Past

Let $F$ be a non-Archimedean local field with ring of integers $\mathcal O$ and maximal ideal $\mathfrak p$. T. Shintani and G. Hill independently introduced a large class of smooth representations of $GL_N(\mathcal O)$, called regular representations. Roughly speaking they correspond to elements in the Lie algebra $M_N(\mathcal O)$ which are regular mod $\mathfrak p$ (i.e, having centraliser of dimension $N$). The study of regular representations of $GL_N(\mathcal O)$ goes back to Shintani in the 1960s, and independently and later, Hill, who both constructed the regular representations with even conductor, but left the much harder case of odd conductor open. In recent simultaneous and independent work, Krakovski, Onn and Singla gave a construction of the regular representations of $GL_N(\mathcal O)$ when the residue characteristic of $\mathcal O$ is not $2$.

In this talk I will present a complete construction of all the regular representations of $GL_N(\mathcal O)$. The approach is analogous to, and motivated by, the construction of supercuspidal representations of $GL_N(F)$ due to Bushnell and Kutzko. This is joint work with Shaun Stevens.
 

The object of this talk is a class of generalised Newtonian fluids with implicit constitutive law.
Both in the steady and the unsteady case, existence of weak solutions was proven by Bul\'\i{}\v{c}ek et al. (2009, 2012) and the main challenge is the small growth exponent qq and the implicit law.
I will discuss the application of a splitting and regularising strategy to show convergence of FEM approximations to weak solutions of the flow. 
In the steady case this allows to cover the full range of growth exponents and thus generalises existing work of Diening et al. (2013). If time permits, I will also address the unsteady case.
This is joint work with Endre Suli.

In this talk, I will present the construction of a family of solutions to
vacuum Einstein equations which consist of an arbitrary number of high
frequency waves travelling in different directions. In the high frequency
limit, our family of solutions converges to a solution of Einstein equations
coupled to null dusts. This construction is an illustration of the so called
backreaction, studied by physicists (Isaacson, Burnet, Green, Wald...) : the
small scale inhomogeneities have an effect on the large scale dynamics in
the form of an energy impulsion tensor in the right-hand side of Einstein
equations. This is a joint work with Jonathan Luk (Stanford).

Protein interaction networks (PINs) allow the representation and analysis of biological processes in cells. Because cells are dynamic and adaptive, these processes change over time. Thus far, research has focused either on the static PIN analysis or the temporal nature of gene expression. By analysing temporal PINs using multilayer networks, we want to link these efforts. The analysis of temporal PINs gives insights into how proteins, individually and in their entirety, change their biological functions. We present a general procedure that integrates temporal gene expression information with a monolayer PIN to a temporal PIN and allows the detection of modular structure using multilayer modularity maximisation.

I will present some recent results obtained in collaboration with V. Banica and F. de la Hoz on the evolution of vortex filaments according to the so called Localized Induction Approximation  (LIA). This approximation is given by a non-linear geometric partial differential equation, that is known under the name of the Vortex Filament Equation (VFE). The aim of the talk is threefold. First, I will recall the Talbot effect of linear optics.  Secondly, I will give some explicit solutions of VFE where this Talbot effect is also present. Finally, I will consider some questions concerning the transfer of energy and momentum for these explicit solutions.

We present a support theorem for subcritical parabolic stochastic partial differential equations (SPDEs) driven by Gaussian noises. In the spirit of the classical theorem by Stroock and Varadhan for ordinary stochastic differential equations, we identify the support of the solution to singular SPDEs with the closure of the union of the support of solutions to approximate and renormalized equations. We implement our approach in the setting of regularity structures and obtain a general result covering a range of singular SPDEs (including $\Phi^4_3$, $\Phi^d_2$, KPZ, PAM (2D+3D), SHE, ...). As a Corollary to our result we obtain the uniqueness of invariant measures for various interesting SPDEs. This is a joint work with Martin Hairer.

