Seminars this semester
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 Gspectra  
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 Gspectra 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 onecentury 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 highresolution 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 largescale 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 nonrotating models and how that behavior changes as simulations are pushed toward more turbulent and/or more rotationallyconstrained 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 reinterpretation. 

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  CohenMacaulay 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 SwinnertonDyer  
Abstract: The conjecture of Birch and SwinnertonDyer 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 zeropressuregradient 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 NavierStokes 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 zeronet mass flow constraint of the actuation velocity. Results are also compared with uniform blowing using the same timeaverage velocity obtained from the nonlinear 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 Obimodules with Oalgebras, with applications.  
Abstract: If O is an operad (in a friendly category, e.g. the category of Smodules of stable homotopy theory), M is an Obimodule, A is an Oalgebra, then the circle product over O of M with A is again an Oalgebra. A useful derived version is the bar construction B(M,O,A). We survey many interesting constructions on Oalgebras that have this form. These include an augmentation ideal filtration of an augmented Oalgebra A, the topological AndreQuillen homology of A, the topological Hochschild homology of A, and the tensor product of A with a space. Right Omodules 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 2algebra, 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 2algebra, 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 2algebra, 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  Grainscale 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 grainsize evolution. The first model is formulated to capture the observed grainsize 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 LewisMaySteinberger and Shimakawa developed generalizations of the operadic approach and the Gammaspace 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  J11  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 halfcircle 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 LAgroupoid. 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  J11  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 Ktheory 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 Ktheory 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 Ktheory. 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 Lfunctions  
Abstract: In many ways Lfunctions 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 Lfunctions, in the spirit of the GanGrossPrasad 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 LAgroupoid. 

Mar 7  Tue  Haluk Sengun (Sheffield)  Number Theory Learning Seminar 
13:00  J11  Background. Part I.  
Mar 7  Tue  Neil Hansford (Sheffield)  Operator Ktheory 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  J11  Background. Part II.  
Abstract: Operators on Hilbert spaces. 

Mar 14  Tue  Jordan Williamson (Sheffield)  Operator Ktheory 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.


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 RempeGillen (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 RiotteLambert (Glasgow)  Mathematical Biology Seminar Series 
14:00  Alfred Denny Conference Room  Consequences of memorybased 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 LAgroupoid, and look at a specific example of an LAgroupoid 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  J11  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 Ktheory and Noncommutative Geometry Seminar 
14:00  J11  Ktheory 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  Metricindependence 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 jinvariant; their coarse moduli space is an affine line with the jinvariant as coordinate. Conversely, it is not difficult to construct an elliptic curve with a specified jinvariant. 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 quasiaffine 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 nonhyperelliptic 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 RempeGillen (Liverpool )  SoMaS Colloquium 
16:05  LT7  Metronomes and fireflies: Stability in the Arnold family  
Abstract: *Phaselocking* (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 onedimensional discretetime model of a periodically forced oscillator as the simplest context in which to study phaselocking phenomena. In this talk, I will describe a longstanding problem concerning the density of stable parameters within this family (arising from phaselocking 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 onedimensional discrete dynamics, including computer experiments of both the Arnold family and the wellknown 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  J11  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 Ktheory and Noncommutative Geometry Seminar 
14:00  J11  Ktheory 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 CMEcapable 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 builtup 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 CMEcapable 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  J11  Real story. Part II.  
Abstract: Representations of $SL(2,\mathbb{R})$. 

Apr 25  Tue  Sarah Browne (Sheffield)  Operator Ktheory 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 CassonGordon invariants  
Abstract: Homology groups provide bounds on the minimal number of handles needed in any handle decomposition of a manifold. We will use CassonGordon invariants to get better bounds in the case of 4dimensional rational homology balls whose boundary is a given rational homology 3sphere. 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. Wellknown examples are provided by thermohaline convection and the salt finger instability. In this talk, we consider threedimensional 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 BrauerManin 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 Kpoint on X despite the existence of points over every completion of K is sometimes explained by nontrivial 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 BrauerManin 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 BeauvilleVoisin 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 'supereruptions' which, were they to happen today, would threaten our whole civilisation. 

May 2  Tue  Rudolf Chow (Sheffield)  Number Theory Learning Seminar 
13:00  J11  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 Gspectra  
Abstract: The Balmer spectrum of the category of rational Gspectra 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 Gspectra. 

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 GulbrandsenHalleHulek 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 groundbased 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 / Gactions / ARquivers, 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  J11  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 CohenMacaulay 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 algebrogeometric invariant of the projective schemes themselves, namely their CastelnuovoMumford 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 eciency, 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 vastpartly conjecturalprogramme 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 Kgroup of $F$ (viz. $K_7(F)$). 

May 11  Thu  Xiaolei Zhao (Northeastern)  Algebra / Algebraic Geometry seminar 
14:30  J11  0cycles 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 0cycles is known to be huge. On the other hand, the 0cycles 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 hyperKähler varieties, and explain a conjectural connection between the K3 surface case and the hyperKähler 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 Bridgelandstable 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 Bridgelandstable 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: Smallscale 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 cospatial to EBlike events in the quietSun 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 Frepresentation type (FFRT) of hypersurfaces  
May 16  Tue  Sarah Browne (Sheffield)  Topology seminar 
00:00  J11  An orthogonal quasispectrum for graded Etheory  
Abstract: Graded Etheory 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 quasitopological space and explain why this notion is necessary in our case. We will define the notion of an orthogonal quasispectrum as an orthogonal spectrum for quasitopological spaces, and further give the quasitopological spaces to form the spectrum for graded Etheory. If time allows I will give the smash product structure. 

May 16  Tue  Ariel Weiss (Sheffield)  Number Theory Learning Seminar 
13:00  J11  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 Ktheory and Noncommutative Geometry Seminar 
14:00  J11  Khomology  
May 16  Tue  Sarah Browne (Sheffield)  Topology seminar 
16:00  J11  Quasitopological assembly for K theory  
May 17  Wed  Jaroslaw Buczynski (IMPAN Warsaw)  Pure Maths Colloquium 
15:00  J11  Constructions of kregular 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 kregular 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 PoissonLie 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  J11  Adelic story. Part III.  
Abstract: Tensor product theorem, odds and ends. 

May 23  Tue  Sven Meinhardt (Sheffield)  Operator Ktheory 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 Gspectra  
Abstract: Recently, there has been some new understanding of various possible commutative ring Gspectra. In this talk I will recall these possibilities and discuss the most naive (or trivial) commutative ring Gspectra. 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 Gspectra. 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 a`categorical Heisenberg action' on \oplus_n D(Hilb_n(X)), which categorifies the NakajimaGrojnowski 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 Ktheory and Noncommutative Geometry Seminar 
14:00  J11  The BaumConnes conjecture.  
Abstract: We make a gentle introduction to the BaumConnes 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  