Seminar history    

2019-02-22 Fri James Cranch THH reading group
14:00 J11 Topological Hochschild Homology

2019-02-21 Thu Farrell Brumley (Paris 13) Pure Maths Colloquium
14:00 J11 Automorphic forms and rational points
In what sense can automorphic forms or Galois representations be viewed as rational points on an algebraic variety? One way to explore this question is by counting arguments. The first result in this direction dates back to an early theorem of Drinfeld, which computes the number of 2-dimensional Galois representations of a function field in positive characteristic; the resulting expression is reminiscent of a Lefschetz fixed point theorem on a smooth algebraic variety over a finite field. More recently it was observed that in the number field setting there are formal similarities between the asymptotic counting problems for rational points on Fano varieties and for automorphic representations on reductive algebraic groups. Very little is known in the latter context. I’ll discuss joint work on this topic with Djordje Milicevic, in which we (mostly) solve the automorphic counting problem on the general linear group. Our results can be viewed as being analogous to the well-known result of Schanuel on the number of rational points of bounded height on projective spaces. If time permits, I may also present a short argument, using sphere packings in large dimensions, to give upper bounds on such automorphic counts.

2019-02-21 Thu Sophia Wright (Warwick) Statistics Seminar
14:00 LT E Bayesian Networks, Total Variation and Robustness
This talk explores the robustness of large Bayesian Networks when applied in decision support systems which have a pre-specified subset of target variables. We develop new methodology, underpinned by the total variation distance, to determine whether simplifications which are currently employed in the practical implementation of such graphical systems are theoretically valid. This same process can identify areas of the system which should be prioritised if elicitation is required. This versatile framework enables us to study the effects of misspecification within a Bayesian network (BN), and also extend the methodology to quantify temporal effects within Dynamic BNs. Unlike current robustness analyses, our new technology can be applied throughout the construction of the BN model; enabling us to create tailored, bespoke models. For illustrative purposes we shall explore the field of Food Security within the UK.

2019-02-20 Wed Farrell Brumley (Paris 13) Northern Number Theory Seminar
11:00 J11 Concentration properties of theta lifts
I will present some results on the concentration properties of automorphic forms obtained through the theta correspondence. Among other things, the method relies on a distinction principle for these lifts, which detect their functorial origin via the non vanishing of orthogonal periods. The examples we treat are in higher rank, and shed light on a purity conjecture of Sarnak. This is joint work with Simon Marshall.

2019-02-20 Wed Heather Harrington (Oxford) Applied Mathematics Colloquium
14:00 Hicks, LT 9 Comparing models and biological data using computational algebra and topology
Many biological problems, such as tumor-induced angiogenesis (the growth of blood vessels to provide nutrients to a tumor), or signaling pathways involved in the dysfunction of cancer (sets of molecules that interact that turn genes on/off and ultimately determine whether a cell lives or dies), can be modeled using differential equations. There are many challenges with analyzing these types of mathematical models, for example, rate constants, often referred to as parameter values, are difficult to measure or estimate from available data. I will present mathematical methods we have developed to enable us to compare mathematical models with experimental data. Depending on the type of data available, and the type of model constructed, we have combined techniques from computational algebraic geometry and topology, with statistics, networks and optimization to compare and classify models without necessarily estimating parameters. Specifically, I will introduce our methods that use computational algebraic geometry (e.g., Gröbner bases) and computational algebraic topology (e.g., persistent homology). I will present applications of our methodology on datasets involving cancer. Time permitting, I will conclude with our current work for analyzing spatio-temporal datasets with multiple parameters using computational algebraic topology. Mathematically, this is studying a module over a multivariate polynomial ring, and finding discriminating and computable invariants.

2019-02-20 Wed Andreea Mocanu (University of Nottingham) Northern Number Theory Seminar
14:00 J11 Newform theory for Jacobi forms of lattice index
I will give a brief introduction to Jacobi forms, including some examples and their relation to other types of modular forms. After that, I will discuss some of the ingredients that go into developing a theory of newforms for Jacobi forms of lattice index, namely Hecke operators, level raising operators and orthogonal groups of discriminant modules.

