# Seminars this semester

Series:

 Jan 16 Mon John Greenlees (Sheffield) 11:00 J11 What we want from G spectra Jan 17 Tue Jordan Williamson (Sheffield) 14:00 J11 Orthogonal G-spectra Jan 17 Tue Sara Kalisnik (Brown) Topology seminar 16:00 J11 A short introduction to applied topology Abstract: In the last two decades applied topologists have developed numerous methods for ‘measuring’ and building combinatorial representations of the shape of the data. The most famous example of the former is persistent homology and of the latter, mapper. I will briefly talk about both of these methods and show several successful applications. Time permitting I will talk about my work on making persistent homology easier to combine with standard machine learning tools. Jan 19 Thu Jordan Williamson (Sheffield) 15:00 J11 Orthogonal G-spectra II Jan 20 Fri Dr Jiajia Liu (University of Science and Technology of China) SP2RC seminar 13:00 LT 11 Energy Rules of Solar Jets from Observational Perspectives Abstract: Solar jets are bulks of plasma materials ejected along elongated trajectories from the solar surface into the atmosphere of the Sun, often leaving the inner corona and determining the physical conditions far outwards in the interplanetary space. These impulsive and energetic ejecta are one of the most common dynamic phenomena occurring within the solar atmosphere. They are often accompanied by (nano-)flares, and some times by Coronal Mass Ejections (CMEs) and radio bursts, which could lead to significant changes of the space weather and terrestrial magnetic fields. After the nearly one-century efforts studying solar jets, we now have mature models for solar jets explaining the process of how magnetic reconnection triggers jets. However, due to the limits of the observational technology, many issues such as the detailed dynamics of, the energy transport during and the interaction with waves of solar jets are not well addressed before. In this talk, I will introduce part of my work during the past few years on the topic of "Energy Rules of Solar Jets from Observational Perspectives". Via high-resolution observations from the SDO and STEREO, I try to address the following questions of solar jets: (1) how the free magnetic energy is distributed between the thermal and kinetic energy during magnetic reconnection, (2) how the kinetic energy of solar jets is gained during and after the magnetic reconnection, and (3) how further release of the free magnetic reconnection proceeds after solar jets. Jan 24 Tue Luca Pol (Sheffield) 14:00 Complex cobordism and K theory with reality Jan 24 Tue Jonathan Sykes Uncertainty Quantification reading group 15:00 J11 Discussion of "Bayesian History Matching of Complex Infectious Disease Models Using Emulation: A Tutorial and a Case Study on HIV in Uganda", by Andrianikis et al. Jan 26 Thu Luca Pol (Sheffield) 15:00 Change of groups Jan 27 Fri Prof. B. Hindman (University of Colorado, Boulder) SP2RC seminar 13:00 LT 11 Solar convection in the rotationally constrained regime Abstract: Despite knowing that convection and rotation are indispensable components of the solar dynamo, we know vexingly little about how the influence of rotation manifests across the broad range of convective scales present in the Sun. We do know that the structure of deep meridional circulation, which may bear on the timing of the solar cycle, is sensitive to the degree of rotational constraint felt by its underlying convective motions. Similarly, the solar differential rotation, a vital source of large-scale shear in some dynamo models, results from convective motions that transport not just heat, but angular momentum. Rotation imbues convection with a sense of helicity, supplying a source of turbulent EMF to the dynamo, and it is only in regimes of strong rotational constraint that fully nonlinear models of stellar convection have evinced cyclic dynamo behavior. Current helioseismic measurements of the convective flows suggest that rotational influence is strong within the deep convection zone, but are inconsistent in how strong. Therefore, it is prudent to ask ourselves how rotation shapes the spectral distribution of convective power. I will present numerical results from a series of nonrotating and rotating convection simulations conducted in full spherical geometry. This presentation will focus on how convective spectra differ between the rotating and non-rotating models and how that behavior changes as simulations are pushed toward more turbulent and/or more rotationally-constrained regimes. I will conclude with a discussion of the implications that strong rotational constraint in the deep convection zone should have on the surface convective and how decades of surface observations may need re-interpretation. Jan 31 Tue Dimitar Kodjabachev (Sheffield) 14:00 Mackey functors Feb 2 Thu Dimitar Kodjabachev (Sheffield) 15:00 Fixed point functors Feb 3 Fri Dr. Rekha Jain (University of Sheffield) SP2RC seminar 13:00 LT 11 Feb 6 Mon Moty Katzman (Sheffield) Algebraic Geometry Learning Seminar 02:00 J11 Cohen-Macaulay modules Feb 6 Mon Torbjorn Lundh (Chalmers) Mathematical Biology Seminar Series 14:00 Hicks LT9 Four surgery problems "solved" by a "mathematical" approach Feb 7 Tue Jeremy Oakley (Sheffield) Uncertainty Quantification reading group 15:00 J11 Discussion of Wu, H., & Browne, M. W. (2015). Quantifying adventitious error in a covariance structure as a random effect. Psychometrika. Feb 7 Tue Jeff Giansiracusa (Swansea) Topology seminar 16:00 J11 Feb 8 Wed John Coates (University of Cambridge) Pure Maths Colloquium 14:00 J11 The conjecture of Birch and Swinnerton-Dyer Abstract: The conjecture of Birch and Swinnerton-Dyer is one of the principal open problems in number theory today. In my lecture, I shall give a brief account of the history of the conjecture, its precise formulation, and the partial results obtained so far in support of it. Feb 8 Wed George Papadakis (Imperial) Applied Mathematics Colloquium 14:00 Hicks, LT 10 Nonlinear optimal control of bypass transition in a boundary layer flow Abstract: We apply and assess a nonlinear optimal control strategy to suppress bypass transition in a zero-pressure-gradient boundary layer. To this end, a Lagrange variational formulation is employed that results in a set of adjoint equations. The optimal wall actuation (blowing and suction from a control slot) is found by solving iteratively the nonlinear Navier-Stokes and the adjoint equations in a forward/backward loop using DNS. The optimization is performed in a finite time horizon. Large values of optimization horizon result in instability of the adjoint equations. The control slot is located exactly in the region of transition. The results show that the