PGR Seminars

Weekly seminars are held by the School's postgraduate research students and post-docs. These generally take the form of a presentation for approximately 30 minutes followed by informal discussion.

Seminars are held in the Rutherford Annex Seminar Room, at 4pm every Friday of term.

There are biscuits!

Please contact us with comments/suggestions, to talk yourself or to volunteer an external speaker for any of the available dates.

Thanks,


Discussion groups

This year we had a couple of PGR discussion groups: in the first term we had Stochastic Calculus, followed by Galois Theory in the second term.

Talks

3/10/2014 Katherine Horan Invariant Theory An introduction to what invariant theory is and some of the maths used in studying it.
10/10/2014 An Kang An Introduction to The Monte Carlo Sampling This week I am giving an introduction on Monte Carlo sampling methods, I will use examples to illustrate the rejection sampling and the Importance sampling.
17/10/2014 Christoph Fischbacher A pedestrian's proof for Weyl's law In 1911, Hermann Weyl published his result on the asymptotic distribution of eigenvalues for the Laplacian on bounded domains in ℝn. I am going to give a self-contained proof of this law for the Dirichlet-Laplacian on bounded domains in ℝ2.
24/10/2014 Theo Gkolias Bayesian prediction for the Game of Thrones Predictions for the number of chapters told from the point of view of each character for the remaining books of A Song of Ice and Fire by fitting a random effects model using Bayesian methods.
Not to worry about spoilers!
31/10/2014 Neal Carr The path-integral formulation of quantum mechanics I will introduce the path-integral formulation of quantum mechanics, perhaps the strangest and yet most immediately accessible formulation of quantum mechanics. I will then use this formalism to derive the Schrödinger equation, the quantum mechanical analogue of Newton's second law of motion.
7/11/2014 Gelly Mitrodima Joint quantile models for the conditional asset return distribution with time- varying shape and scale Dynamic joint quantile models with inter- quantile range are used as a convenient basis for the estimation of the scale and the shape of the conditional asset return distribution. By using a small number of quantile estimates the distribution of asset return is approximated. Comparisons are conducted based on in- sample and out- of- sample criteria, and findings suggest that the proposed models exhibit a superior performance. In particular, the time series of the quantile forecasts better describe the evolution of the right and the left tail in- sample and produce accurate expected number of exceedances out- of- sample.
14/11/2014 Mark Roelands Basic Topology and a curious application This talk will consist of a brief introduction of topological spaces and some of its basic concepts like continuity and convergence. Finally, a topological proof will be presented for the classical result stating that there are infinitely many prime numbers.
21/11/2014 MingJie Hao An introduction to actuarial science and its interactions with mathematics and statistics As a student who has studied actuarial science for years (and is still working on it), I will give a brief introduction to actuarial science (e.g. what is it) and its links with maths and stats. A few examples will be given before some explanations for the 'actuarial professions' and 'the notorious' exam system. The talk will be very general, and everyone is welcomed!
28/11/2014 Chris Parsons Simplices and the Generalised Triforce Fundamental to mathematics is the study of patterns and symmetries. It is then somewhat surprising that some problems which are so intuitive in understanding that small cases appear in video games remain unsolved. We examine the accessible problem of pairwise touching regular n-simplices, methods used to examine the maximal configurations and a surprising connection with equilateral sets in normed spaces.
5/12/2014 Sam Oduro Modelling transaction-by-transaction Asset price Changes Innovations in asset prices have been suggested to convey the arrival of new information. In the classical finance literature these studies have predominantly used asset prices sampled at low frequencies. In this work we approach the same problem using high frequency market data with a simple but economically interpretable market microstructure model.
23/01/2015 Edmund Judge Hugh Everett and His Many Worlds Interpretation As a student of functional analysis I often encounter the equations employed in quantum mechanics, but without any of their real-world context. Recently, I have sought to remedy this and in my readings discovered the imaginative Many Worlds Interpretation, posited by Hugh Everett III over fifty years ago. Today I intend to discuss this as well as its philosophical implications.
30/01/2015 Matteo Giacomini
CMAP Ecole Polytechnique 		A complementary energy approach to the Adaptive Boundary Variation Algorithm We consider the Adaptive Boundary Variation Algorithm for shape optimization problems introduced by the authors in a previous work. It is known in the literature that the error due to the numerical approximation of the state equation may prevent the classical Boundary Variation Algorithm from converging to a sequence of minimizing shapes, thus we investigate the coupling of a posteriori error estimators with shape optimization procedures. In the present work, we introduce a novel, constant-free strategy inspired by the complementary energy principle to fully compute an a posteriori estimator providing a certified upper bound of the error in the shape derivative. We compare the new estimator with a Dual-Weighted Residual approach discussed in a previous work by applying the resulting guaranteed shape optimization strategy to the scalar inverse identification problem of Electrical Impedance Tomography. Some numerical simulations are presented.
6/02/2015 Oscar Mendez Maldonado
University of Surrey 		Swarm Strategies for Simultaneous Localisation and Mapping A brief overview of how Projective Geometry and Bayesian Inference can be used to create Simultaneous Localisation and Mapping (SLAM) systems. We will also explore the current state of the art through videos.
27/02/2015 Gelly Mitrodima
 Decomposition of the conditional asset return distribution: A Bayesian approach We estimate the conditional asset return distribution by modelling a finite number of quantiles. The motivation for this is to jointly incorporate time- varying dynamics of shape and scale of the asset return distribution in a robust manner and avoid any violations of the quantile orderings. We also want to address the well- known estimation issues of regression quantile models. Thus, we perform a Bayesian analysis using Adaptive MCMC methods. We choose to use Adaptive MCMC methods because they offer solutions in cases where the target distribution is not tractable, as here, and address the crossing problem.
06/03/2015 Andrea Cremaschi Introduction to Bayesian Accelerated Failure Time (AFT) modelling