We present a numerical investigation of stochastic transport for the damped and driven incompressible 2D Euler fluid flows. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a physically meaningful, data-driven approach for decomposing the fluid transport velocity into its drift and stochastic parts, for a certain class of fluid flows. We develop a new methodology to implement this velocity decomposition and then numerically integrate the resulting stochastic partial differential equation using a finite element discretisation. We show our numerical method is consistent.
Numerically, we perform the following analyses on this velocity decomposition. We first perform uncertainty quantification tests on the Lagrangian trajectories by comparing an ensemble of realisations of Lagrangian trajectories driven by the stochastic differential equation, and the Lagrangian trajectory driven by the ordinary differential equation. We then perform uncertainty quantification tests on the resulting stochastic partial differential equation by comparing the coarse-grid realisations of solutions of the stochastic partial differential equation with the ``true solutions'' of the deterministic fluid partial differential equation, computed on a refined grid. In these experiments, we also investigate the effect of varying the ensemble size and the number of prescribed stochastic terms. Further experiments are done to show the uncertainty quantification results "converge" to the truth, as the spatial resolution of the coarse grid is refined, implying our methodology is consistent. The uncertainty quantification tests are supplemented by analysing the L2 distance between the SPDE solution ensemble and the PDE solution. Statistical tests are also done on the distribution of the solutions of the stochastic partial differential equation. The numerical results confirm the suitability of the new methodology for decomposing the fluid transport velocity into its drift and stochastic parts, in the case of damped and driven incompressible 2D Euler fluid flows. This is the first step of a larger data assimilation project which we are embarking on. This is joint work with Colin Cotter, Dan Crisan, Darryl Holm and Igor Shevchenko.

 

3d N=4 supersymmetric gauge theories provide a method for constructing HyperK\”ahler singularities, known as the Coulomb branch.
This method is complementary to the more traditional way of construction using HyperK\”ahler quotients, known in physics as the “Higgs branch”.
Out of all possible gauge theories there is an interesting subclass of quiver varieties, where the Coulomb branch has been studied in some detail.
Some examples are moduli spaces of classical and exceptional instantons and closures of nilpotent orbits. An interesting feature of Coulomb and Higgs branches is the phenomenon of "3d mirror symmetry” where for a pair of gauge theories, the Higgs branch and Coulomb branch exchange.
There is a large class of “mirror pairs” which I will discuss in some detail.

A topic of recent interest is the notion of implosions. I will argue that there is a simple operation on the quiver which leads to implosion. In other words, given a quiver such that its Coulomb branch is moduli space A, a simple operation of the quiver (making a bouquet) provides the implosion of A.
This has been tested on closures of nilpotent orbits of A type and on nilpotent cones of orthogonal groups and found to agree with the expected results.
If time permits, I will discuss isometries of Coulomb branches

The horizon conjecture, proved in a case by case basis, states that every supersymmetric smooth horizon admits an sl(2, R) symmetry algebra. However it is unclear how string corrections modify the statement. In this talk I will present the analysis of supersymmetric near-horizon geometries in heterotic supergravity up to two loop order in sigma model perturbation theory, and show the conditions for the horizon to admit an sl(2, R) symmetry algebra. In the second part of the talk, I shall consider the inverse problem of determining all extreme black hole solutions associated to a prescribed near-horizon geometry. I will expand the horizon fields in the radial co-ordinate, the so-called moduli, and show that the moduli must satisfy a system of elliptic PDEs, which implies that the moduli space is finite dimensional.

The talk is based on arXiv:1605.05635 [hep-th] and arXiv:1610.09949 [hep-th].

Who are you? What motivates you? What's important to you? How do you react to challenges and adversities? In this session we will explore the power of self-awareness (understanding our own characters, values and motivations) and introduce assertiveness skills in the context of building positive and productive relationships with colleagues, collaborators, students and others.
 

