# Seminars this semester

Series:

 Jan 16 Wed Atsushi Takahashi (Osaka) Algebra / Algebraic Geometry seminar 16:00 J11 On a full exceptional collection in the category of maximally graded matrix factorizations of an invertible polynomial of chain type Abstract: In ’77 Orlik-Randell asked about the existence of a certain distinguished basis of vanishing cycles in the Milnor fiber associated to an invertible polynomial of chain type. With my student, Daisuke Aramaki we transport their conjecture to the category of matrix factorizations by the (conjectural) homological mirror symmetry equivalence and then prove the resulting statement. Jan 17 Thu Ricardo Gaferia (Instituto de Astrofísica de Andalucía - CSIC ) SP2RC seminar 10:00 LT 10 Machine learning assisted parallel inversions Abstract: With the increase of data volume and the need of more complex inversion codes to interpret and analyze solar observations, it is necessary to develop new tools to boost inversions and reduce computation times and costs. In this presentation, I discuss the possibilities and limitations of using machine learning as a tool to estimate optimum initial physical atmospheric models necessary for initializing spectral line inversions. Tests have been carried out for the SIR and DeSIRer inversion codes. This approach allows firstly to reduce the number of cycles in the inversion and increase the number of nodes and secondly to automatically cluster pixels which is an important step to invert maps where completely different regimes are present. Finally, I also present a warp for SIR and DeSIRer inversion codes that allows the user to easily set up parallel inversions. Jan 18 Fri Norbert Gyenge (Sheffield) SP2RC seminar 13:00 LT 10 The Nonaxisymmetric Behaviour Of Solar Eruptive Events Abstract: This thesis investigates new approaches for predicting the occurrence of solar eruptive events based on coronal mass ejection (CME), solar flare and sunspot group observations. The scope of the present work is to study the spatio-temporal properties of the above-mentioned solar features. The analysis may also provide a deeper understanding of the subject of solar magnetic field reorganisation. Furthermore, the applied approaches may open opportunities for connecting these local phenomena with the global physical processes that generate the magnetic field of the Sun, called the solar dynamo. The investigation utilises large solar flare statistical populations and advanced computational tools, such as clustering techniques, wavelet analysis, autoregressive moving average (ARIMA) forecast, kernel density estimations (KDEs) and so on. This work does not attempt to make actual predictions because it is out of the scope of the recent investigation. However, the thesis introduces new possible approaches in the subject of flare and CME forecasting. The future aim is to construct a real-time database with the ability to forecast eruptive events based on the findings of this thesis. This potential forecasting model may be crucial for protecting a wide range of satellite systems around the Earth or predicting space weather based on the obtained results may also assist to plan safe space exploration in the future. Jan 23 Wed Richard Webb (Cambridge) Pure Maths Colloquium 14:00 J11 An interplay between topology, geometry, and the algebra of the mapping class group Abstract: The braid groups were defined by Artin in 1925, and are usually defined in terms of strings in 3-dimensional space. However there is a fruitful 2-dimensional perspective of the braid groups as homeomorphisms (up to some natural equivalence) of a disc with holes, in other words, the braid groups are special cases of mapping class groups of surfaces. Mapping class groups can be viewed in a number of ways, and are of interest in several different fields, such as dynamics, algebraic geometry, surface bundles, hyperbolic geometry, to name a few. A key theorem that demonstrates this intradisciplinary feature is the Nielsen--Thurston classification. I will explain what the Nielsen--Thurston classification is, describe some basic examples and analogies, and highlight its importance. I will then explain how to view this from the geometric group theory perspective, and discuss my work with Mark Bell that uses this point of view to solve the conjugacy problem for mapping class groups in polynomial time. At the end of the talk I will discuss some new ideas that may lead to applications in knot theory via the braid groups. Jan 25 Fri Kalevi Mursula (University of Oulu) SP2RC seminar 10:30 LT E Centennial evolution and terrestrial effects of the global solar magnetic field Jan 31 Thu Prof. Valery Nakariakov (Centre for Fusion, Space and Astrophysics, University of Warwick) Plasma Dynamics Group 15:00 Lecture theatre 1 (Hicks Building) The effect of thermal misbalance on compressive oscillations in solar coronal loops Abstract: Fast and slow magnetoacoustic waves are a promising tool for the seismological diagnostics of physical parameters of various plasma structures in the corona of the Sun. In particular, compressive waves can provide us with information about the thermodynamic equilibrium in the coronal plasma, and hence the heating function. Compressive perturbations of the thermodynamic equilibrium by magnetoacoustic waves can cause the misbalance of the radiative cooling and unspecified heating. The effect of the misbalance is determined by the derivatives of the combined heating/cooling function with respect to the plasma density and temperature, and can lead to either enhanced damping of the compressive oscillations or their magnification. Moreover, in the regime of strong misbalance, compressive MHD waves are subject to wave dispersion that can slow down the formation of shocks and can cause the formation of quasi-periodic wave trains. Feb 6 Wed Viveka Erlandsson (Bristol) Pure Maths Colloquium 14:00 J11 Determining the shape of a billiard table from its bounces Abstract: Consider a billiard table shaped as a Euclidean polygon with labeled sides. A ball moving around on the table determines a bi-infinite “bounce sequence” by recording the labels of the sides it bounces off. We call the set of all possible bounce sequences the “bounce spectrum” of the table. In this talk I will explain why the bounce spectrum essentially determines the shape of the table: with the exception of a very small family (right-angled tables), if two tables have the same bounce spectrum, then they have to be related by a Euclidean similarity. The main ingredient in proving this fact is a technical result about non-singular geodesics on surfaces equipped with flat cone metrics. This is joint work with Moon Duchin, Chris Leininger, and Chandrika Sadanand. Feb 7 Thu Jeremy Colman (Sheffield) Statistics Seminar 14:00 LT E Accounting for Uncertainty in Estimates of Extremes Abstract: Devastating consequences can flow from the failure of certain structures, such as coastal flood defences, nuclear installations, and oil rigs. Their design needs to be robust under rare (p < 0.0001) extreme conditions, but how can the designers use data typically from only a few decades to predict the size of an event that might occur once in 10,000 years? Extreme Value Theory claims to provide a sound basis for such far-out-of-sample prediction, and using Bayesian methods a full posterior distribution can be obtained. If the past data are supplemented by priors that take into account expert opinion, seemingly tight estimates result. Are such claims justified? Has all uncertainty been taken into account? My research is addressing these questions. Feb 7 Thu Masahiro Nakahara (Manchester) Number Theory seminar 14:00 J11 Index of Fibrations and Brauer classes that never obstruct the Hasse principle Abstract: Let X be a smooth projective variety over a number field with a fibration into varieties that satisfy a certain condition. We study the classes in the Brauer group of X that never obstruct the Hasse principle for X. We prove that if the generic fiber has a zero-cycle of degree d over the generic point, then the Brauer classes whose orders are prime to d do not play a role in the Brauer-Manin obstruction. As a result we show that the odd torsion Brauer classes never obstruct the Hasse principle for del Pezzo surfaces of degree 2, certain K3 surfaces, and Kummer varieties. Feb 13 Wed Ana Caraiani (Imperial) Pure Maths Colloquium 14:00 J11 On the Ramanujan conjecture and its generalisations Abstract: In 1916, Ramanujan made a conjecture that can be stated in completely elementary terms: he predicted an upper bound on the coefficients of a power series obtained by expanding a certain infinite product. In this talk, I will discuss a more sophisticated interpretation of this conjecture, via the Fourier coefficients of a highly symmetric function known as a modular form. I will give a hint of the idea in Deligne’s proof of the conjecture in the 1970’s, who related it to the arithmetic geometry of smooth projective varieties over finite fields. Finally, I will discuss generalisations of this conjecture and some recent progress on these using the machinery of the Langlands program. The last part is based on joint work with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne. Feb 14 Thu Carolina Robustini (Stockholm University) 10:00 Chromospheric observations and magnetic configuration of a supergranular structure Abstract: We present high spatial resolution narrow-band images in three different chromospheric spectral lines, including Ca II K with the new CHROMospheric Imaging Spectrometer installed at the Swedish 1-m Solar Telescope. These observations feature a unipolar region enclosed in a supergranular cell, and located 68º off the disk-centre. The observed cell exhibits a radial arrangement of the fibrils which recalls of a chromospheric rosette. However, in this case, the convergence point of the fibrils is located at the very centre of the supergranular cell. Our study aims to show how the chromosphere appears in this peculiar region and retrieve its magnetic field and velocity distribution. In the centre of the cell, we measured a significant blue-shift in the Ca II K nominal line core associated to an intensity enhancement. We interpreted it as the product of a strong velocity gradient along the line of sight. In this talk, we will discuss the techniques employed to obtain magnetic field maps so close to the limb and suggest a possible configuration that takes into account also the measured velocity within the unipolar region. Feb 14 Thu Eleanor Stillman (Sheffield) 12:00 Hicks LT5 An overview of the HEA direct application process. Abstract: This talk will outline the process of directly applying to become a (associate-principal) fellow of the HEA. The talk will help Ph.D. students to Professors understand what is required in the application and how to be successful. We may also discuss the value and implications of receiving professional recognition from the HEA. Feb 14 Thu Andrey Lazarev (Lancaster) Topology seminar 16:00 J11 Homotopy theory of monoids Abstract: I will explain how the category of discrete monoids models the homotopy category of connected spaces. This correspondence is based on derived localization of associative algebras and could be viewed as an algebraization result, somewhat similar to rational homotopy theory (although not as structured). Closely related to this circle of ideas is a generalization of Adams’s cobar construction to general nonsimply connected spaces due to recent works of Rivera-Zeinalian and Hess-Tonks. (joint with J. Chuang and J. Holstein) Feb 14 Thu Will Hulme / Nick Monk / Rhoda Hawkins (Manchester / Sheffield / Sheffield) RSS Seminar Series 16:30 Hicks Room F38 Experiences of AIMS Abstract: AIMS is an academic network that enables Africa’s talented students to become innovators who propel scientific, educational and economic self-sufficiency. The RSS Local Group are delighted to welcome Will Hulme (University of Manchester, taught at AIMS Cameroon), Prof Nick Monk (University of Sheffield, SOMAS, taught at AIMS Ghana) and Dr Rhoda Hawkins (University of Sheffield, Department of Physics and Astronomy, taught at AIMS South Africa, Senegal and Ghana) to present on their experiences on the AIMS project. Tutor/lecturer opportunities that may be of interest will be highlighted. Feb 15 Fri Dan Graves THH reading group 14:00 J11 Hochschild Homology and Cyclic Homology of rings Feb 20 Wed Farrell Brumley (Paris 13) Northern Number Theory Seminar 11:00 J11 Concentration properties of theta lifts Abstract: I will present some results on the concentration properties of automorphic forms obtained through the theta correspondence. Among other things, the method relies on a distinction principle for these lifts, which detect their functorial origin via the non vanishing of orthogonal periods. The examples we treat are in higher rank, and shed light on a purity conjecture of Sarnak. This is joint work with Simon Marshall. Feb 20 Wed Heather Harrington (Oxford) Applied Mathematics Colloquium 14:00 Hicks, LT 9 Comparing models and biological data using computational algebra and topology Abstract: Many biological problems, such as tumor-induced angiogenesis (the growth of blood vessels to provide nutrients to a tumor), or signaling pathways involved in the dysfunction of cancer (sets of molecules that interact that turn genes on/off and ultimately determine whether a cell lives or dies), can be modeled using differential equations. There are many challenges with analyzing these types of mathematical models, for example, rate constants, often referred to as parameter values, are difficult to measure or estimate from available data. I will