control is able to significantly reduce the objective function, which is defined as the spatial and temporal integral of the quadratic deviation from the Blasius profile plus a term that quantifies the control cost. The physical mechanism with which the actuation interacts with the flow field is investigated and analysed in relation to the objective function employed. The spanwise averaged velocity is distorted by the control action, resulting in a significant reduction of the skin friction coefficient. We performed simulations with and without zero-net mass flow constraint of the actuation velocity. Results are also compared with uniform blowing using the same time-average velocity obtained from the non-linear optimal algorithm. Feb 10 Fri Dr Andrew Leonard (University of Sheffield) SP2RC seminar 13:00 F41 Feb 13 Mon Moty Katzman (Sheffield) Algebraic Geometry Learning Seminar 02:00 J11 Maximal Cohen Macaulay modules over hypersurfaces: matrix factorizations and periodic resolutions Feb 14 Tue Nick Kuhn (Virginia) Topology seminar 16:00 J11 The circle product of O-bimodules with O-algebras, with applications. Abstract: If O is an operad (in a friendly category, e.g. the category of S-modules of stable homotopy theory), M is an O-bimodule, A is an O-algebra, then the circle product over O of M with A is again an O-algebra. A useful derived version is the bar construction B(M,O,A). We survey many interesting constructions on O-algebras that have this form. These include an augmentation ideal filtration of an augmented O-algebra A, the topological Andre-Quillen homology of A, the topological Hochschild homology of A, and the tensor product of A with a space. Right O-modules come with canonical increasing filtrations, and this leads to filtrations of all of the above. In particular, I can show that a filtration on TAQ(A) defined recently by Behrens and Rezk agrees with one I defined about a decade ago, as was suspected. This is joint work with Luis Pereira. Feb 15 Wed Nicola Gambino (University of Leeds) Pure Maths Colloquium 14:00 J11 Commutative 2-algebra, operads, and analytic functors Abstract: Standard commutative algebra is based on commutative monoids, Abelian groups and commutative rings. In recent years, there has been some progress in developing an area that may be referred to as commutative 2-algebra, in which the familiar notions used in commutative algebra are replaced by their categorified counterparts (for example, commutative monoids are replaced by symmetric monoidal categories). The aim of this talk is to explain the analogy between standard commutative algebra and commutative 2-algebra, and to outline how this analogy suggests analogues of basic aspects of algebraic geometry. In particular, I will describe how some joint work with Andre’ Joyal on operads and analytic functors fits in this context. Feb 15 Wed Felix Ng (Department of Geography, Sheffiled) Applied Mathematics Colloquium 15:00 Hicks, LT 10 Grain-scale processes in the Earth's polar ice sheets Abstract: The spreading of the Antarctic and Greenland Ice Sheets is a slow viscous flow with nonlinear rheology. Besides temperature, grain sizes and crystal orientation within the polycrystalline ice are important factors behind the rheology. After giving this glaciological background, I will describe two mathematical models recently built to understand grain-size evolution. The first model is formulated to capture the observed grain-size profiles in ice cores. The second model tackles the fundamental process of normal grain growth (NGG), a coarsening process that occurs in metals as well as ice. Feb 20 Mon Nebojsa Pavic (Sheffield) Algebraic Geometry Learning Seminar 02:00 J11 Singularity category and MCM sheaves Feb 20 Mon Gary Mirams (Nottingham) Mathematical Biology Seminar Series 14:00 Alfred Denny Conference Room Feb 21 Tue Paul Gardner (Sheffield) Uncertainty Quantification reading group 15:00 J11 The use of Bayesian calibration in the prediction of damage in structures Abstract: This talk will include an overview of the field of structural health monitoring and damage identification, where the use of Bayesian calibrated models fit in and the aims of using this technique. It will conclude with challenges and future aims of using Bayesian calibrated subsystem models to make full system predictions of damage. Feb 21 Tue Angelica Osorno (Reed College) Topology seminar 16:00 J11 On equivariant infinite loop space machines Abstract: An equivariant infinite loop space machine is a functor that constructs genuine equivariant spectra out of simpler categorical or space level data. In the late 80's Lewis-May-Steinberger and Shimakawa developed generalizations of the operadic approach and the Gamma-space approach respectively. In this talk I will describe work in progress that aims to understand these machines conceptually, relate them to each other, and develop new machines that are more suitable for certain kinds of input. This work is joint with Anna Marie Bohmann, Bert Guillou, Peter May and Mona Merling. Feb 23 Thu Number Theory Learning Seminar 13:00 J-11 Organizational First Seminar Abstract: Organizational meeting: all interested parties are invited. Feb 24 Fri Alex Shukhobodskiy (University of Sheffield) SP2RC seminar 13:00 F41 Kink oscillations of expanding coronal loops Abstract: Kink waves and oscillations in a thin expanding magnetic tube in the presence of flow are studied. The tube consists of a core region and a thin transitional region at the tube boundary. In this region the plasma density monotonically decreases from its value in the core region to the value outside the tube. Both the plasma density and velocity of background flow vary along the tube and in time. Using the multiscale expansions the system of two equations describing the kink oscillations is derived. When there is no transitional layer the oscillations are described by the first of these two equations. This equation is used to study the effect of plasma density variation with time on kink oscillations of expanding tube with a sharp boundary. It is assumed that the characteristic time of the density variation is much larger than the characteristic time of kink oscillations. Then the WKB method is used to derive the expression for the aidiabatic invariant, which is the quantity that is coserved when the plasma density varies. The general theoretical results are applied to the kink oscillations of coronal magnetic loops. The expanding loops with the half-circle shape is considered and it is assumed that the plasma temperature inside a loop decays exponentially. The dependencies of the fundamental mode frequency, the ratio of frequencies of the first overtone and fundamental mode, and the oscillation amplitude