2019-02-20 Wed Clark Barwick (Edinburgh) Topology seminar
16:00 LT11 Primes, knots, and exodromy
Half a century ago, Barry Mazur and David Mumford suggested a remarkable dictionary between prime numbers and knots. I will explain how the story of exodromy permits one to make this dictionary precise, and I will describe some applications.

2019-02-15 Fri Dan Graves THH reading group
14:00 J11 Hochschild Homology and Cyclic Homology of rings

2019-02-14 Thu Carolina Robustini (Stockholm University)
10:00 Chromospheric observations and magnetic configuration of a supergranular structure
We present high spatial resolution narrow-band images in three different chromospheric spectral lines, including Ca II K with the new CHROMospheric Imaging Spectrometer installed at the Swedish 1-m Solar Telescope. These observations feature a unipolar region enclosed in a supergranular cell, and located 68º off the disk-centre. The observed cell exhibits a radial arrangement of the fibrils which recalls of a chromospheric rosette. However, in this case, the convergence point of the fibrils is located at the very centre of the supergranular cell. Our study aims to show how the chromosphere appears in this peculiar region and retrieve its magnetic field and velocity distribution. In the centre of the cell, we measured a significant blue-shift in the Ca II K nominal line core associated to an intensity enhancement. We interpreted it as the product of a strong velocity gradient along the line of sight. In this talk, we will discuss the techniques employed to obtain magnetic field maps so close to the limb and suggest a possible configuration that takes into account also the measured velocity within the unipolar region.

2019-02-14 Thu Eleanor Stillman (Sheffield)
12:00 Hicks LT5 An overview of the HEA direct application process.
This talk will outline the process of directly applying to become a (associate-principal) fellow of the HEA. The talk will help Ph.D. students to Professors understand what is required in the application and how to be successful. We may also discuss the value and implications of receiving professional recognition from the HEA.

2019-02-14 Thu Andrey Lazarev (Lancaster) Topology seminar
16:00 J11 Homotopy theory of monoids
I will explain how the category of discrete monoids models the homotopy category of connected spaces. This correspondence is based on derived localization of associative algebras and could be viewed as an algebraization result, somewhat similar to rational homotopy theory (although not as structured). Closely related to this circle of ideas is a generalization of Adams’s cobar construction to general nonsimply connected spaces due to recent works of Rivera-Zeinalian and Hess-Tonks. (joint with J. Chuang and J. Holstein)

2019-02-14 Thu Will Hulme / Nick Monk / Rhoda Hawkins (Manchester / Sheffield / Sheffield) RSS Seminar Series
16:30 Hicks Room F38 Experiences of AIMS
AIMS is an academic network that enables Africa’s talented students to become innovators who propel scientific, educational and economic self-sufficiency. The RSS Local Group are delighted to welcome Will Hulme (University of Manchester, taught at AIMS Cameroon), Prof Nick Monk (University of Sheffield, SOMAS, taught at AIMS Ghana) and Dr Rhoda Hawkins (University of Sheffield, Department of Physics and Astronomy, taught at AIMS South Africa, Senegal and Ghana) to present on their experiences on the AIMS project. Tutor/lecturer opportunities that may be of interest will be highlighted.

2019-02-13 Wed Ana Caraiani (Imperial) Pure Maths Colloquium
14:00 J11 On the Ramanujan conjecture and its generalisations
In 1916, Ramanujan made a conjecture that can be stated in completely elementary terms: he predicted an upper bound on the coefficients of a power series obtained by expanding a certain infinite product. In this talk, I will discuss a more sophisticated interpretation of this conjecture, via the Fourier coefficients of a highly symmetric function known as a modular form. I will give a hint of the idea in Deligne’s proof of the conjecture in the 1970’s, who related it to the arithmetic geometry of smooth projective varieties over finite fields. Finally, I will discuss generalisations of this conjecture and some recent progress on these using the machinery of the Langlands program. The last part is based on joint work with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne.