In this talk, I show how concepts from non-equilibrium statistical physics can be employed in the study of climate. The specific problem addressed is the geophysical-scale evolution of Arctic sea ice. Using an analogy with Brownian motion, the original evolution equation for the sea ice thickness distribution function by Thorndike et al. (J. Geophys. Res. 80(33), pp. 4501 — 4513, 1975) is transformed to a Fokker-Planck-like conservation law. The steady solution is $g(h) = {\cal N}(q) h^q \mathrm{e}^{-~ h/H}$, where $q$ and $H$ are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for $h \ll 1$, $g(h)$ is controlled by both thermodynamics and mechanics, whereas for $h \gg 1$ only mechanics controls $g(h)$. We also derive the underlying Langevin equation governing the dynamics of the ice thickness $h$, from which we predict the observed $g(h)$. Further, seasonality is introduced by using the Eisenman-Wettlaufer model (Proc. Natl. Acad. Sci. USA 106, pp. 28-32, 2009) for the thermal growth of sea ice. The time-dependent problem is studied by numerically integrating the Fokker-Planck equation. The results obtained from these numerical integrations and their comparison with satellite observations are discussed.

Dr Nicola Beer heads up the Department of Stem Cell Engineering at the new Novo Nordisk Research Centre Oxford. Her team will use human stem cells to derive metabolically-relevant cells and tissues such as islets, hepatocytes, and adipocytes todiscover novel secreted factors and corresponding signalling pathways which modify cell function, health, and viability. Bycombining in vitro-differentiated human stem cell-derived models with CRISPR and other genomic targeting techniques, the teamassay cell function from changes in a single gene up to a genome-wide scale. Understanding the genes and pathways underlying cell function (and dysfunction) highlights potential targets for new Type 2 Diabetes therapeutics. Dr Beer will talk about the work ongoing in her team, as well as more broadly about the role of human stem cells in drug discovery and patient treatment.

This talk will discuss efficient numerical methods for estimating the
probability of a large portfolio loss, and associated risk measures such
as VaR and CVaR.  These involve nested expectations, and following
Bujok, Hambly & Reisinger (2015) we use the number of samples for the
inner conditional expectation as the key approximation parameter in the
Multilevel Monte Carlo formulation.  The main difference in this case is
the indicator function in the definition of the probability. Here we
build on previous work by Gordy & Juneja (2010) who analyse the use of a
fixed number of inner samples , and Broadie, Du & Moallemi (2011) who
develop and analyse an adaptive algorithm.  I will present the
algorithm, outline the main theoretical results and give the numerical
results for a representative model problem.  I will also discuss the
extension to real portfolios with a large number of options based on
multiple underlying assets.

Joint work with Abdul-Lateef Haji-Ali

I will present Vidit Nanda's paper "Local homology and stratification" (https://arxiv.org/abs/1707.00354), and briefly explain how in my master thesis I am applying ideas from the paper to study word embedding problems.

Abstract of the paper:  We outline an algorithm to recover the canonical (or, coarsest) stratification of a given regular CW complex into cohomology manifolds, each of which is a union of cells. The construction proceeds by iteratively localizing the poset of cells about a family of subposets; these subposets are in turn determined by a collection of cosheaves which capture variations in cohomology of cellular neighborhoods across the underlying complex. The result is a finite sequence of categories whose colimit recovers the canonical strata via (isomorphism classes of) its objects. The entire process is amenable to efficient distributed computation.
 

A theorem of Gromov states that the number of generators of the fundamental group of a manifold with nonnegative 
curvature is bounded by a constant which only depends on the dimension of the manifold. The main ingredient 
in the proof is Toponogov’s theorem, which roughly speaking says that the triangles on spaces with positive 
curvature, such as spheres, are thick compared to triangles in the Euclidean plane. In the talk I shall explain 
this more carefully and deduce Gromov’s result.

I will give a gentle introduction to joint work in progress with George Boxer, Frank Calegari, and Vincent Pilloni, in which we prove that all abelian surfaces over totally real fields are potentially modular. We also prove that infinitely many abelian surfaces over Q are modular.