on time are calculated numerically. Feb 27 Mon Evgeny Shinder (Sheffield) Algebraic Geometry Learning Seminar 02:00 J11 Knorrer periodicity Feb 27 Mon David Grimes (Oxford) Mathematical Biology Seminar Series 14:00 Alfred Denny Conference Room Feb 28 Tue Sam Morgan (Sheffield) Differential geometry seminar 11:00 J11 Double Lie groupoids and their double Lie algebroids, I Abstract: The series of talks will consist of a precise formulation of the double Lie algebroid of a double Lie groupoid. We will also discuss some of the examples arising in Poisson geometry. In the first talk we will consider the construction of the double Lie algebroid of an LA-groupoid. This will be a stepping stone in the general construction for a double Lie groupoid. Knowledge of the standard formation of the Lie algebroid of a Lie groupoid will not be assumed, and the notions of a Lie groupoid and a Lie algebroid will be recalled. Feb 28 Tue Haluk Sengun (Sheffield) Number Theory Learning Seminar 13:00 J-11 Automorphic Forms and Representation Theory: An Overview Abstract: We shall sketch the path that goes from modular forms to automorphic representations. Feb 28 Tue Operator K-theory and Noncommutative Geometry Seminar 14:00 J11 Organizational First Meeting Feb 28 Tue Gareth Williams (Open) Topology seminar 16:00 J11 Weighted projective spaces, equivariant K-theory and piecewise algebra Abstract: Weighted projective spaces are interesting through many lenses: for example, as natural generalisations of ordinary projective spaces, as toric varieties and as orbifolds. From the point of view of algebraic topology, it is natural to study their algebraic topological invariants – notably, their (equivariant) cohomology rings. Recent work has provided satisfying qualitative descriptions for these rings, in terms of piecewise algebra, for various cohomology theories. This talk will introduce weighted projective spaces as toric varieties and survey results on their (equivariant) cohomology rings, with particular focus on equivariant K-theory. It will conclude with recent results of Megumi Harada, Tara Holm, Nige Ray and the speaker, and indicate the flavour of current work of Tara Holm and the speaker. Mar 1 Wed Anne Taormina (University of Durham) Pure Maths Colloquium 15:00 J11 The riches of Mathieu Moonshine Abstract: In 2009, three Japanese theoretical particle physicists observed that the elliptic genus of a K3 surface, when expressed in terms of mock modular forms, exposes numbers that can be linked to the dimensions of finite dimensional representations of the sporadic group Mathieu 24. Since then, this intriguing connection has been studied from several points of view, other examples of the same type of phenomenon for other finite groups and mock modular forms have been discovered, and the research topic of New Moonshines’ has slowly caught the attention of researchers across fields. In this talk, I will describe the 2009 observation, now referred to as Mathieu Moonshine’, and explain the challenges faced by the theoretical physics community in understanding the origin and role of the huge Mathieu 24 finite symmetry in the context of strings compactified on K3 surfaces. In particular, I will discuss how this phenomenon is related to the geometry of K3 surfaces and introduce the concept of symmetry surfing. Mar 2 Thu Andrew Corbett (Bristol) Number Theory seminar 13:00 J11 Period integrals and special values of L-functions Abstract: In many ways L-functions have been seen to contain interesting arithmetic information; evaluating at special points can make this connection very explicit. In this talk we shall ask what information is contained in central values of certain automorphic L-functions, in the spirit of the Gan--Gross--Prasad conjectures, and report on recent progress. We also describe some surprising applications in analytic number theory regarding the size' of a modular form. Mar 2 Thu Mark Walters (Queen Mary) Probability 14:00 Mar 7 Tue Sam Morgan (Sheffield) Differential geometry seminar 11:00 J11 Double Lie groupoids and their double Lie algebroids, II Abstract: In the second talk, we will briefly discuss some examples of Lie algebroids arising from Lie groupoids; this should tie in with the description of the Lie functor, given in the first seminar. We shall then continue the construction of a double Lie algebroid of an LA-groupoid. Mar 7 Tue Haluk Sengun (Sheffield) Number Theory Learning Seminar 13:00 J-11 Background. Part I. Mar 7 Tue Neil Hansford (Sheffield) Operator K-theory and Noncommutative Geometry Seminar 14:00 J11 An introduction to C*-algebras. Part I. Mar 7 Tue Jeremy Colman (Sheffield) Uncertainty Quantification reading group 15:00 J11 Discussion of "Modelling extremes using approximate Bayesian Computation", by R. Erhardt and S. A. Sisson Mar 7 Tue Will Mycroft Topology seminar 16:00 J11 Plethories of Cohomology Operations Abstract: Cohomology operations are a very useful property of a cohomology theory. The collection of cohomology operations has a very rich structure. Historically the dual notion, of homology cooperations, have been the main target of attention and a nice algebraic structure called a Hopf ring has been used to understand these. Unfortunately, the Hopf ring contains no structure that is dual to the notion of composition. Boardman, Wilson and Johnson attempt to rectify this situation by defining an enriched Hopf ring, although this structure is rather less pleasant. A 2009 theorem of Stacey and Whitehouse shows that the collection of cohomology operations has the structure of an algebraic object called a plethory and this expresses all the structure, including composition. In this talk I shall define the above concepts and illustrate some examples of plethories for known cohomology theories. Mar 14 Tue Jordan Williamson (Sheffield) Number Theory Learning Seminar 13:00 J-11 Background. Part II. Abstract: Operators on Hilbert spaces. Mar 14 Tue Jordan Williamson (Sheffield) Operator K-theory and Noncommutative Geometry Seminar 14:00 J11 An introduction to C*-algebras. Part II. Mar 14 Tue Dimitar Kodjabachev (Sheffield) Topology seminar 16:00 J11 Mar 14 Tue Dimitar Kodjabachev (Sheffield) Topology seminar 16:00 J11 Gorenstein duality for topological modular forms with level structure Abstract: Gorenstein duality is a homotopy theoretic framework that allows one to view a number of dualities in algebra, geometry and topology as examples of a single phenomenon. I will briefly introduce the framework and concentrate on illustrating it with examples coming from derived algebraic geometry, especially topological modular forms with level structure. Mar 15 Wed Andrei Jaikin (Autonomous University of Madrid) Pure Maths Colloquium 14:00 J11 On $l^2$-Betti numbers and their analogues in positive characteristic Abstract: Let $G$ be a group, $K$ a field and $A$ a $n$ by $m$ matrix over the group ring $K[G]$. Let $G=G_1>G_2>G_3\cdots$ be a chain of normal subgroups of $G$ of finite index with trivial intersection. The multiplication on the right side by $A$ induces linear maps $$\begin{array}{cccc} \phi_i: & K[G/G_i]^n & \to& K[G/G_i]^m\\ &&&\\ &(v_1,\ldots,v_n) &\mapsto& (v_1,\ldots,v_n)A.