size suggest the presence of fast and slow MHD sausage modes in the small magnetic structures. In addition, the high-frequency fluctuations in transverse displacement are likely Alfvénic and can be representative of MHD kink mode. Furthermore, we have compared the outcomes between the two ALMA frequency bands as they are considered to be formed at distinct heights in the solar chromosphere and have used the simulations to discuss the context of the observational results. Finally, this study confirms the diagnostic potential of solar ALMA observations with very good cadence and resolution, as well as their essential role as complementary with respect to other diagnostics. |
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Mar 16 | Wed | Hossein Movasati (IMPA) | Pure Maths Colloquium |

Abstract:Clemens' conjecture states that the the number of rational curve in a generic quintic threefold is finite. If it is false we prove that certain periods of rational curves in such a quintic threefold must vanish. Our method is based on a generalization of a proof of Max Noether's theorem using infinitesimal variation of Hodge structures and its reformulation in terms of integrals and Gauss-Manin connection. |
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Mar 16 | Wed | Andrew Wade (Durham) | Probability |

Abstract:I will talk about an interacting particle model motivated by nanoscale growth of ultra-thin films. Particles are deposited (according to a space-time Poisson process) on an interval substrate and perform Brownian motions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier to subsequent particles. This is a continuum version of a lattice model studie in the applied literature. We are interested in the induced interval-splitting process. In particular, we show that the long-time evolution converges to a Markovian interval-splitting process, which we describe. The density that appears in this description is derived from an exit problem for planar Brownian motion from a right-angled triangle, extending work of Smith and Watson. The splitting density has a compact Fourier series expansion but, apparently, no simple closed form. This talk is based on joint work with Nicholas Georgiou (Durham): https://arxiv.org/abs/2010.00671 |
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Mar 14 | Mon | Murad Alim (Hamburg) | The Sheffield Geometry and Physics Seminar |

Abstract:BPS invariants of certain physical theories correspond to Donaldson-Thomas (DT) invariants of an associated Calabi-Yau geometry. BPS structures refer to the data of the DT invariants together with their wall-crossing structure. On the same Calabi-Yau geometry another set of invariants are the Gromov-Witten (GW) invariants. These are organized in the GW potential, which is an asymptotic series in a formal parameter and can be obtained from topological string theory. A further asymptotic series in two parameters is obtained from refined topological string theory which contains the Nekrasov-Shatashvili (NS) limit when one of the two parameters is sent to zero. I will discuss in the case of the resolved conifold how all these asymptotic series lead to difference equations which admit analytic solutions in the expansion parameters. A detailed study of Borel resummation allows one to identify these solutions as Borel sums in a distinguished region in parameter space. The Stokes jumps between different Borel sums encode the BPS invariants of the underlying geometry and are captured in turn by another set of difference equations. I will further show how the Borel analysis of the NS limit connects to the exact WKB study of quantum curves. This is based on joint works with Lotte Hollands, Arpan Saha, Iván Tulli and Jörg Teschner. |
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Mar 14 | Mon | Dimitri Zvonkine (Laboratoire Mathématiques de Versailles) | The Sheffield Geometry and Physics Seminar |

Abstract:We show that there is an effective way to compute all Gromov-Witten (GW) invariants of all complete intersections. The main tool is Jun Li's degeneration formula: it allows one to express GW invariants of a complete intersection from GW invariants of simpler complete intersections. The main difficulty is that, in general, the degeneration formula does not apply to primitive cohomology insertions. To circumvent this difficulty we introduce simple nodal GW invariants. These invariants do not involve primitive cohomology classes, but instead make use of imposed nodal degenerations of the source curve. The algorithm for computing GW invariants relies on two main statements: (i) simple nodal GW invariants can be computed by the degeneration formula, (ii) simple nodal GW invariants determine all GW invariants of a complete intersection. The first statement is geometric; the second uses the invariance of GW invariants under monodromy and some representation theory. This is joint work with Hulya Arguz, Pierrick Bousseau and Rahul Pandharipande. |
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Mar 10 | Thu | Category Theory | |

Abstract:This week we'll be reading sections 2.1, 2.2, 2.3 and 2.4. Find the book here: http://davidjaz.com/Papers/DynamicalBook.pdf |
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Mar 10 | Thu | Abdulaziz Alharbi (Sheffield) | Plasma Dynamics Group |