What if one desires to have a World perfectly slippery to water? What are the strategies that can be adopted? And how can smart slippery surfaces be created? In this seminar, I will outline approaches to creating slippery surfaces, which all involve reducing or removing droplet contact with the solid, whilst still supporting the droplet. The first concept is to decorate the droplet surface with particles, thus creating liquid marbles and converting the droplet-solid contact into a solid-solid contact. The second concept is to use the Leidenfrost effect to instantly vaporize a layer of water, thus creating a film of vapor and converting the droplet-solid contact into vapor-solid contact. The third concept is to infuse oil into the surface, thus creating a layer of oil and converting the droplet-solid contact into a lubricant-solid contact. I will also explain how we design such to have smart functionality whilst retaining and using the mobility of contact lines and droplets. I will show how Leidenfrost levitation can lead to new types of heat engines [1], how a microsystems approach to the Leidenfrost effect can reduce energy input and lead to a new type of droplet microfluidics [2] (Fig. 1a) and how liquid diodes can be created [3]. I will explain how lubricant impregnated surfaces lead to apparent contact angles [4] and how the large retained footprint of the droplet allows droplet transport and microfluidics using energy coupled via a surface acoustic wave (SAW) [5]. I will argue that droplets confined between reconfigurable slippery boundaries can be continuously translated in an energy invariant manner [6] (Fig. 1b). I will show that a droplet Cheerios effect induced by the menisci arising from structuring the underlying lubricated surface or by droplets in close proximity to each other can be used to guide and position droplets [7] (Fig. 1c). Finally, I will show that active control of droplet spreading by electric field induced control of droplet spreading, via electrowetting or dielectrowetting, can be achieved with little hysteresis [8] and can be a new method to investigate the dewetting of surfaces [9].

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Figure 1 Transportation and positioning of droplets using slippery surfaces: (a) Localized Leidenfrost effect, (b) Reconfigurable boundaries, and (c) Droplet Cheerio’s effect.

Acknowledgements The financial support of the UK Engineering & Physical Sciences Research Council (EPSRC) and Reece Innovation ltd is gratefully acknowledged. Many collaborators at Durham, Edinburgh, Nottingham Trent and Northumbria Universities were instrumental in the work described.

[1] G.G. Wells, R. Ledesma-Aguilar, G. McHale and K.A. Sefiane, Nature Communications, 2015, 6, 6390.

[2] L.E. Dodd, D. Wood, N.R. Geraldi, G.G. Wells, et al., ACS Applied & Materials Interfaces, 2016, 8, 22658.

[3] J. Li, X. Zhou , J. Li, L. Che, J. Yao, G. McHale, et al., Science Advances, 2017, 3, eaao3530.

[4] C. Semprebon, G. McHale, and H. Kusumaatmaja, Soft Matter, 2017, 13, 101.

[5] J.T. Luo, N.R. Geraldi, J.H. Guan, G. McHale, et al., Physical Review Applied, 2017, 7, 014017.

[6] É. Ruiz-Gutiérrez, J.H. Guan, B.B. Xu, G. McHale, et al., Physical Review Letters, 2017, 118, 218003.

[7] J.H. Guan, É. Ruiz-Gutiérrez, B.B. Xu, D. Wood, G. McHale, et al., Soft Matter, 2017, 13, 3404.

[8] Z. Brabcová, G. McHale, G.G. Wells, et al., Applied Physics Letters, 2017, 110, 121603.