present mathematical methods we have developed to enable us to compare mathematical models with experimental data. Depending on the type of data available, and the type of model constructed, we have combined techniques from computational algebraic geometry and topology, with statistics, networks and optimization to compare and classify models without necessarily estimating parameters. Specifically, I will introduce our methods that use computational algebraic geometry (e.g., Gröbner bases) and computational algebraic topology (e.g., persistent homology). I will present applications of our methodology on datasets involving cancer. Time permitting, I will conclude with our current work for analyzing spatio-temporal datasets with multiple parameters using computational algebraic topology. Mathematically, this is studying a module over a multivariate polynomial ring, and finding discriminating and computable invariants. Feb 20 Wed Andreea Mocanu (University of Nottingham) Northern Number Theory Seminar 14:00 J11 Newform theory for Jacobi forms of lattice index Abstract: I will give a brief introduction to Jacobi forms, including some examples and their relation to other types of modular forms. After that, I will discuss some of the ingredients that go into developing a theory of newforms for Jacobi forms of lattice index, namely Hecke operators, level raising operators and orthogonal groups of discriminant modules. Feb 20 Wed Clark Barwick (Edinburgh) Topology seminar 16:00 LT11 Primes, knots, and exodromy Abstract: Half a century ago, Barry Mazur and David Mumford suggested a remarkable dictionary between prime numbers and knots. I will explain how the story of exodromy permits one to make this dictionary precise, and I will describe some applications. Feb 21 Thu Farrell Brumley (Paris 13) Pure Maths Colloquium 14:00 J11 Automorphic forms and rational points Abstract: In what sense can automorphic forms or Galois representations be viewed as rational points on an algebraic variety? One way to explore this question is by counting arguments. The first result in this direction dates back to an early theorem of Drinfeld, which computes the number of 2-dimensional Galois representations of a function field in positive characteristic; the resulting expression is reminiscent of a Lefschetz fixed point theorem on a smooth algebraic variety over a finite field. More recently it was observed that in the number field setting there are formal similarities between the asymptotic counting problems for rational points on Fano varieties and for automorphic representations on reductive algebraic groups. Very little is known in the latter context. I’ll discuss joint work on this topic with Djordje Milicevic, in which we (mostly) solve the automorphic counting problem on the general linear group. Our results can be viewed as being analogous to the well-known result of Schanuel on the number of rational points of bounded height on projective spaces. If time permits, I may also present a short argument, using sphere packings in large dimensions, to give upper bounds on such automorphic counts. Feb 21 Thu Sophia Wright (Warwick) Statistics Seminar 14:00 LT E Bayesian Networks, Total Variation and Robustness Abstract: This talk explores the robustness of large Bayesian Networks when applied in decision support systems which have a pre-specified subset of target variables. We develop new methodology, underpinned by the total variation distance, to determine whether simplifications which are currently employed in the practical implementation of such graphical systems are theoretically valid. This same process can identify areas of the system which should be prioritised if elicitation is required. This versatile framework enables us to study the effects of misspecification within a Bayesian network (BN), and also extend the methodology to quantify temporal effects within Dynamic BNs. Unlike current robustness analyses, our new technology can be applied throughout the construction of the BN model; enabling us to create tailored, bespoke models. For illustrative purposes we shall explore the field of Food Security within the UK. Feb 22 Fri James Cranch THH reading group 14:00 J11 Topological Hochschild Homology Feb 27 Wed Raven Waller (Nottingham) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks Level structures - a crossroads between topology, representation theory, and number theory Abstract: The arithmetic, algebraic, and topological properties of local fields are intimately related. For higher dimensional local objects these relationships begin to break down, and this may cause considerable difficulty when studying them. The notion of a level structure allows us to work around some of these issues. We will discuss various applications of level structures, including the explicit study of representations of reductive groups over higher dimensional local fields, which is also related to the geometric Langlands program. Feb 28 Thu Björn Löptien (Max Planck Institute for Solar System Research ) 10:00 F41 A new method for measuring the Wilson depression of sunspots Abstract: The Wilson depression is the difference in geometric height of the layer of unit continuum optical depth between the sunspot umbra and the quiet Sun. Measuring the Wilson depression is important for understanding the geometry of sunspots. Current methods suffer from systematic effects or need to make assumptions on the geometry of the magnetic field. This leads to large systematic uncertainties of the derived Wilson depressions. Here we present a method for deriving the Wilson depression that only requires the information about the magnetic field that are accessible by spectropolarimetry and that does not rely on assumptions on the geometry of sunspots or on its magnetic field. Our method is based on minimizing the divergence of the magnetic field vector derived from spectropolarimetric observations. We focus on large spatial scales only in order to reduce the number of free parameters. We test the performance of our method using synthetic Hinode data derived from two sunspot simulations. We find that the maximum and the umbral averaged Wilson depression for both spots determined with our method typically lies within 100 km of the true value obtained from the simulations. In addition, we apply the method to spots from the Hinode sunspot database at MPS. The derived Wilson depressions (500-700 km) are consistent with results typically obtained from the Wilson effect. In our sample, larger spots with a stronger magnetic field exhibit a higher Wilson depression than smaller spots. Feb 28 Thu Dan Graves and Sarah Whitehouse Teaching Lunch 13:00 Hicks LT6 Analysis and AiM Abstract: Sarah will start by talking about various changes that have been made to MAS221 Analysis to address issues of poor student engagement and poor exam