2019-02-07 Thu Jeremy Colman (Sheffield) Statistics Seminar
14:00 LT E Accounting for Uncertainty in Estimates of Extremes
Devastating consequences can flow from the failure of certain structures, such as coastal flood defences, nuclear installations, and oil rigs. Their design needs to be robust under rare (p < 0.0001) extreme conditions, but how can the designers use data typically from only a few decades to predict the size of an event that might occur once in 10,000 years? Extreme Value Theory claims to provide a sound basis for such far-out-of-sample prediction, and using Bayesian methods a full posterior distribution can be obtained. If the past data are supplemented by priors that take into account expert opinion, seemingly tight estimates result. Are such claims justified? Has all uncertainty been taken into account? My research is addressing these questions.

2019-02-07 Thu Masahiro Nakahara (Manchester) Number Theory seminar
14:00 J11 Index of Fibrations and Brauer classes that never obstruct the Hasse principle
Let X be a smooth projective variety over a number field with a fibration into varieties that satisfy a certain condition. We study the classes in the Brauer group of X that never obstruct the Hasse principle for X. We prove that if the generic fiber has a zero-cycle of degree d over the generic point, then the Brauer classes whose orders are prime to d do not play a role in the Brauer-Manin obstruction. As a result we show that the odd torsion Brauer classes never obstruct the Hasse principle for del Pezzo surfaces of degree 2, certain K3 surfaces, and Kummer varieties.

2019-02-06 Wed Viveka Erlandsson (Bristol) Pure Maths Colloquium
14:00 J11 Determining the shape of a billiard table from its bounces
Consider a billiard table shaped as a Euclidean polygon with labeled sides. A ball moving around on the table determines a bi-infinite “bounce sequence” by recording the labels of the sides it bounces off. We call the set of all possible bounce sequences the “bounce spectrum” of the table. In this talk I will explain why the bounce spectrum essentially determines the shape of the table: with the exception of a very small family (right-angled tables), if two tables have the same bounce spectrum, then they have to be related by a Euclidean similarity. The main ingredient in proving this fact is a technical result about non-singular geodesics on surfaces equipped with flat cone metrics. This is joint work with Moon Duchin, Chris Leininger, and Chandrika Sadanand.

2019-01-31 Thu Prof. Valery Nakariakov (Centre for Fusion, Space and Astrophysics, University of Warwick) Plasma Dynamics Group
15:00 Lecture theatre 1 (Hicks Building) The effect of thermal misbalance on compressive oscillations in solar coronal loops
Fast and slow magnetoacoustic waves are a promising tool for the seismological diagnostics of physical parameters of various plasma structures in the corona of the Sun. In particular, compressive waves can provide us with information about the thermodynamic equilibrium in the coronal plasma, and hence the heating function. Compressive perturbations of the thermodynamic equilibrium by magnetoacoustic waves can cause the misbalance of the radiative cooling and unspecified heating. The effect of the misbalance is determined by the derivatives of the combined heating/cooling function with respect to the plasma density and temperature, and can lead to either enhanced damping of the compressive oscillations or their magnification. Moreover, in the regime of strong misbalance, compressive MHD waves are subject to wave dispersion that can slow down the formation of shocks and can cause the formation of quasi-periodic wave trains.