[9] A.M.J. Edwards, R. Ledesma-Aguilar, et al., Science Advances, 2016, 2, e1600183

A classical construction principle for dependent failure times is to consider shocks that destroy components within a system. The arrival times of shocks can destroy arbitrary subsets of the system, thus introducing dependence. The seminal model – based on independent and exponentially distributed shocks - was presented by Marshall and Olkin in 1967, various generalizations have been proposed in the literature since then. Such models have applications in non-life insurance, e.g. insurance claims caused by floods, hurricanes, or other natural catastrophes. The simple interpretation of multivariate fatal shock models is clearly appealing, but the number of possible shocks makes them challenging to work with, recall that there are 2^d subsets of a set with d components. In a series of papers we have identified mixture models based on suitable stochastic processes that give rise to a different - and numerically more convenient - stochastic interpretation. This representation is particularly useful for the development of efficient simulation algorithms. Moreover, it helps to define parametric families with a reasonable number of parameters. We review the recent literature on multivariate fatal shock models, extreme-value copulas, and related dependence structures. We also discuss applications and hierarchical structures. Finally, we provide a new characterization of the Marshall-Olkin distribution.

Authors: Mai, J-F.; Scherer, M.;

The rapidly increasing number of cores in high-performance computing systems causes a multitude of challenges for developers of numerical methods. New parallel algorithms are required to unlock future growth in computing power for applications and energy efficiency and algorithm-based fault tolerance are becoming increasingly important. So far, most approaches to parallelise the numerical solution of partial differential equations focussed on spatial solvers, leaving time as a bottleneck. Recently, however, time stepping methods that offer some degree of concurrency, so-called parallel-in-time integration methods, have started to receive more attention.

I will introduce two different numerical algorithms, Parareal (by Lions et al., 2001) and PFASST (by Emmett and Minion, 2012), that allow to exploit concurrency along the time dimension in parallel computer simulations solving partial differential equations. Performance results for both methods on different architectures and for different equations will be presented. The PFASST algorithm is based on merging ideas from Parareal, spectral deferred corrections (SDC, an iterative approach to derive high-order time stepping methods by Dutt et al. 2000) and nonlinear multi-grid. Performance results for PFASST on close to half a million cores will illustrate the potential of the approach. Algorithmic modifications like IPFASST will be introduced that can further reduce solution times. Also, recent results showing how parallel-in-time integration can provide algorithm-based tolerance against hardware faults will be shown.

When nematic liquid crystal droplets are produced in the form or tori (or such is the shapes of confining cavities), they may be called toroidal nematics, for short. When subject to degenerate planar anchoring on the boundary of a torus, the nematic director acquires a natural equilibrium configuration within the torus, irrespective of the values of Frank's elastic constants. That is the pure bend arrangement whose integral lines run along the parallels of all inner deflated tori. This lecture is concerned with the stability of such a universal equilibrium configuration. Whenever its stability is lost, new equilibrium configurations arise in pairs, the members of which are symmetric and exhibit opposite chirality. Previous work has shown that a rescaled saddle-splay constant may be held responsible for such a chiral symmetry breaking. We shall show that that is not the only possible instability mechanism and, perhaps more importantly, we shall attempt to describe the qualitative properties of the equilibrium nematic textures that prevail when the chiral symmetry is broken.

Cube Complexes with Coupled Links (CLCC) are a special family of non-positively curved cube complexes that are constructed by specifying what the links of their vertices should be. In this talk I will introduce the construction of CLCCs and try to motivate it by explaining how one can use information about the local geometry of a cube complex to deduce global properties of its fundamental group (e.g. hyperbolicity and cohomological dimension). On the way, I will also explain what fly maps are and how to use them to deduce that a CAT(0) cube complex is hyperbolic.

Let n be a positive integer. In this talk we provide a recipe to 
construct full orbit sequences in the affine n-dimensional space over a 
finite field. For n=1 our construction covers the case of the well 
studied pseudorandom number generator ICG.

This is a joint work with Federico Amadio Guidi.

A longstanding open question asks whether every unstable NIP theory interprets an infinite linear order. I will present a construction that almost provides a positive answer. I will also discuss some conjectural applications to the classification of omega-categorical NIP structure, generalizing what is known for omega-stable, and classification of models mimicking the superstable case.
 