performance. This includes use of the AiM online test system for mid-term assessment. Dan will present examples of the type of AiM questions that have been used in MAS221 and in MAS220 Algebra, including proofs and multiple choice questions. Feb 28 Thu Wil Ward (Sheffield) Statistics Seminar 14:00 LT E A Variational Approach to Approximating State Space Gaussian Processes Abstract: The state space representation of a Gaussian process (GP) models the dynamics of an unknown (non-linear) function as a white-noise driven Itô differential equation. Representation in this form allows for the construction of joint models that mix known dynamics (e.g. population) with latent unknown input. Where these interactions are non-linear, or observed through non-Gaussian likelihoods, there is no exact solution and approximation techniques are required. This talk introduces an approach using black box variational inference to model surrogate samples and estimate the underlying parameters. The approximations are compared with full batch solutions and demonstrated to be indistinguishable in two-sample tests. Software and implementation challenges will also be addressed. Feb 28 Thu Scott Balchin (Warwick) Topology seminar 16:00 J11 Adelic reconstruction in prismatic chromatic homotopy theory Abstract: Prismatic homotopy theory is the study of stable monoidal homotopy theories through their Balmer spectrum. In this talk, I will discuss how one can use localised p-complete data at each Balmer prime in an adelic fashion to reconstruct the homotopy theory in question. There are two such models, one is done by moving to categories of modules, which, for example, recovers the algebraic models for G-equivariant cohomology theories. The other, newer model, works purely at the categorical level and requires the theory of weighted homotopy limits. This is joint work with J.P.C Greenlees. Feb 28 Thu Mark Wrigley (Chair IOP Yorkshire) Plasma Dynamics Group 16:00 Room K14 (Hicks Building) 1201 Alarm Project Abstract: The 1201 Alarm Project is the restoration, exhibition and sharing of materials recorded in 1969 of the Apollo moon landings from a domestic television. The talk will review the Apollo flight plan, the recording technologies of the day and the impact that it had on the speaker. The materials will form the basis for an exhibition celebrating the 50th anniversary of moon landings to be held at the National Science and Media Museum in Bradford, Yorkshire. Mar 1 Fri Luca Pol THH reading group 14:00 J11 Computations of THH Mar 6 Wed Matt Aldridge / Sarah Penington / Helena Stage / Henning Sulzbach (Leeds / Bath / Manchester / Birmingham) Probability in the North East 12:30 LT C Mar 6 Wed Gwyneth Stallard (Open University) Pure Maths Colloquium 14:00 J11 Complex dynamics: the intriguing case of wandering domains Abstract: Complex dynamics concerns the iteration of analytic functions of the complex plane. For each function, the plane is split into two sets: the Fatou set (where the behaviour of the iterates is stable under local variation) and the Julia set (where the behaviour is chaotic). The dynamical behaviour of the iterates inside the periodic components of the Fatou set was classified into four different types by the founders of the subject and this classification has played a key role in the development of the subject. One of the most dramatic breakthroughs was given by Sullivan in the 1980s when he proved that, for rational functions, all components of the Fatou set are eventually periodic and there are no so-called wandering domains. For transcendental functions, however, wandering domains can exist and the rich variety of possible behaviours that can occur is only just becoming apparent. Mar 6 Wed Rachael Hardman (SoMaS) Applied Mathematics Colloquium 14:00 Hicks, K14 Measuring the Ocean Spectrum using HF Radar Data and a Neural Network Abstract: High frequency, or HF, coastal radars can provide continuous high resolution measurements of ocean surface currents, winds and waves. First derived in 1972, the expected radar signal when electromagnetic waves are scattered by the ocean surface can be modelled by the radar cross section, a nonlinear integral equation which enables us to predict the radar output for any ocean state. Methods for inverting the radar cross section - which ultimately permit us to measure ocean parameters from HF radar data - have been developed over the last few decades; however there are times when the measured data cannot be modelled by the mathematical equations and are therefore not suitable for inversion using the existing methods. Using a neural network, trained on simulated radar data, we have successfully inverted HF radar data not modelled by the radar cross section. In this talk, I will give an overview of how HF radar is used in ocean sensing before introducing neural networks. I will finish by presenting the results of a validation experiment, showing how a neural network can learn the complex inverse relationship between HF radar and the ocean surface. Mar 6 Wed Paolo Dolce (Nottingham) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks Two dimensional adelic geometry Abstract: I will give an overview of a novel approach to the study of two dimensional algebraic and arithmetic geometry by means of adelic and idelic structures. Particular emphasis will be given to the case of arithmetic surfaces since the aim of the theory is to give a two dimensional version of Tate's thesis. Mar 7 Thu Christian Fonseca Mora (Costa Rica) Statistics Seminar 14:00 LT E Stochastic PDEs in Infinite Dimensional Spaces Abstract: In this talk we will give an introduction to SPDEs in spaces of distributions. In the first part of the talk we consider a model of environmental pollution with Poisson deposits that will help to introduce the basic concepts for the study of SPDEs on infinite dimensional spaces. In the second part of the talk, we introduce a generalized form of SPDEs in spaces of distributions and explain conditions for the existence and uniqueness of its solutions. For this talk we will not assume any previous knowledge on SPDEs. Mar 7 Thu Jean-Stefan Koskivirta (Tokyo) Number Theory seminar 14:00 J11 Ampleness and vanishing results Abstract: We explain an application of the existence of generalized Hasse invariants to show ampleness of certain line bundles on flag spaces of Shimura varieties of Hodge type in positive characteristic. These methods generalize to other types of schemes which carry a universal G-zip. We deduce vanishing results for the cohomology of automorphic vector bundles. We compare them with similar results of Lan-Suh. Mar 7 Thu Irakli Patchkoria (Aberdeen) Topology seminar 16:00 J11 Computations in real topological Hochschild and cyclic homology Abstract: The real topological Hochschild and cyclic homology (THR, TCR) are invariants for rings with