2019-01-25 Fri Kalevi Mursula (University of Oulu) SP2RC seminar
10:30 LT E Centennial evolution and terrestrial effects of the global solar magnetic field

2019-01-23 Wed Richard Webb (Cambridge) Pure Maths Colloquium
14:00 J11 An interplay between topology, geometry, and the algebra of the mapping class group
The braid groups were defined by Artin in 1925, and are usually defined in terms of strings in 3-dimensional space. However there is a fruitful 2-dimensional perspective of the braid groups as homeomorphisms (up to some natural equivalence) of a disc with holes, in other words, the braid groups are special cases of mapping class groups of surfaces. Mapping class groups can be viewed in a number of ways, and are of interest in several different fields, such as dynamics, algebraic geometry, surface bundles, hyperbolic geometry, to name a few. A key theorem that demonstrates this intradisciplinary feature is the Nielsen--Thurston classification. I will explain what the Nielsen--Thurston classification is, describe some basic examples and analogies, and highlight its importance. I will then explain how to view this from the geometric group theory perspective, and discuss my work with Mark Bell that uses this point of view to solve the conjugacy problem for mapping class groups in polynomial time. At the end of the talk I will discuss some new ideas that may lead to applications in knot theory via the braid groups.

2019-01-18 Fri Norbert Gyenge (Sheffield) SP2RC seminar
13:00 LT 10 The Nonaxisymmetric Behaviour Of Solar Eruptive Events
This thesis investigates new approaches for predicting the occurrence of solar eruptive events based on coronal mass ejection (CME), solar flare and sunspot group observations. The scope of the present work is to study the spatio-temporal properties of the above-mentioned solar features. The analysis may also provide a deeper understanding of the subject of solar magnetic field reorganisation. Furthermore, the applied approaches may open opportunities for connecting these local phenomena with the global physical processes that generate the magnetic field of the Sun, called the solar dynamo. The investigation utilises large solar flare statistical populations and advanced computational tools, such as clustering techniques, wavelet analysis, autoregressive moving average (ARIMA) forecast, kernel density estimations (KDEs) and so on. This work does not attempt to make actual predictions because it is out of the scope of the recent investigation. However, the thesis introduces new possible approaches in the subject of flare and CME forecasting. The future aim is to construct a real-time database with the ability to forecast eruptive events based on the findings of this thesis. This potential forecasting model may be crucial for protecting a wide range of satellite systems around the Earth or predicting space weather based on the obtained results may also assist to plan safe space exploration in the future.

2019-01-17 Thu Ricardo Gaferia (Instituto de Astrofísica de Andalucía - CSIC ) SP2RC seminar
10:00 LT 10 Machine learning assisted parallel inversions
With the increase of data volume and the need of more complex inversion codes to interpret and analyze solar observations, it is necessary to develop new tools to boost inversions and reduce computation times and costs. In this presentation, I discuss the possibilities and limitations of using machine learning as a tool to estimate optimum initial physical atmospheric models necessary for initializing spectral line inversions. Tests have been carried out for the SIR and DeSIRer inversion codes. This approach allows firstly to reduce the number of cycles in the inversion and increase the number of nodes and secondly to automatically cluster pixels which is an important step to invert maps where completely different regimes are present. Finally, I also present a warp for SIR and DeSIRer inversion codes that allows the user to easily set up parallel inversions.

2019-01-16 Wed Atsushi Takahashi (Osaka) Algebra / Algebraic Geometry seminar
16:00 J11 On a full exceptional collection in the category of maximally graded matrix factorizations of an invertible polynomial of chain type
In ’77 Orlik-Randell asked about the existence of a certain distinguished basis of vanishing cycles in the Milnor fiber associated to an invertible polynomial of chain type. With my student, Daisuke Aramaki we transport their conjecture to the category of matrix factorizations by the (conjectural) homological mirror symmetry equivalence and then prove the resulting statement.

2019-01-08 Tue Josep Alvarez-Montaner (Universitat Politecnica de Catalunya) Algebra / Algebraic Geometry seminar
14:00 J11 Local cohomology of binomial edge ideals and their generic initial ideals
The aim of this talk is to give a detailed study of local cohomology modules of binomial edge ideals. Our main result is a Hochster type decomposition formula for these modules. As a consequence, we obtain a simple criterion for the Cohen-Macaulayness of these ideals and we describe their Castelnuovo-Mumford regularity and their Hilbert series. We also prove a conjecture of Conca, De Negri and Gorla relating the graded components of the local cohomology modules of binomial edge ideals and their generic initial ideals.