\end{array}$$ We are interested in properties of the sequence $\{\frac{\dim_K \ker \phi_i}{|G:G_i|}\}$. In particular, we would like to answer the following questions. Is there the limit $\lim_{i\to \infty}\frac{\dim_K \ker \phi_i}{|G:G_i|}$? If the limit exists, how does it depend on the chain $\{G_i\}$? What is the range of possible values for $\lim_{i\to \infty}\frac{\dim_K \ker \phi_i}{|G:G_i|}$ for a given group $G$? It turns out that the answers on these questions are known for many groups $G$ if $K$ is a number field, less known if $K$ is an arbitrary field of characteristic 0 and almost unknown if $K$ is a field of positive characteristic. In my talk I will give several motivations to consider these questions, describe the known results and present recent advances in the case where $K$ has characteristic 0. Mar 16 Thu Martin Dickson (King's College) Number Theory seminar 13:00 J11 Central $L$-values of twists of Siegel cusp forms of degree two Abstract: The $L$-functions attached to Siegel cusp forms of degree two are conjectured, and in some cases known, to satisfy algebraicity properties at central values. This algebraicity is particularly interesting for those cusp forms which are expected to correspond to rational abelian surfaces. I will discuss these conjectures, the periods for these $L$-values, and finally the formulation of exact formula for the central values of twists of the degree four $L$-function. This includes some joint work with A. Saha, A. Pitale, and R. Schmidt. Mar 16 Thu Lasse Rempe-Gillen (Liverpool) SoMaS Colloquium 16:00 LT7 Mar 16 Thu Lesley Longstone (Independent Police Complaints Commission) RSS Seminar Series 16:30 Hicks Room K14 Independent Police Complaints Commission: using statistics to improve public confidence Abstract: As part of the IPCC’s role in securing and maintaining public confidence in the complaints system, the IPCC uses learning from its work to influence changes in policing, ensure accountability and spreads best practice and high standards of service. We are responsible for producing national statistics on deaths in or following police contact and official statistics on public complaints made about the police. We also procure a nationally representative survey in England and Wales to measure public confidence in the police complaints system. The presentation provides an overview of the methodologies for these main statistical outputs and the challenges faced, including external interpretations and quality issues. It also considers uses of the data and making evidenced based decisions that allow us to drive continuous improvement. Mar 20 Mon Evgeny Shinder (Sheffield) Algebraic Geometry Learning Seminar 02:00 J11 BGG correspondence Mar 20 Mon Louise Riotte-Lambert (Glasgow) Mathematical Biology Seminar Series 14:00 Alfred Denny Conference Room Consequences of memory-based movement at the individual and population levels Mar 21 Tue Sam Morgan (Sheffield) Differential geometry seminar 11:00 J11 Double Lie groupoids and their double Lie algebroids, III Abstract: In the third talk we will complete the construction of a double Lie algebroid of an LA-groupoid, and look at a specific example of an LA-groupoid arising naturally from a Poisson Lie group. We will finish by discussing the general notion of a double Lie algebroid of a double Lie groupoid. Mar 21 Tue Prathan Jarupoonphol (Sheffield) Number Theory Learning Seminar 13:00 J-11 Background. Part III. Abstract: The Lie algebra of $SL(2,\mathbb{R})$, the universal enveloping algebra and its centre, action on smooth functions on $SL(2,\mathbb{R})$. Mar 21 Tue Paul Mitchener (Sheffield) Operator K-theory and Noncommutative Geometry Seminar 14:00 J11 K-theory of C*-algebras. Part I. Mar 22 Wed Martin Lotz (University of Manchester) Pure Maths Colloquium 14:00 J11 Geometric Probability and Phase Transitions: Applications of the Steiner and Weyl Tube Formula Abstract: The tube formulas of Steiner and Weyl express the measure of tubular neighbourhoods of geometric objects (convex sets and Riemannian manifolds, respectively) as polynomials with certain curvature invariants as coefficients. We introduce these formulas and discuss recent applications to fields such as geometric probability, concentration of measure, numerical analysis, and convex optimization. Based on work with D. Amelunxen, M.B. McCoy, J.A. Tropp, F. Cucker, P. Buergisser Mar 22 Wed Abraham Harte (Dublin City University) Applied Mathematics Colloquium 14:00 Hicks, LT 10 Metric-independence of electromagnetic fields Mar 23 Thu Jeroen Sijsling (Ulm) Number Theory seminar 13:00 J11 Reconstructing plane quartics from their invariants Abstract: Up to isomorphism, elliptic curves over $\mathbb{C}$ are classified by their j-invariant; their coarse moduli space is an affine line with the j-invariant as coordinate. Conversely, it is not difficult to construct an elliptic curve with a specified j-invariant. In higher genus the situation is quite a bit more complicated. The moduli space of smooth genus 2 curves, as determined by Igusa, is already no longer a quasi-affine space, although it is still birational. In this genus Clebsch and Mestre have developed methods to reconstruct curves from their invariants, which also apply to hyperelliptic curves of higher genus. These methods are however very specific to the hyperelliptic case and do not at all generalize. This talk describes joint work with Reynald Lercier and Christophe Ritzenthaler that describes how reconstruction is possible in the next simplest case: that of non-hyperelliptic curves in genus 3, or in other words smooth plane quartics in $\mathbb{P}^2$. Mar 23 Thu Jordan Williamson (Sheffield) Category Theory 14:00 LT10 The category of representations of a finite group Mar 23 Thu Weijun Xu (Warwick) Probability 14:00 Mar 23 Thu Lasse Rempe-Gillen (Liverpool ) SoMaS Colloquium 16:05 LT7 Metronomes and fireflies: Stability in the Arnold family Abstract: *Phase-locking* (or phase synchronisation) is a phenomenon, first discovered by Huygens in the 17th century, in which two interacting oscillators synchronise their frequencies. It occurs in a plethora of physical and biological systems, from simple interacting pendula (search for “metronomes synchronise” on youtube …) to the synchronised behaviour of