anti-involution which approximate the real algebraic K-theory. In this talk we will introduce these objects and report about recent computations. In particular we will dicuss components of THR and TCR and some recent and ongoing computations for finite fields. This is all joint with E. Dotto and K. Moi. Mar 7 Thu Patrick Antolin (University of St Andrews) Plasma Dynamics Group 16:00 Room K14 (Hicks Building) Transverse MHD Waves and associated dynamic instabilities in the solar atmosphere Abstract: A large amount of recent simulations and analytical work indicate that standing transverse MHD waves in loops should easily lead to the generation of dynamic instabilities at their edges, and in particular of the Kelvin-Helmholtz kind. While a direct observation of these transverse wave-induced Kelvin-Helmholtz rolls (or TWIH rolls) is still lacking, the forward modelling of these simulations give us an indication of what to look for in next generation instrumentation, and which currently observed features could actually be the result of TWIKH rolls. In this talk I will go through some of these results, comparing observations with various instruments with simulations of coronal loops, prominences and spicules. Mar 7 Thu David Robinson (Capital One) RSS Seminar Series 16:30 F38 Data Science & Machine Learning Abstract: David will start his talk with a brief history of Statistics and Data Science at Capital One: how we got here, what's changed, and what the current expectations and challenges are in the era of "Big Data" and "Machine Learning". The main technical focus will then be on the use of "Gradient Boosting Machines", which over the last few years have emerged as the modelling method of choice for most classification problems within Financial Services. David will cover what they are, why they have become popular and how many of the practical considerations and pitfalls of traditional statistical techniques still very much apply. Example uses will focus on credit risk and affordability, looking at how we can ensure we make fair lending decisions when faced with unfair and biased data. Mar 8 Fri Hope Thackray, Jake Percival, Bryony Moody (Sheffield) Postgraduate seminars 16:00 J11 PGR Student Seminar Abstract: Hope Thackray - How do we see inside the Sun? Much like the waves known to exist above the solar surface, the Sun itself exhibits a widespread pulsation, mimicking the beating of a heart. Sound waves resonate inside the Sun, buffeting the surface, and causing light emitted to experience Doppler-shifting. The structures of these resonant cavities may then be deduced from observations of these shifts, allowing us to "see'' the Sun's interior. Here, one such method of deriving the Sun's sub-surface flows is described, in a technique known as Ring Diagram Analysis. Jake Percival - RNG's: How computers handle randomness When we want a “random” number in everyday life, such as when playing a board game, we rely on processes that aren't truly random, such as rolling a die. Perhaps more reliable would be to ask a computer to produce a random number for us. The code used to give these numbers is called a Random Number Generator (RNG) and like rolling a die, they aren't truly random! But if they aren't random, what is actually happening “under the hood”? In this talk we'll look at how RNG's work and how they can go wrong, including a fun example from the world of video games! Bryony Moody - The hidden layer of statistics in archaeology This talk will give a brief overview of Bayesian inference and the concepts of prior and posterior knowledge. Then I will discuss the various forms of prior knowledge available in archaeology, as well as the data that are used in conjunction with the prior knowledge to form a posterior. Finally I will conclude by discussing the priors I am focusing on for my PhD and what my plans are for modelling them. Mar 12 Tue Giovanni Marchetti Algebraic Geometry Learning Seminar 13:00 J11 Motivic Homotopy Reading Seminar Abstract: Talk 1: Ouverture. Mar 13 Wed Fatemeh Mohammadi (Bristol) Pure Maths Colloquium 14:00 J11 Chip-firing game and Riemann-Roch theory for graphs Abstract: Theory of divisors on graphs is analogous to the classical theory for algebraic curves. The combinatorial language in this setting is "chip-firing game” which has been independently introduced in other fields. A divisor on a graph is simply a configuration of dollars (integer numbers) on its vertices. In each step of the chip-firing game we are allowed to select a vertex and then lend one dollar to each of its neighbors, or borrow one dollar from each of its neighbors. The goal of the chip-firing game is to get all the vertices out of debt. In this setting, there is a combinatorial analogue of the classical Riemann-Roch theorem. I will explain the mathematical structure arising from this process and how it sits in a more general framework of (graphical) hyperplane arrangements. Mar 13 Wed Tobias Grafke (Warwick) Applied Mathematics Colloquium 14:00 Hicks, LT 9 Hydrodynamic instantons and the universal route to rogue waves Abstract: In stochastic systems, extreme events are known to be described by "instantons", saddle point configurations of the action of the associated stochastic field theory. In this talk, I will present experimental evidence of a hydrodynamic instanton in a real world fluid system: A 270m wave channel experiment in Norway. The experiment attempts to model conditions on the ocean in order to observe so-called rogue waves, realisations of extreme ocean surface elevation out of relatively calm surroundings. These rogue waves are also observed in the ocean, where they are rare and hard to predict but pose significant danger to naval vessels. We show that the instanton approach, which is rigorously grounded in large deviation theory, offers a unified description of rogue waves in the water tank, covering the entire range of parameters for deep water waves in the ocean. In particular, this approach allows for a unified description of both the predominantly linear and the highly nonlinear regimes, and is able to explain the experimental data in the tank regardless of the strength of the nonlinearity. Mar 13 Wed Karoline Van Gemst (Birmingham) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks Enumerative geometry in projective space and Kontsevich's formula Abstract: Enumerative geometers are interested in counting certain geometric objects given a set of conditions. One example of such a counting problem is how many degree d rational curves pass through 3d-1 generically placed given points in the projective plane. This particular problem proved extremely difficult using classical methods, even for low d. In the 1990s however, a revolution within this area took place, originating in the world of physics. This led to Kontsevich solving the counting problem by proving a