Abstract:The solar atmospheric plasma is a complex environment, where the plasma changes with height from being controlled by pressure forces to a regime where dynamics is driven by magnetic forces, but also where the plasma changes from being partially ionised to fully ionised. In this talk, I will give an overview of the research I have undertaken throughout my PhD studies on this topic where I discuss results on waves and their properties in strongly and weakly partially ionised plasma using a multi-fluid framework. |
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Mar 9 | Wed | Vesna Stojanoska (University of Illinois Urbana-Champaign) | Pure Maths Colloquium |

Abstract:In classical algebra, the integer primes p help decompose objects as well as problems into their p-primary parts, which may be easier to study. The same is true in homotopy theory, but the situation is more interesting since for each integer prime p, there are infinitely many nested homotopical primes. For each of those homotopical primes, there is an (unramified) Galois group that governs the local story and encodes the symmetries of chromatic homotopy theory. These Galois groups turn out to be particularly nice profinite groups, known as compact p-adic analytic. Such groups and their fascinating duality properties within algebra were studied by Lazard. I will try to explain a newer result, which shows that their homotopical duality properties are even better, giving powerful implications for the chromatic Galois extensions that they govern. |
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Mar 9 | Wed | Susanne Schander (Perimeter Institute ) | Cosmology, Relativity and Gravitation |

Abstract:Several approaches to quantum gravity suggest that the big bang singularity is resolved and is often replaced by a big bounce. This raises the question of whether there are phenomenological consequences of such a scenario. As the physics involved in particular concerns the Planck era before inflation, one expects that quantum backreaction between the homogeneous and inhomogeneous degrees of freedom cannot be neglected in this regime. After a brief introduction to these concepts and the current status of the phenomenology involved, we review space adiabatic perturbation theory (SAPT) which was invented by Panati, Spohn and Teufel as an extension of the well known Born-Oppenheimer approach (BOA) for quantum mechanical systems with backreaction. We explain why BOA is insufficient for quantum cosmology and why an extension of SAPT to quantum field theory is non-trivial. Finally, we apply SAPT to quantum backreaction in cosmology, list which challenges had to be overcome and present the current status of our calculations. |
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Mar 3 | Thu | Szabolcs Soós (Eötvös Loránd University (ELTE), Hungary) | SP2RC/ESPOS |

Abstract:Observational precursors of large solar flares provide a basis for future operational systems for forecasting. We studied the evolution of the normalized emergence (EM), shearing (SH), and total (T) magnetic helicity flux components for 14 flaring (with at least one X-class flare) and 14 nonflaring ( |
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Mar 3 | Thu | William Elbæk Mistegård (Centre for Quantum Mathematics) | The Sheffield Geometry and Physics Seminar |

Abstract:The moduli space of Higgs bundles on a compact Riemann surface was introduced by Hitchin in his study of the self-duality equations on a Riemann surface. This is a quasi-projective hyper-Kähler variety, which supports an algebraic torus-action and a torus-equivariant line bundle generating the Picard group. This line bundle is called the determinant line bundle of cohomology, or determinant line bundle for short. Given an automorphism of the Riemann surface, there is an induced lift to the determinant line bundle. We define and study the automorphism equivariant Hitchin index (AEHI). This the trace of the derived action on the torus-weight spaces of the cohomology of the determinant line bundle. Our study is motivated by topological quantum field theory and complex Chern-Simons theory via non-abelian Hodge theory, which identifies the moduli space of Higgs bundles with the moduli space of flat complex connections on the Riemann surface. We prove that the AEHI is a topological invariant of the three-manifold obtained as the mapping torus of the automorphism of the Riemann surface and we provide an explicit formula for the AEHI in terms of: cohomological pairings of the Atiyah-Bott generators on the moduli space of parabolic bundles on the quotient Riemann surface (i.e. the orbit space of the automorphism), cohomological pairings on symmetric powers of the quotient Riemann surface and Seifert invariants of the mapping torus. These results provides new links between algebraic geometry and quantum topology, and our topological invariant can be seen as a generalization of the Witten-Reshetikhin-Turaev quantum invariant of the mapping torus. This is joint work with J.E. Andersen and T. Hausel. |
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Mar 3 | Thu | Kento Osuga (Warsaw) | The Sheffield Geometry and Physics Seminar |

Abstract:Topological recursion is a recursive formalism that takes an algebraic curve as the initial data, and computes a variety of invariants such as Kontsevich-Witten intersection numbers or knot invariants. Another interesting application of topological recursion is a quantisation of algebraic curves which are often called quantum curves. For degree two curves, topological recursion admits a suitable 1-parameter refinement so-called refined topological recursion. In this talk I will address properties of refined topological recursion and construct explicit form of refined quantum curves for genus zero curves. If time permits, I will also discuss about a somewhat unexpected relation between topological recursion and BPS structures in the refined setting. |
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Mar 2 | Wed | Dr David Kuridze (Aberystwyth University) | SP2RC seminar |