fireflies. In the 1960s, Vladimir Arnold proposed a one-dimensional discrete-time model of a periodically forced oscillator as the simplest context in which to study phase-locking phenomena. In this talk, I will describe a long-standing problem concerning the density of stable parameters within this family (arising from phase-locking phenomena), which we were able to resolve in recent work with van Strien (Duke Math. J., 2015). The talk will begin with a gentle introduction to one-dimensional discrete dynamics, including computer experiments of both the Arnold family and the well-known logistic family from population dynamics. These experiments naturally lead to the formulation of the density problem. The talk will hence be accessible to a general mathematical audience, including postgraduate students. Time permitting, I will also discuss how these developments are connected to, and were made possible by, recent progress in the study of the dynamics of transcendental entire functions. Mar 24 Fri Eleanor Vickers (Sheffield) SP2RC seminar 13:00 F41 MHD surface waves in an inclined magnetic field Mar 27 Mon John Greenlees (Sheffield) Algebraic Geometry Learning Seminar 02:00 J11 Graded singularity category Mar 28 Tue David Spencer (Sheffield) Number Theory Learning Seminar 13:00 J-11 Real story. Part I. Abstract: Automorphic forms on $SL(2,\mathbb{R})$, automorphic form associated to a classical cusp form. Mar 28 Tue Paul Mitchener (Sheffield) Operator K-theory and Noncommutative Geometry Seminar 14:00 J11 K-theory of C*-algebras. Part II. Mar 29 Wed Ulrike Tillmann (University of Oxford) Pure Maths Colloquium 14:00 J11 Riemann's moduli spaces and operads Abstract: Riemann's moduli spaces are at the heart of much modern mathematics. In this lecture we will explore their properties as an operad. Operads were introduced in the 1970 in homotopy theory to study loop spaces. Infinite loop spaces are of particular interest as they give rise to generalised cohomology theories. In the 1990's operads had a renaissance with much interest stimulated from mathematical physics. In particular, Segal's axiomatic approach to conformal field theory defines an operad of Riemann surfaces. We will show that this is an example of a new generation of operads detecting infinite loop spaces. The talk will introduce the main concepts and is addressed to a general mathematical audience. Mar 30 Thu Sven Meinhardt (Sheffield) Category Theory 14:00 J11 The Drinfeld Double and the Drinfeld Centre Mar 31 Fri Norbert Gyenge (Sheffield) SP2RC seminar 13:00 F41 On Active Longitudes and their Relation to Loci of Coronal Mass Ejections Abstract: The spatial inhomogeneity of the distribution of coronal mass ejection (CME) loci in the solar atmosphere could provide a new tool to estimate the longitudinal position of the most probable CME-capable active regions in the Sun. The anomaly in the longitudinal distribution of active regions themselves is often referred to as active longitude (AL). In order to reveal the connection between the AL and CME loci, here, we investigate the morphological properties of active regions. The first morphological property studied is the separateness parameter, which is suitable to characterise the probability of the locus of an energetic event, such as solar flare or CME. The second morphological property we focus on is the tilt angle of sunspot groups. Analysis of tilt angle of sunspot groups allows us to estimate the helicity of active regions. An increased helicity leads to a more complex built-up of the magnetic structure and also can be the cause of CME eruption. We found that the most complex active regions appear statisticlly significantly near to the AL and that the AL itself is associated with the most tilted active regions. Therefore, the number of CME loci is higher around the enhanced longitudinal activity. Further, the origin of the fast CMEs is also found to be associated with the AL belt. We concluded that the source of the most probably CME-capable active regions is at the AL. Applying our method may allow us to predict the potential flare and CME sources several Carrington Rotation (CR) in advance, and, our further findings could provide new information for solar dynamo modelling. Apr 4 Tue Richard Wilkinson (Sheffield) Uncertainty Quantification reading group 15:00 Hicks LT9 Discussion of Wong, R. K. W., Storlie, C. B. and Lee, T. C. M. (2017), A frequentist approach to computer model calibration. J. R. Stat. Soc. B, 79: 635–648. Apr 24 Mon Sven Meinhardt (Sheffield) Algebraic Geometry Learning Seminar 02:00 J11 Matrix factorizations and Homological Mirror Symmetry Apr 24 Mon Mirela Domijan (Liverpool) Mathematical Biology Seminar Series 14:00 Alfred Denny Conference Room Apr 25 Tue Di Zhang (Sheffield) Number Theory Learning Seminar 13:00 J-11 Real story. Part II. Abstract: Representations of $SL(2,\mathbb{R})$. Apr 25 Tue Sarah Browne (Sheffield) Operator K-theory and Noncommutative Geometry Seminar 14:00 J11 Bott periodicity. Abstract: We present a proof of the Bott Periodicity theorem. Apr 25 Tue Ana Lecuona Topology seminar 16:00 J11 Complexity and Casson-Gordon invariants Abstract: Homology groups provide bounds on the minimal number of handles needed in any handle decomposition of a manifold. We will use Casson-Gordon invariants to get better bounds in the case of 4-dimensional rational homology balls whose boundary is a given rational homology 3-sphere. This analysis can be used to understand the complexity of the discs associated to ribbon knots in S^3. This is a joint work with P. Aceto and M. Golla. Apr 26 Wed Vidit Nanda (Oxford) Pure Maths Colloquium 14:00 J11 Local cohomology and canonical stratifications Abstract: Every finite regular CW complex is, ipso facto, a cohomologically stratified space when filtered by skeleta. In this talk, I will outline a method to discover the canonical (i.e., coarsest possible) stratification of such a complex that is compatible with its underlying cell structure. The construction proceeds by first localizing and then resolving a complex of cosheaves which capture local cohomology at every cell. The result is a sequence of categories whose limit recovers the desired strata via its (isomorphism classes of) objects. As a bonus, the entire process is algorithmic and amenable to efficient computations. Apr 26 Wed Cedric Beaume (Leeds) Applied Mathematics Colloquium 14:00 Hicks, LT 10 From convectons to complexity in doubly diffusive convection Abstract: Doubly diffusive convection arises frequently in natural phenomena and industrial processes. It occurs in systems where heat and another quantity diffuse at different rates. Well-known examples are provided by thermohaline convection and the salt finger