recursive formula for calculating this number for any d. Kontsevich’s formula requires a single initial datum, the case of d=1, which translates to the fact that a single line passes through two given points in the plane. In this talk, I will present some of the crucial ingredients in setting up for and proving Kontsevich’s formula, and illustrate how it makes sense through a few examples. If time permits, I will also motivate how the formula can be viewed as expressing the associativity of the quantum product. Mar 14 Thu Luca Giovannelli (University of Rome Tor Vergata) SP2RC seminar 10:00 F28 Emerging bipolar magnetic pairs in the solar photosphere: diffusion properties and contribution to the coronal heating Abstract: The ubiquitous presence of small magnetic elements in the Quiet Sun represents a prominent coupling between the photosphere and the upper layers of the Sun’s atmosphere. Small magnetic element tracking has been widely used to study the transport and diffusion of the magnetic field on the solar photosphere. From the analysis of the displacement spectrum of these tracers, it has been recently agreed that a regime of super-diffusivity dominates the solar surface. In this talk we will focus on the analysis of the bipolar magnetic pairs in the solar photosphere and their diffusion properties, using a 25-h dataset from the HINODE satellite. Interestingly, the displacement spectrum for bipolar couples behaves similarly to the case where all magnetic pairs are considered. We also measure, from the same dataset, the magnetic emergence rate of the bipolar magnetic pairs and we interpret them as the magnetic footpoints of emerging magnetic loops. The measured magnetic emergence rate is used to constrain a simplified model that mimics the advection on the solar surface and evolves the position of a great number of loops, taking into account emergence, reconnection and cancellation events. In particular we compute the energy released by the reconnection between different magnetic loops in the nano-flares energy range. Our model gives a quantitative estimate of the energy released by the reconfiguration of the magnetic loops in a quiet Sun area as a function of height in the solar atmosphere, from hundreds of Km above the photosphere up to the corona, suggesting that an efficiency of ~10% in the energy deposition might sustain the million degree corona. Mar 14 Thu Jeremy Oakley (Sheffield) Statistics Seminar 14:00 LT E Variational inference reading group Abstract: We will be spending two seminar slots on the following: Variational Inference: A Review for Statisticians https://arxiv.org/abs/1601.00670 David M. Blei, Alp Kucukelbir, Jon D. McAuliffe Mar 14 Thu Neil Strickland (Sheffield) Topology seminar 16:00 J11 Dilation of formal groups, and potential applications Abstract: I will describe an extremely easy construction with formal group laws, and a slightly more subtle argument to show that it can be done in a coordinate-free way with formal groups. I will then describe connections with a range of other phenomena in stable homotopy theory, although I still have many more questions than answers about these. In particular, this should illuminate the relationship between the Lambda algebra and the Dyer-Lashof algebra at the prime 2, and possibly suggest better ways to think about related things at odd primes. The Morava K-theory of symmetric groups is well-understood if we quotient out by transfers, but somewhat mysterious if we do not pass to that quotient; there are some suggestions that dilation will again be a key ingredient in resolving this. The ring $MU_*(\Omega^2S^3)$ is another object for which we have quite a lot of information but it seems likely that important ideas are missing; dilation may also be relevant here. Mar 15 Fri Jonathan Potts (Sheffield) Teaching Lunch 13:00 Hicks LT10 MOLE exams are great Abstract: We explain our use of MOLE exams in MAS222 and why it is a win-win tool for students and staff alike. The "win" for staff is particularly wonderful as it removes that most onerous task: exam marking. We'll start with a very brief presentation of how to set a MOLE exam up and how we've used them in MAS222. Then we'll open the floor to discussion about how they might be used more widely in SoMaS. Mar 15 Fri Luca Pol THH reading group 14:00 J11 $E_n$ algebras Mar 20 Wed Sven Meinhardt (Sheffield) Pure Maths Colloquium 14:00 J11 New developments in modern moduli theory Abstract: The idea of moduli spaces classifying structures in various fields of mathematics dates back to Riemann who tried to classify complex structures on a compact surface. It took another hundred years and many ingenious ideas of Grothendieck, Mumford and other mathematicians to write down a proper definition of moduli spaces and to construct nontrivial examples including Riemann‘s vague idea of a moduli space of complex structures on a surface. However, it became quite obvious that the concept of moduli spaces/stacks developed in the 60‘s and 70‘s is not sufficient to describe all moduli problems. Another 50 years and a fair amount of homotopy theory was needed to provide a definition of moduli spaces having all required properties. A large class of examples comes from (higher) representation theory. The aim of my talk is to provide a gentle introduction into these new concepts and thereby to show how nicely algebraic geometry, topology and representation theory interact with each other. If time permits, I will also sketch applications in Donaldson-Thomas theory. Mar 20 Wed Gianmarco Brocchi (Birmingham) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks What does extremise a Strichartz estimate? Abstract: This will be a blunt talk on sharp inequalities. Roughly speaking, these are inequalities which cannot be improved. In particular, I will introduce inequalities for the restriction of the Fourier transform, explaining why I got interested in them and how they are related to other inequalities in PDE, such as Strichartz estimates. These are a key tool in understanding the evolution of waves in dispersive PDE. If time allows, I will discuss a sharp Strichartz estimate for the fourth order Schrödinger equation from a joint work with Diogo Oliveira e Silva and René Quilodrán. Mar 21 Thu Theo Kypraios (Nottingham) Statistics Seminar 14:00 LT E Recent Advances in Identifying Transmission Routes of Healthcare Associated Infections using Whole Genome Sequence Data Abstract: Healthcare-associated infections (HCAIs) remain a problem worldwide, and can cause severe illness and death. It is estimated that 5-10% of acute-care patients are affected by nosocomial infections in developed countries, with higher levels in developing countries. Statistical modelling has played a significant role in increasing understanding of HCAI transmission dynamics. For instance, many studies have investigated