Following Grothendieck's vision that many cohomological invariants of of an algebraic variety should be captured by a common motive, Voevodsky introduced a triangulated category of mixed motives which partially realises this idea. After describing this category, I will explain how to define the motive of certain algebraic stacks in this context. I will then report on joint work in progress with Victoria Hoskins, in which we study the motive of the moduli stack of vector bundles on a smooth projective curve and show that this motive can be described in terms of the motive of this curve and its symmetric powers.
 

We generalise the existence of combinatorial designs to the setting of subset sums in lattices with coordinates indexed by labelled faces of simplicial complexes. This general framework includes the problem of decomposing hypergraphs with extra edge data, such as colours and orders, and so incorporates a wide range of variations on the basic design problem, notably Baranyai-type generalisations, such as resolvable hypergraph designs, large sets of hypergraph designs and decompositions of designs by designs. Our method also gives approximate counting results, which is new for many structures whose existence was previously known, such as high dimensional permutations or Sudoku squares.

We consider the problem of localising non-negative point sources, namely finding their locations and amplitudes from noisy samples which consist of the convolution of the input signal with a known kernel (e.g. Gaussian). In contrast to the existing literature, which focuses on TV-norm minimisation, we analyse the feasibility problem. In the presence of noise, we show that the localised error is proportional to the level of noise and depends on the distance between each source and the closest samples. This is achieved using duality and considering the spectrum of the associated sampling matrix.

A simple experiment in the field of electrochemistry involves  controlling the applied potential in an electrochemical cell. This  causes electron transfer to take place at the electrode surface and in turn this causes a current to flow. The current depends on parameters in  the system and the inverse problem requires us to estimate these  parameters given an experimental trace of the current. We briefly  describe recent work in this area from simple least squares approximation of the parameters, through bootstrapping to estimate the distributions of the parameters, to MCMC methods which allow us to see correlations between parameters.

Protein interaction networks (PINs) allow the representation and analysis of biological processes in cells. Because cells are dynamic and adaptive, these processes change over time. Thus far, research has focused either on the static PIN analysis or the temporal nature of gene expression. By analysing temporal PINs using multilayer networks, we want to link these efforts. The analysis of temporal PINs gives insights into how proteins, individually and in their entirety, change their biological functions. We present a general procedure that integrates temporal gene expression information with a monolayer PIN to a temporal PIN and allows the detection of modular structure using multilayer modularity maximisation.

The structure of the state of art of scientific research is an important object of study motivated by the understanding of how research evolves and how new fields of study stem from existing research. In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks, in particular keyword co-occurrence networks proved useful to provide maps of knowledge inside a scientific domain. The network approach focuses on pairwise relationships, often compressing multidimensional data structures and inevitably losing information. In this paper we propose to adopt a simplicial complex approach to co-occurrence relations, providing a natural framework for the study of higher-order relations in the space of scientific knowledge. Using topological methods we explore the shape of concepts in mathematical research, focusing on homological cycles, regions with low connectivity in the simplicial structure, and we discuss their role in the understanding of the evolution of scientific research. In addition, we map authors’ contribution to the conceptual space, and explore their role in the formation of homological cycles.

Authors: Daniele Cassese, Vsevolod Salnikov, Renaud Lambiotte
 

Some of the most studied examples of conformal field theories
include
the Wess-Zumino-Witten models. These are conformal field theories exhibiting
affine Lie algebra symmetry at non-negative integers levels. In this talk I
will
discuss conformal field theories exhibiting affine Lie algebra symmetry at
certain rational (hence fractional) levels whose structure is arguably even
more intricate than the structure of the non-negative integer levels,
provided
one is prepared to look beyond highest weight modules.

In a given ambient Riemannian manifold with boundary, geometric objects of particular interest are those properly embedded submanifolds that are critical points of the volume functional, when allowed variations are only those that preserve (but not necessarily fix) the ambient boundary. This variational condition translates into a quite nice geometric condition, namely, minimality and orthogonal intersection with the ambient boundary. Even when the ambient manifold is simply a ball in the Euclidean space, the theory of these objects is very rich and interesting. We would like to discuss several aspects of the theory, including our own contributions to the subject on topics such as: classification results, index estimates and compactness (joint works with different groups of collaborators - I. Nunes, A. Carlotto, B. Sharp, R. Buzano -  will be appropriately mentioned). 