instability. In this talk, we consider three-dimensional thermohaline convection where a binary mixture is confined between vertical walls maintained at different temperatures and salinities. In this configuration, we found stationary spatially localised solutions consisting of spots of convection embedded in a background conduction state. These convectons are formed through a subcritical bifurcation from the conductive state (motionless fluid) and display a variety of patterns while simulations above onset reveal chaotic dynamics. Apr 27 Thu Rachel Newton (Reading) Number Theory seminar 13:00 J11 Transcendental Brauer-Manin obstructions on Kummer surfaces Abstract: In 1970, Manin observed that the Brauer group Br(X) of a variety X over a number field K can obstruct the Hasse principle on X. In other words, the lack of a K-point on X despite the existence of points over every completion of K is sometimes explained by non-trivial elements in Br(X). The 'algebraic' part of Br(X) is the part which becomes trivial upon base change to an algebraic closure of K. It is generally easier to handle than the remaining 'transcendental' part and has been widely studied. Until recently, very little was known about the transcendental part of the Brauer group. Results of Skorobogatov and Zarhin allow one to compute the transcendental Brauer group of a product of elliptic curves. Ieronymou and Skorobogatov used these results to compute the odd order torsion in the transcendental Brauer group of diagonal quartic surfaces. The first step in their approach is to relate a diagonal quartic surface to a product of elliptic curves with complex multiplication by the Gaussian integers. I will show how to extend their methods to compute transcendental Brauer groups of products of other elliptic curves with complex multiplication. Using these results, I will give examples of Kummer surfaces where there is no Brauer-Manin obstruction coming from the algebraic part of the Brauer group but a transcendental Brauer class causes a failure of weak approximation. Apr 27 Thu Sven Meinhardt (Sheffield) Category Theory 14:00 J11 The Drinfeld Double and the Drinfeld Centre (II) Apr 27 Thu Nick Bingham Probability 14:00 Apr 27 Thu Nebojsa Pavic (Sheffield) Algebra / Algebraic Geometry seminar 16:00 J11 Relative zero cycles on the universal polarized K3 surface Abstract: The generalized Franchetta Conjecture on K3 surfaces, claimed by O'Grady, says that any codimension 2 cycle of the universal K3 surface $\mathcal{X}_g\to \mathcal{F}_g$ restricted to any (closed) fibre lies in the group generated by the Beauville-Voisin class. In this talk, Chow groups will be introduced and some main results will be mentioned, especially some properties of Chow groups of K3 surfaces. Finally, the generalized Franchetta Conjecture will be stated and a proof for the cases $g=3,\ldots ,10,12,18,20$ will be presented using Mukai's characterization of the moduli space of K3 surfaces with these genera. Apr 27 Thu Jonty Rougier (Bristol) SoMaS Colloquium 16:00 LT7 Assessing the risk from large volcanic eruptions Abstract: Volcanoes threaten many millions of people worldwide, disproportionately in developing countries. Fortunately, large explosive volcanic eruptions are rare, but this also makes it harder to assess the rate of eruptions for the purposes of risk assessment. This difficulty is compounded by an unreliable historical record, in which the probability of an eruption being recorded in a modern database is affected by the size of the eruption, and also the time and location. In joint work with volcanologists Steve Sparks and Kathy Cashman, I have been quantifying the frequency/magnitude relationship for large explosive eruptions, up to and beyond the 'super-eruptions' which, were they to happen today, would threaten our whole civilisation. May 2 Tue Rudolf Chow (Sheffield) Number Theory Learning Seminar 13:00 J-11 Real sotry. Part III. Abstract: Spectral decomposition of $L^2(\Gamma \backslash SL(2,\mathbb{R}))$, the Duality Theorem. May 2 Tue John Greenlees (Sheffield) Topology seminar 16:00 J11 Thick and localizing subcategories of rational G-spectra Abstract: The Balmer spectrum of the category of rational G-spectra as a poset is the closed subgroups of G under cotoral inclusion. In December, I posted a preprint on the arXiv that proved this for tori: the talk will describe a much simpler proof of a theorem for all compact Lie groups. The method applies in other contexts with only a few special inputs from equivariant topology: the Localization Theorem, The calculation of the Burnside ring and a method of calculation for maps between free G-spectra. May 4 Thu Sam Edis (Sheffield) Number Theory seminar 13:00 J11 Congruent numbers in totally real number fields Abstract: In this talk we will extend the definition of congruent numbers to totally real number fields. Adapting methods of Tunnell we will show that some real quadratic fields possess finite time tests to determine if a number is congruent. May 4 Thu Ziyu Zhang (Hannover) Algebra / Algebraic Geometry seminar 16:00 J11 Degenerations of Hilbert schemes of points on K3 surfaces Abstract: It is a widely open problem to understand the degenerations of higher dimensional hyperkähler manifolds. The simplest case would be to study the degenerations of Hilbert schemes of points on K3 surfaces. Given a simple degeneration family of K3 surfaces, there are two constructions of degenerations of their Hilbert schemes in the literature, due to Nagai and Gulbrandsen-Halle-Hulek respectively, which result in different central fibers. I will compare the two constructions with an emphasis on the geometry of the latter. Based on joint work in progress with M.G.Gulbrandsen, L.H.Halle and K.Hulek. May 5 Fri Dr Nabil Freij (University of the Balearic Islands) SP2RC seminar 13:00 F41 Coronal loop seismology using NOGIS Abstract: Coronal loops have been observed to host a myriad of magnetohydrodynamics (MHD) waves over the past two decades. Frequently, kink oscillations have been shown to be damped and this damping has allowed the calculation of several key plasma properties such as density and magnetic field strength. I will showcase the first detection of both kink and longitudinal MHD waves with a ground-based coronal imager called NOGIS. Using a recently derived theoretical framework for kink wave damping by mode conversion, it is possible to calculate background properties of the loop system with improved accuracy. This information is important to solve current outstanding problems in coronal seismology. May 8 Mon Joseph Karmazyn (Sheffield) Algebraic Geometry Learning Seminar 02:00 J11 McKay correspondence / G-actions / AR-quivers, or something similar May 8 Mon