the dynamics of MRSA transmission in hospitals, estimating transmission rates and the effectiveness of various infection control measures. However, uncertainty about the true routes of transmission remains and that is reflected on the uncertainty of parameters governing transmission. Until recently, the collection of whole genome sequence (WGS) data for bacterial organisms has been prohibitively complex and expensive. However, technological advances and falling costs mean that DNA sequencing is becoming feasible on a larger scale. In this talk we first describe how to construct statistical models which incorporate WGS data with regular HCAIs surveillance data (admission/discharge dates etc) to describe the pathogen's transmission dynamics in a hospital ward. Then, we show how one can fit such models to data within a Bayesian framework accounting for unobserved colonisation times and imperfect screening sensitivity using efficient Markov Chain Monte Carlo algorithms. Finally, we illustrate the proposed methodology using MRSA surveillance data collected from a hospital in North-East Thailand. Mar 21 Thu Tom Fisher (Cambridge) Number Theory seminar 14:00 J11 The proportion of genus one curves that are everywhere locally soluble Abstract: I will describe joint work with Bhargava and Cremona, and with Ho and Park, on the probability that a randomly chosen genus one curve is soluble over the p-adics. A striking feature of this work is that we obtain exact answers in the form of explicit rational functions of p. I will also discuss what is expected to happen globally. Mar 21 Thu Mike Prest (Manchester) Topology seminar 16:00 J11 Categories of imaginaries for additive categories Abstract: There is a construction of Freyd which associates, to any ring R, the free abelian category on R. That abelian category may be realised as the category of finitely presented functors on finitely presented R-modules. It has an alternative interpretation as the category of (model-theoretic) imaginaries for the category of R-modules. In fact, this extends to additive categories much more general than module categories, in particular to finitely accessible categories with products and to compactly generated triangulated categories. I will describe this and give some examples of its applications. Mar 21 Thu Peter Keys (Queen's University (Belfast)) Plasma Dynamics Group 16:00 Room K14 (Hicks Building) Small-scale magnetic field evolution with high resolution observations. Abstract: Small-scale magnetic fields, ubiquitous across the solar surface, manifest as intensity enhancements in intergranular lanes and, thus, often receive the moniker of magnetic bright point (MBP). MBPs are frequently studied as they are considered as a fundamental building block of magnetism in the solar atmosphere. The theory of convective collapse developed in the late 70’s and early 80’s is often used to explain how kilogauss fields form in MBPs. The dynamic nature of MBPs coupled with these kilogauss fields means that they are frequently posited as a source of wave phenomena in the solar atmosphere. Here, with high resolution observations of the quiet Sun with full Stokes spectropolarimetry, we investigate the magnetic properties of MBPs. By analysing the temporal evolution of various physical properties obtained from inversions, we show that kilogauss fields in MBPs can appear due to a variety of reasons, and is not limited to the process of convective collapse. Analysis of MURaM simulations confirms the processes we observe in our data. Also, magnetic field amplification happens on rapid timescales, which has significant implications for many wave studies. Mar 22 Fri Steffen Gielen (Nottingham) Applied Mathematics Colloquium 14:00 TBA The universe as a condensate of spacetime atoms Abstract: In the standard picture of cosmology, the Universe began at the Big Bang; the Big Bang itself is a singularity where the laws of physics break down. A quantum theory of gravity should resolve this singularity and help in understanding the initial state of the Universe needed to account for present observations. I will present some progress towards this goal in the group field theory approach to quantum gravity, using the idea of a universe formed as a "condensate", i.e. a very homogeneous quantum configuration, from a large number of discrete building blocks of geometry. I will show how this setting produces new cosmological models without an initial singularity; demanding that such models be both theoretically self-consistent and potentially compatible with observation then gives new ways for constraining theories of quantum gravity. Mar 22 Fri Nicola Bellumat THH reading group 14:00 J11 Periodic Theories Mar 27 Wed Daniele Avitabile (Nottingham) Applied Mathematics Colloquium 14:00 Hicks, LT 9 Interfacial dynamics for neurobiological networks: from excitability thresholds to localised spatiotemporal chaos Abstract: We will discuss level-set based approaches to study the existence and bifurcation structure of spatio-temporal patterns in biological neural networks. Using this framework, which extends previous ideas in the study of neural field models, we study the first example of canards in an infinite-dimensional dynamical system, and we give a novel characterisation of localised structures, informally called “bumps”, supported by spiking neural networks. We will initially consider a spatially-extended network with heterogeneous synaptic kernel. Interfacial methods allow for the explicit construction of a bifurcation equation for localised steady states. When the model is subject to slow variations in the control parameters, a new type of coherent structure emerges: the structure displays a spatially-localised pattern, undergoing a slow-fast modulation at the core. Using interfacial dynamics and geometric singular perturbation theory, we show that these patterns follow an invariant repelling slow manifold, hence we name them "spatio-temporal canards". We classify spatio-temporal canards and give conditions for the existence of folded-saddle and folded-node canards. We also find that these structures are robust to changes in the synaptic connectivity and firing rate. The theory correctly predicts the existence of spatio-temporal canards with octahedral symmetries in a neural field model posed on a spherical domain. We will then discuss how the insight gained with interfacial dynamics may be used to perform coarse-grained bifurcation analysis on neural networks, even in models where the network does not evolve according to an integro-differential equation. As an example I will consider a well-known event-driven network of spiking neurons, proposed by Laing and Chow. In this setting, we construct numerically travelling waves whose profiles possess an arbitrary number of spikes. An open question is the origin of the travelling