Abstract:The magnetic field is key to the dynamics, evolution, and heating of the solar atmosphere, yet direct measurements are rare and highly uncertain. In this seminar I will discuss about the techniques and challenges of measuring the magnetic field in the corona. I will also present the results from my work where we reported on the unique observations of the flaring coronal loops at the solar limb using high resolution imaging spectropolarimetry from the Swedish 1-meter Solar Telescope. The vantage position, orientation and nature of the chromospheric material that filled the observed flare loops allowed us to determine their magnetic field with unprecedented accuracy. |
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Feb 24 | Thu | Leigh Orf | Plasma Dynamics Group |

Abstract:Supercell thunderstorms are recognized as the one of the earth's most powerful atmospheric phenomena, producing heavy rain, hail, and tornadoes that sometimes result in catastrophic devastation and loss of life. Accurately predicting supercell behavior in order to alert the public remains a top priority for federal forecasters, and much work remains to be done to achieve this goal. Part of the difficulty of forecasting the behavior of these storms stems from our poor understanding of processes that occur within supercells that result in violent tornadoes. In this talk, I will first provide a brief background that includes the mathematical equations and numerical model used in the study, and describe my own specific code development involving I/O and lossy floating point compression. I will then present results from tornado-resolving large eddy supercell thunderstorm simulations conducted on some of the world's most powerful research supercomputers, focusing on processes that are associated with tornado formation and maintenance. I will also present recent research that focuses on the tops of the thunderstorms (what is visible to orbiting meteorological satellites) exploring the behavior of simulated cloud-top features that are associated with the most severe thunderstorms. |
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Feb 23 | Wed | Justin Vines (Albert Einstein Institute Potsdam; UCLA) | Cosmology, Relativity and Gravitation |

Abstract:We will explore some questions, and some (historical and recent) beginnings of answers to them, concerning the scattering of classical and/or quantum waves/fields (massless/massive; spin-0, spin-1/2, ...) off of a spinning black hole, i.e., in a background Kerr spacetime --- and the relationships of such processes to the scattering (and bound states) of various particle-like objects around black holes. |
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Feb 10 | Thu | Prof Thomas Neukirch (University of St Andrews) | SP2RC seminar |

Abstract:Equilibrium models have a variety of useful applications in solar physics, despite the fact that the Sun is highly dynamical. At a fundamental level it is often advisable to start the study of a complex system by finding its steady states. These states can then, for example, be used as a basis for investigating waves and instabilities. Furthermore, the response of the equilibria to the variation of system parameters or boundary conditions can help to explore and predict aspects of the nonlinear behaviour of the system. However, in this talk I will mainly focus on a more practical aspect, namely the use of equilibrium models in the extrapolation of photospheric magnetic field measurements into the solar corona. While potential and force-free magnetic field models are still the most widely used equilibrium solutions for this task, over the past few years some extrapolation methods have employed magnetohydrostatic solutions. I plan to discuss some of the approaches used, with an emphasis on analytical methods. |
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Feb 10 | Thu | Samuel Skirvin (University of Sheffield) | Plasma Dynamics Group |

Abstract:In this talk I will give an overview of the research I have undertaken throughout my PhD journey. I will introduce a numerical eigensolver that is capable of finding the permissible wave solutions in any symmetrically non-uniform equilibrium relevant to the solar atmosphere, in both a Cartesian and cylindrical geometry. Results of the numerical approach are compared with known analytical solutions which are then extended to investigate a number of non-uniform case studies including (i) non-uniform plasma density in a magnetic slab (ii) non-uniform plasma flow in a coronal slab (iii) non-uniform plasma density in a magnetic flux tube (iv) non-uniform plasma flow in a coronal flux tube (v) linear and non-linear rotational plasma flow in a magnetic flux tube. For a number of case studies, both 2D and 3D visualisations of the resulting propagating MHD modes are shown. Implications of the results for observations and seismological purposes are discussed. |
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Feb 9 | Wed | David Stefanyszyn (Cambridge) | Cosmology, Relativity and Gravitation |