It is a truth universally acknowledged, that a local system on a connected topological manifold is completely determined by its attached monodromy representation of the fundamental group. Similarly, lisse ℓ-adic sheaves on a connected variety determine and are determined by representations of the profinite étale fundamental group. Now if one wants to classify constructible sheaves by representations in a similar manner, new invariants arise. In the topological category, this is the exit path category of Robert MacPherson (and its elaborations by David Treumann and Jacob Lurie), and since these paths do not ‘run around once’ but ‘run out’, we coined the term exodromy representation. In the algebraic category, we define a profinite ∞-category – the étale fundamental ∞-category – whose representations determine and are determined by constructible (étale) sheaves. We describe the étale fundamental ∞-category and its connection to ramification theory, and we summarise joint work with Saul Glasman and Peter Haine.

I will talk about recent work that uses recent ideas from stochastic analysis to develop robust and non-parametric statistical tests for stochastic processes. 

In this talk, we will show how sharp bounds on the moments of the solutions to some stochastic heat equations can lead to various qualitative properties of the solutions. A major part of the method consists of approximating the solution by “independent quantities”. These quantities together with the moments bounds give us sharp almost sure properties of the solution.

For many moduli problems, in order to construct a moduli space as a geometric invariant theory quotient, one needs to impose a notion of (semi)stability. Using recent results in non-reductive geometric invariant theory, we explain how to stratify certain moduli stacks in such a way that each stratum admits a coarse moduli space which is constructed as a geometric quotient of an action of a linear algebraic group with internally graded unipotent radical. As many stacks are
naturally filtered by quotient stacks, this involves describing how to stratify certain quotient stacks. Even for quotient stacks for reductive group actions, we see that non-reductive GIT is required to construct the coarse moduli spaces of the higher strata. We illustrate this point by studying the example of the moduli stack of coherent sheaves over a projective scheme. This is joint work with G. Berczi, J. Jackson and F. Kirwan.

I will start with briefly describing the HISH ( Holography Inspired Hadronic String) model and reviewing the fits of the spectra of mesons, baryons, glue-balls and exotic hadrons. 

I will present the determination of the hadron strong decay widths. The main decay mechanism is that of a string splitting into two strings. The corresponding total decay width behaves as $\Gamma =\frac{\pi}{2}A T L $ where T and L are the tension and length of the string and A is a dimensionless universal constant. The partial width of a given decay mode is given by $\Gamma_i/\Gamma = \Phi_i \exp(-2\pi C m_\text{sep}^2/T$ where $\Phi_i$ is a phase space factor, $m_\text{sep}$ is the mass of the "quark" and "antiquark" created at the splitting point, and C is adimensionless coefficient close to unity. I will show the fits of the theoretical results to experimental data for mesons and baryons. I will examine both the linearity in L and the exponential suppression factor. The linearity was found to agree with the data well for mesons but less for baryons. The extracted coefficient for mesons $A = 0.095\pm  0.01$  is indeed quite universal. The exponential suppression was applied to both strong and radiative decays. I will discuss the relation with string fragmentation and jet formation. I will extract the quark-diquark structure of baryons from their decays. A stringy mechanism for Zweig suppressed decays of quarkonia will be proposed and will be shown to reproduce the decay width of  states. The dependence of the width on spin and symmetry will be discussed. I will further apply this model to the decays of glueballs and exotic hadrons.