Steve Webb (Liverpool John Moores) Mathematical Biology Seminar Series 14:00 Alfred Denny Conference Room Development and Mathematical Modelling of Liver Bioreactors for In Vitro to In Vivo Extrapolation of Systemic Chemical Toxicity May 9 Tue Dimitar Kodjabachev (Sheffield) Number Theory Learning Seminar 13:00 J-11 Adelic story. Part I. Abstract: Adeles, ideles. $GL(2)$ over the adeles, strong approximation. May 10 Wed Barbara Bolognese (Sheffield) Pure Maths Colloquium 14:00 J11 On the connectivity of dual graphs of projective curves Abstract: In 1962, Hartshorne proved that the dual graphs of an arithmetically Cohen-Macaulay scheme is connected. After establishing a correspondence between the languages of algebraic geometry, commutative algebra and combinatorics, we are going to refine Hartshorne's result and measure the connectedness of the dual graphs of certain projective schemes in terms of an algebro-geometric invariant of the projective schemes themselves, namely their Castelnuovo-Mumford regularity. Time permitting, we are also going to address briefly the inverse problem of Hartshorne's result, by showing that any connected graph is the dual graph of a projective curve with nice geometric properties. This is joint work with Bruno Benedetti and Matteo Varbaro. May 10 Wed Schuyler Nicholson (U Mass Boston) Applied Mathematics Colloquium 14:00 Hicks, LT 10 Information, patterns, and learning the rules of an explosion Abstract: At the right pressures and temperatures, gaseous mixtures of hydrogen and oxygen explode. Experimental advances continue to extract chemical processes at ever shorter timescales. The goal of these experiments is to transform this data into chemical mechanisms which describe the sequences of transient chemical species formed during an explosion. Constructing this chemical mechanism will enhance the eciency, reliability, and safety of hydrogen technologies from combustion engines to fuel cells. However, this need to learn the basic rules of combustion is hampered by constraints on the experimentally accessible information. In this talk, I will introduce our recent work applying theoretical tools from information theory and statistical mechanics, which respects these constraints and allows for the systematic discovery of chemical mechanisms. May 11 Thu Herbert Gangl (Durham) Number Theory seminar 13:00 J11 Zagier's polylogarithm conjecture revisited Abstract: In the early nineties, Goncharov proved the weight 3 case of Zagier's Conjecture stating that the special value $\zeta_F(3)$ of a number field $F$ is essentially expressed as a determinant of trilogarithm values taken in that field. He also envisioned a vast--partly conjectural--programme of how to approach the conjecture for higher weight. We can remove one important obstacle in weight~4 by solving one of Goncharov's conjectures. It further allows us to deduce a functional equation for $Li_4$ in four variables as one expects to enter in a more explicit definition of a certain algebraic K-group of $F$ (viz. $K_7(F)$). May 11 Thu Xiaolei Zhao (Northeastern) Algebra / Algebraic Geometry seminar 14:30 J11 0-cycles on moduli spaces of sheaves on K3 surfaces and second Chern classes Abstract: The Chow groups of algebraic cycles on algebraic varieties have many mysterious properties. For K3 surfaces, on the one hand, the Chow group of 0-cycles is known to be huge. On the other hand, the 0-cycles arising from intersections of divisors and the second Chern class of the tangent bundle all lie in a one dimensional subgroup. In my talk, I will recall some recent attempt to generalize this property to hyper-Kähler varieties, and explain a conjectural connection between the K3 surface case and the hyper-Kähler case. In particular, this proves a conjecture of O’Grady. If time permits, I will also explain how to extend this connection to Fano varieties of lines on a cubic fourfold containing a plane. This talk is based on a joint work with Junliang Shen and Qizheng Yin. May 11 Thu Alistair Craw (Bath) Algebra / Algebraic Geometry seminar 16:00 J11 Birational geometry and Bridgeland stability for compact support Abstract: I'll discuss joint work with Arend Bayer and Ziyu Zhang in which we define a nef divisor class on moduli spaces of Bridgeland-stable objects in the derived category of coherent sheaves with compact support, generalising earlier work of Bayer and Macri for smooth projective varieties. This work forms part of a programme to study the birational geometry of moduli spaces of Bridgeland-stable objects for a nice class of varieties that are not projective. May 12 Fri Chris Nelson (University of Sheffield) SP2RC seminar 13:00 F41 Bursts, Bombs, and Jets In The Lower Solar Atmosphere Abstract: Small-scale explosive phenomena in the lower solar atmosphere were first discovered exactly one century ago by Ferdinand Ellerman. These ‘Ellerman bombs’ (EBs) went relatively unexplored for around 80 years, however, the research output from the Flare Genesis Experiment and the development of instruments such as the CRisp Imaging SpectroPolarimeter (CRISP) has driven an exponential increase in interest in these events over the past two decades. It is now thought that these features pinpoint the locations of energetic photospheric magnetic reconnection, which heats pockets of photospheric gas to temperatures as high as 80,000 K. In this talk, we introduce the EB phenomena (including outlining their observational signatures), discuss exciting links between these events and other transient explosive features (such as IRIS bursts), and explore the validity of magnetic reconnection as the driving force behind these events. Finally, signatures of IRIS bursts co-spatial to EB-like events in the quiet-Sun will be presented providing the first evidence that magnetic reconnection energetic enough to heat photospheric plasma to temperatures close to 80,000 K can occur throughout the lower solar atmosphere. May 15 Mon Khaled Alhazmy (Sheffield) Algebraic Geometry Learning Seminar 02:00 J11 On the finite F-representation type (FFRT) of hypersurfaces May 16 Tue Sarah Browne (Sheffield) Topology seminar 00:00 J11 An orthogonal quasi-spectrum for graded E-theory Abstract: Graded E-theory is a bivariant functor from the category where objects are graded C*-algebras and arrows are graded *-homomorphisms to the category where objects are abelian groups and arrows are group homomorphisms. It is bivariant in the sense that it is a cohomology theory in its first variable and a homology theory in its second variable. In this talk I'll give a description of a quasi-topological space and explain why this notion is necessary in our case. We will define the notion of an orthogonal quasi-spectrum as an orthogonal