Abstract:Our understanding of observables in AdS space and Minkowski space is well developed. We can construct boundary observables in AdS space, and the S-matrix in Minkowski space, using fundamental physical principles such as symmetries, locality and unitarity while avoiding the numerous redundancies associated with local Lagrangians. Our understanding of observables in dS space is however significantly less well developed even though dS space is an integral part of our best descriptions of the early and late universe. In this talk I will present recent progress on our efforts to bootstrap cosmological correlation functions in dS space. I will mostly concentrate on inflationary correlators and explain how we can construct them directly using symmetries, locality and unitarity without having to work with specific models. I will illustrate the power of these bootstrap methods by showing how gravitational three-point functions are heavily constrained by these physical principles despite the complications of the corresponding Lagrangian descriptions. |
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Feb 7 | Mon | Jeongseok Oh (Imperial College) | The Sheffield Geometry and Physics Seminar |

Abstract:For a compact quasi-smooth derived scheme M with (-1)-shifted cotangent bundle N, there are at least two ways to localise the virtual cycle of N to M via torus and cosection localisations, introduced by Jiang-Thomas. We produce virtual cycles on both the projective completion and projectivisation of N and show the ones on the former push down to Jiang-Thomas cycles and the one on the latter computes the difference. Using the idea we study the difference between quintic and formal quintic Gromov-Witten invariants. |
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Feb 7 | Mon | Qaasim Shaafi (Imperial College) | The Sheffield Geometry and Physics Seminar |

Abstract:Gromov-Witten invariants play an essential role in mirror symmetry and enumerative geometry. Despite this, there are few effective tools for computing Gromov-Witten invariants of blow-ups. Blow-ups of X can be rewritten as subvarieties of Grassmann bundles over X. In joint work with Tom Coates and Wendelin Lutz, we exploit this fact and extend the abelian/non-abelian correspondence, a modern tool in Gromov-Witten theory. Combining these two steps allows us to get at the genus 0 invariants of a large class of blow-ups. |
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Feb 2 | Wed | David Benisty (Cambridge) | Cosmology, Relativity and Gravitation |

Abstract:From the assumption that the slow roll parameter $\epsilon$ has a Lorentzian form as a function of the e-folds number N, a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of $\epsilon$ to 1 at the end of the inflationary epoch. In the late universe $\epsilon$ becomes small again and this leads to the Dark Energy epoch. The observables that the models predict fits with the latest Planck data: r ∼ 10−3 , ns ≈ 0.965. Naturally a large dimensionless factor that exponentially amplifies the inflationary scale and exponentially suppresses the dark energy scale appears, producing a sort of cosmological seesaw mechanism. We find the corresponding scalar Quintessential Inflationary potential with two flat regions - one inflationary and one as a dark energy with slow roll behavior. |
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Jan 20 | Thu | Vigeesh Gangadharan (Leibniz Institute for Solar Physics (KIS), Germany) | SP2RC/ESPOS |

Abstract:Internal gravity waves (IGWs) are buoyancy-driven waves common in the Earth’s atmosphere and oceans. IGWs have also been observed in the Sun’s atmosphere and are thought to play an important role in the overall dynamics of the solar atmosphere. They supply bulk of the wave energy for the lower solar atmosphere, but their existence and role in the energy balance of the upper layer remains unclear. Using radiation-magnetohydrodynamic (R-MHD) simulations, we study naturally excited IGWs in realistic models of the solar atmosphere. In this talk, we discuss some of our recent results on the influence of the Sun’s magnetic field on the propagation of IGWs and their energy transport. Our analysis suggests that the IGWs are generated independent of the mean magnetic property of the atmosphere. However, their propagation into higher layers is strongly affected by the presence and the topology of the magnetic field. We discuss how IGWs may play a significant role in the heating of the chromospheric layers in regions where horizontal fields are thought to be prevalent, like the internetwork region. |
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Jan 13 | Thu | Prof James McLaughlin (Northumbria University) | SP2RC seminar |

Abstract:Oscillatory Reconnection – a relaxation mechanism with periodic changes in connectivity – has been proposed as a potential physical mechanism underpinning several periodic phenomena in the solar atmosphere, including quasi-periodic pulsations (QPPs). At its heart, Oscillatory Reconnection is a time-dependent reconnection process and the dynamic release of stored magnetic energy is central to multiple fields of study (including solar physics, astrophysics, fusion, laboratory-based plasma, computational MHD and space weather). This talk will review the state-of-the-art in this area, and we reveal a relationship between the equilibrium magnetic field strength, decay rate and period, which opens the tantalising possibility of utilising Oscillatory Reconnection as a seismological tool. Reference: McLaughlin et al. (2018, Space Science Reviews, 214, 45) + Zimovets, McLaughlin, et al. (2021, Space Science Reviews, 217, 66) + Karampelas, McLaughlin, et al. (2022, Astrophysical Journal, accepted) |
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