Lincoln Wallen is the Former CTO, Dreamworks Animation. All are welcome

A wide range of chronic degenerative diseases of mankind result from the accumulation of altered forms of self proteins, resulting in cell toxicity, tissue destruction and chronic inflammatory processes in which the body’s immune system contributes to further cell death and loss of function. A hallmark of these conditions, which include major disease burdens such as Alzheimer’s Disease and type II diabetes, is the formation of long fibrillar polymers that are deposited in expanding tangled masses called plaques. Recently, similarities between these pathological accumulations and physiological mechanisms for organising intracellular space have been recognised, and formal demonstrations that amyloid accumulations form hydrogels have confirmed this link. We are interested in the pathological consequences of amyloid hydrogel formation and in order to study these processes we combine modelling of the assembly process with biophysical measurement of gelation and its cellular consequences.

Please see https://www.eventbrite.co.uk/e/qbiox-colloquium-dunn-school-seminar-hil…

for further details

T cells stimulation by antigen (peptide-MHC, pMHC) initiates adaptive immunity, a major factor contributing to vertebrate fitness. The T cell antigen receptor (TCR) present on the surface of T cells is the critical sensor for the recognition of and response to “foreign" entities, including microbial pathogens and transformed cells. Much is known about the complex molecular machine physically connected to the TCR to initiate, propagate and regulate signals required for cellular activation. However, we largely ignore the physical distribution, dynamics and reaction energetics of this machine before and after TCR binding to pMHC. I will illustrate a few basic notions of TCR signalling and potent quantitative in-cell approaches used to interpret TCR signalling behaviour. I will provide two examples where mathematical formalisation will be welcome to better understand the TCR signalling process.

Please see https://www.eventbrite.co.uk/e/qbiox-colloquium-dunn-school-seminar-hil… for further details.

Bacteria swim by rotating semi-rigid helical flagellar filaments, using an ion driven rotary motor embedded in the membrane. Bacteria are too small to sense a spatial gradient and therefore sense changes in time, and use the signals to bias their direction changing pattern to bias overall swimming towards a favourable environment. I will discuss how interdisciplinary research has helped us understand both the mechanism of motor function and its control by chemosensory signals.

Please see https://www.eventbrite.co.uk/e/qbiox-colloquium-dunn-school-seminar-hil…

for details.

This is the continuation of a discussion of  Ezra Miller's paper https://arxiv.org/abs/1709.08155.

I will talk about some recent work with Chantal David and Matilde Lalin about the mean value of L-functions associated to cubic characters over F_q[t] when q=1 (mod 3). I will explain how to obtain an asymptotic formula with a (maybe a little surprising) main term, which relies on using results from the theory of metaplectic Eisenstein series about cancellation in averages of cubic Gauss sums over functions fields.

A polymer, or microscopic elastic filament, is often modelled as a linear chain of rigid bodies interacting both with themselves and a heat bath. Then the classic notions of persistence length are related to how certain correlations decay with separation along the chain. I will introduce these standard notions in mathematical terms suitable for non specialists, and describe the standard results that apply in the simplest cases of wormlike chain models that have a straight, minimum energy (or ground or intrinsic) shape. Then I will introduce an appropriate  splitting of a matrix recursion in the group SE(3) which deconvolves the distinct effects of stiffness and intrinsic shape in the more complicated behaviours of correlations that arise when the polymer is not intrinsically straight. The new theory will be illustrated by fully implementing it within a simple sequence-dependent rigid base pair model of DNA. In that particular context, the persistence matrix factorisation generalises and justifies the prior scalar notions of static and dynamic persistence lengths.

Our general theory, which encompasses two different aggregation properties (Neuberger, 2012; Bondarenko, 2014) establishes a wide variety of new, unbiased and efficient risk premia estimators. Empirical results on meticulously-constructed daily, investable, constant-maturity  S&P500 higher-moment premia reveal significant, previously-undocumented, regime-dependent behavior. The variance premium is fully priced by Fama and French (2015) factors during the volatile regime, but has significant negative alpha in stable markets.  Also only during stable periods, a small, positive but significant third-moment premium is not fully priced by the variance and equity premia. There is no evidence for a separate fourth-moment premium.