waves, which have been conjectured to form via a destabilisation of a bump solution. We provide numerical evidence that this mechanism is not in place, by showing that disconnected branches of travelling waves with countably many spikes exist, and terminate at grazing points; the grazing points correspond to travelling waves with an increasing number of spikes, a well-defined width, and decreasing propagation speed. We interpret the so called “bumps” and “meandering bumps”, supported by this model as localised states of spatiotemporal chaos, whereby the dynamics visits a large number of unstable localised travelling wave solutions. Mar 27 Wed Andreea Mocanu (Nottingham) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks Mar 28 Thu Mark Quinn (Sheffield) Teaching Lunch 13:00 Hicks LT6 Colcalc and Sagemath Mar 28 Thu Jeremy Oakley (Sheffield) Statistics Seminar 14:00 LT E Variational inference reading group Abstract: We will be spending two seminar slots on the following: Variational Inference: A Review for Statisticians https://arxiv.org/abs/1601.00670 David M. Blei, Alp Kucukelbir, Jon D. McAuliffe Mar 29 Fri Jordan Williamson THH reading group 14:00 J11 Tate Diagonal Apr 2 Tue Arne Grauer, Lukas Lüchtrath (Cologne) Statistics Seminar 16:00 F28 Apr 3 Wed Mahesh Kakde (King's College London) Pure Maths Colloquium 14:00 J11 Apr 3 Wed Matt Turner (Surrey) Applied Mathematics Colloquium 14:00 Hicks, LT 9 Apr 4 Thu Fabrizio Leisen (Kent) Statistics Seminar 14:00 LT E Apr 4 Thu Chris Birkbeck (UCL) Number Theory seminar 14:00 J11 TBA Apr 4 Thu Richard Hepworth (Aberdeen) Topology seminar 16:00 J11 Apr 5 Fri Luca Pol THH reading group 14:00 J11 Topological Cyclic Homology Apr 12 Fri James Brotherston THH reading group 14:00 J11 Loop Spaces May 1 Wed Sam Falle (Leeds) Applied Mathematics Colloquium 14:00 Hicks, LT 9 Shock structures described by hyperbolic balance laws Abstract: In this talk I will consider shock structures that arise in systems of hyperbolic balance laws, i.e. hyperbolic systems of conservation laws with source terms. I show how the Whitham criterion for the existence of such shock structures can be extended to systems with more than one relaxation variable. In addition, I descibe a method based on the Hermite-Biehler theorem that is useful for determining the stability of the equilibrium states of such systems. The utility of this method is illustrated by a number of examples: ideal gas with two internal degrees of freedom, two fluid magnetohydrodynamics and magnetohydrodynamics with tensor resistivity. May 1 Wed Esmee te Winkel (Warwick) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks May 2 Thu Daniel Williamson (Exeter) Statistics Seminar 14:00 LT E May 8 Wed Aditi Kar (Royal Holloway) Pure Maths Colloquium 14:00 J11 May 8 Wed Kasia Rejzner (York) Applied Mathematics Colloquium 14:00 Hicks, LT 9 May 9 Thu Rebecca Killick (Lancaster) Statistics Seminar 14:00 LT E May 14 Tue Anna Krystalli / Alison Parton / Lyn Taylor (Sheffield / Sheffield / Phastar) RSS Seminar Series 16:00 LT 5 Putting the R in Reproducible Research / Cloud Computing with R / R Validation Hub Project Abstract: R and its ecosystem of packages offers a wide variety of statistical and graphical techniques and is increasing in popularity as the tool of choice for data analysis in academia. In addition to its powerful analytical features, the R ecosystem provides a large number of tools and conventions to help support more open, robust and reproducible research. This includes tools for managing research projects, building robust analysis workflows, documenting data and code, testing code and disseminating and sharing analyses. In this talk we’ll take a whistle-stop tour of the breadth of available tools, demonstrating the ways R and the Rstudio integrated development environment can be used to underpin more open reproducible research and facilitate best practice. R has cemented itself as the language of choice for many a statistician and data scientist, but is often heckled as a sluggish competitor to the likes of python. This talk will discuss one avenue for maintaining the comfort and power of R (see Anna’s talk!) without having to wait days for your desktop analysis to complete. The foreach package is a set of functions that allow virtually anything that can be expressed as a for-loop as a set of parallel tasks. By registering a parallel backend through the doParallel package, you can speed up the run-time of your work by utilising the full capacity of your machine. I’ll introduce how to rewrite workflows to utilise the foreach approach and show how you can implement a parallel workflow on your own machine with doParallel. For a low-range machine, this will reduce your run-time by 4-fold and for those lucky few with high-range budgets you’ll receive something around 16-fold. So how about going one step further, and increasing to hundreds-fold? We can achieve this by using cloud computing services, taking the load away from your own machine. Cloud computing services have been seen to have a steep learning curve and this has led to many shying away from using such a useful resource. I’ll introduce you to the doAzureParallel package for R, create by Microsoft to bypass this learning curve and allow you to implement the foreach package in parallel in the cloud with only minor amendments to the R code that has been blighting you for months. To date, the use of R Software in the pharmaceutical industry has been relatively limited to exploratory work and not routinely used in regulatory submissions where SAS® Software is still favored. One of the difficulties in using R for submissions is being able to provide the regulators with appropriate documentation of testing and validation for the packages used. In June 2018 the R consortium granted funding for a PSI AIMS SIG initiative to create an online ‘R package validation repository’. With representatives from Abbvie, Amgen, Biogen, Eli Lilly, FDA, GSK, J&J, Merck, Merck KGaA, Novartis, PPD, PRA, Pfizer, Roche / Genentech, Syne qua non and the Transcelerate project, the ‘R Validation Hub’ team launched a free to access web site to host validation documentation and metrics for R packages (https://www.pharmar.org/). Although, the project is still in its early stages, we are looking to expand on the website content and encourage contribution of R metrics and tests for packages from all R-users. The talk will discuss what is meant by validation, how R differs to SAS, justify our approach to the validation issue and present the future capabilities of the website and how all R-users are set to benefit from the work. May 15 Wed Martina Balagovic (Newcastle) Pure Maths Colloquium 14:00 J11 May 15 Wed Didier Leibovici (Sheffield) Applied Mathematics Colloquium 14:00 Hicks, LT 9 May 16 Thu Christopher Fallaize (Nottingham) Statistics Seminar 14:00 LT E