spectrum for quasi-topological spaces, and further give the quasi-topological spaces to form the spectrum for graded E-theory. If time allows I will give the smash product structure. May 16 Tue Ariel Weiss (Sheffield) Number Theory Learning Seminar 13:00 J-11 Adelic story. Part II. Abstract: Automorphic forms on $GL(2)$ over the adeles, the automorphic representation associated to a classical cuspidal modular form. May 16 Tue David O'Sullivan (Sheffield Hallam ) Operator K-theory and Noncommutative Geometry Seminar 14:00 J11 K-homology May 16 Tue Sarah Browne (Sheffield) Topology seminar 16:00 J11 Quasi-topological assembly for K theory May 17 Wed Jaroslaw Buczynski (IMPAN Warsaw) Pure Maths Colloquium 15:00 J11 Constructions of k-regular maps using finite local schemes Abstract: A continuous map $\mathbb{R}^m \rightarrow \mathbb{R}^N$ or $\mathbb{C}^m \rightarrow \mathbb{C}^N$ is called $k$-regular if the images of any $k$ distinct points are linearly independent. Given integers m and k a problem going back to Chebyshev and Borsuk is to determine the minimal value of $N$ for which such maps exist. The methods of algebraic topology provide lower bounds for $N$, however there are very few results on the existence of such maps for particular values m. During the talk, using the methods of algebraic geometry, we will construct $k$-regular maps. We will relate the upper bounds on the minimal value of $N$ with the dimension of the a Hilbert scheme. The computation of the dimension of this space is explicit for $k< 10$, and we provide explicit examples for $k$ at most $5$. We will also provide upper bounds for arbitrary m and k. The problem has its interpretation in terms of interpolation theory: for a topological space X and a vector space $V$, a map $X \rightarrow V$ is k-regular if and only if the dual space $V^*$ embedded in space of continuous maps from $X$ to the base field $\mathbb{R}$ or $\mathbb{C}$ is $k$-interpolating, i.e. for any $k$ distinct points $x_1,...,x_k$ of $X$ and any values $f_i$, there is a function in $V^*$, which takes values $f_i$ at $x_i$. Similarly, we can interpolate vector valued continuous functions, and analogous methods provide interesting results. May 17 Wed Matthew Peddie (Manchester) Differential geometry seminar 16:00 LT5 A super approach to Drinfeld doubles Abstract: Drinfeld's double construction for a Lie bialgebra produces a unique Lie bialgebra suitable for quantisation. With the introduction of Lie bialgebroids as linearisations of Poisson-Lie groupoids, followed the same question as to whether a double can be constructed. This proved to be not so straightforward, and indeed, can be considered to be only partially answered. We will review these double constructions for Lie bialgebras and Lie bialgebroids using the language of supermathematics, and will discuss some of the problems encountered for the bialgebroid case. We will then define the Drinfeld double of a homotopy Lie bialgebra, or an $L_\infty$-bialgebra, and find a necessary condition for the existence. May 18 Thu Sean Ledger (Bristol) Probability 14:00 Hicks LT E May 22 Mon Barbara Bolognese (Sheffield) Algebraic Geometry Learning Seminar 02:00 J11 Categorical resolutions of singularities May 23 Tue Haluk Sengun (Sheffield) Number Theory Learning Seminar 13:00 J-11 Adelic story. Part III. Abstract: Tensor product theorem, odds and ends. May 23 Tue Sven Meinhardt (Sheffield) Operator K-theory and Noncommutative Geometry Seminar 14:00 J11 Group actions, group C*-algebra, crossed product algebras. May 23 Tue Magdalena Kedziorek (Lausanne) Topology seminar 16:00 J11 Rational commutative ring G-spectra Abstract: Recently, there has been some new understanding of various possible commutative ring G-spectra. In this talk I will recall these possibilities and discuss the most naive (or trivial) commutative ring G-spectra. Then I will sketch the main ingredients coming into the proof that if G is finite and we work rationally these objects correspond to (the usual) commutative differential algebras in the algebraic model for rational G-spectra. This is joint work with David Barnes and John Greenlees. May 24 Wed Kasia Rejzner (University of York) Pure Maths Colloquium 14:00 J11 Mathematical quantum field theory: from analysis to homological algebra Abstract: In this talk I will give an overview of mathematical structures used in modern quantum filed theory. I will focus on notions from functional analysis, like nets of operator algebras, and show how these combine with homological algebra methods to provide a rigorous description of perturbative gauge theories on curved spacetimes and of effective quantum gravity. The framework I present is called perturbative algebraic quantum field theory (pAQFT) and it is an emerging new way of approaching mathematical foundations of QFT. May 24 Wed Alvar Daza (Universidad Rey Juan Carlos) Applied Mathematics Colloquium 14:00 Hicks, LT 10 Fractal basins and unpredictability in dynamical systems Abstract: Basins of attraction take its name from hydrology, and in dynamical systems they refer to the set of initial conditions that lead to a particular final state. When different final states are possible, the predictability of the system depends on the structure of these basins. In this talk, we will revise the main kinds of fractal basin boundaries appearing in dissipative and Hamiltonian systems. Finally, we will introduce the concept of basin entropy in order to answer an apparently naïve question: how can we say that one basin is more unpredictable than another? May 25 Thu Anthony Licata (Canberra) Algebra / Algebraic Geometry seminar 16:00 J11 Hilbert schemes, Heisenberg algebras, and braid group actions Abstract: Let X be the minimal resolution of an ADE simple singularity. The derived category of the Hilbert scheme of points on X is acted on by a number of interesting algebraic objects. For example, there is acategorical Heisenberg action' on \oplus_n D(Hilb_n(X)), which categorifies the Nakajima-Grojnowski action on cohomology; in addition, there is also a braid group action on each D(Hilb_n(X)). The goal of the talk will be to explain how the categorical Heisenberg action gives rise to the categorical braid group action. Time permitting, we'll discuss the connection to Khovanov homology, and state some conjectures. Jun 1 Thu TBA Algebra / Algebraic Geometry seminar 16:00 J11 Jun 7 Wed Haluk Sengun (Sheffield) Operator K-theory and Noncommutative Geometry Seminar 14:00 J11 The Baum-Connes conjecture. Abstract: We make a gentle introduction to the Baum-Connes conjecture. Jun 8 Thu Ciaran Meachan (Glasgow) Algebra / Algebraic Geometry seminar 16:00 J11 Jun 9 Fri Nikos Diamantis (Nottingham) Number Theory seminar 11:00 J11 TBA