Observables often represent the time when a particular event is recorded. In this case, the observation "status" is set to 0 before the event happens, and 1 afterwards. If a change in status can happen only once, we refer to them as failure times. Some examples are the life of a light bulb tested under high-voltage current, the day of death of a lab rat under a specific treatment, and so on...

The talk will start with an introduction to what regression is and why it is used in statistics. I will then focus on AFT models (that can be seen as Generalised Linear regression Models), explaining how they can be used to estimate and predict the failure times of censored data, i.e. those data for which we haven't observed "status=1" yet. Both aspects of frequentist and Bayesian methodology are explored, with more attention on the latter and on predictive distributions.

An application of AFT? Game of Thrones, of course!
13/03/2015 Neal Carr
 Mathematics of special relativity This talk will be a speedy introduction to the mathematics of special relativity. I'll first define spacetime, and then the transformations that leave this spacetime invariant. With these, we can derive all the crazy physical consequences of special relativity; a couple of examples will be time dilation and length contraction. Lastly, I'll demonstrate a quick derivation of Einstein's famous formula, E = mc^2.
20/03/2015 Veronika Witzke
City University

Magnetohydrodynamics applied to stellar objects

Investigating pure hydrodynamical flows, including turbulent regimes, as well as magnetohydrodynamical flows is of interest to a wide variety of communities and find application in for example astrophysics, fusion research and aerospace engineering. My particular research focus is to understand stellar interior dynamics by means of compressible flow dynamics in an appropriate parameter space. This is crucially important for a comprehensive understanding of processes that are responsible for the generation and sustainment of magnetic fields in stars, which is still an important open question that concerns the fundamental understanding of stellar objects. In this talk a basic introduction to Magnetohydrodynamics will be given along with an outline of my research where I focus on shear flow instabilities in a polytropic atmosphere.
27/03/2015 Freddy Symons
Cardiff University

An introduction to Sturm-Liouville problems

We will explore some of the basics of the theory of the Sturm-Liouville (S-L) equation -(pu’)’ + qu = λ wu, in both the regular and the singular-at-infinity-half-line cases. After a brief foray into the history of the equation, including some of its physical motivation and original mathematical context, we will outline the development of more recent theory concerning it. This will involve defining the fundamental concept that is the so-called Weyl-Titchmarsh m-function, m(λ), in the regular, limit-circle and limit-point cases. Time permitting, we will conclude by highlighting an important application of this theory, namely in spectral inverse problems related to the S-L equation, i.e., problems involving the recovery of the coefficients p, q and/or w from certain spectral data; these data include such objects as the aforementioned m-function.
10/04/2015 Jun Yang

Dynamic Asset-Liability Management with Inflation Hedging and Regulatory Constraints

We examine how inflation risk affects the asset-liability investment allocation problem of a fund manager who is constrained by regulatory rules. The liability driven investment framework faces a time-varying investment opportunity set, characterized by a two-factor affine model of term structure, and is subject to annually-checked Value-at-Risk and maximum funding constraints required by regulatory authorities. We show that inflation-hedging is of particular importance for the long-term ALM investor and has an influential impact on asset allocation by interacting with liability-hedging and intertemporal hedge demands simultaneously. We also explain the practical fact that many managers tend to act myopically, instead of rebalancing strategically.
17/04/2015 Nicola Cooper

Data Curator

My talk will cover Research Data Management (RDM) and the drivers for RDM, including Researcher Funder requirements. Of the Researcher Funder requirements, I will focus on the Engineering and Physical Sciences Research Council Policy Framework on Research Data – this has a compliance date of 01 May 2015.
15/05/2015 Qing Xu

Investment timing and optimal capital structure under debt illiquidity risk

Deterioration in debt market liquidity reduces debt value and affects a levered firm's optimal decisions. Considering debt illiquidity risk, we develop an investment timing model and obtain analytic solutions. We carry out a comprehensive analysis in optimal financing, default and investment strategies, and stockholder-bondholder conflicts. We obtain six new insights for decision makers. We propose a ``new trade-off theory" for optimal capital structure, a new tax effect, and a new explanation of ``debt conservatism puzzle". Failure in recognizing illiquidity risk results in substantially overleveraging, early bankruptcy or investment, overpriced options, and undervalued coupons and credit spreads. In addition, agency costs are surprisingly small for a high illiquidity risk or a low project risk. Interestingly, the risk shifting incentive and debt overhang problem decrease with illiquidity risk under moderate tax rates while they increase under high tax rates.
22/05/2015 Dr Constanze Roitzheim

An introduction to rubber geometry
29/05/2015 Ben Fahs
Université Catholique de Louvain

Random matrices with merging singularities and the Painlevé V equation

We study an nxn hermitian random matrix ensemble M asymptotically for large n. As n grows, we consider the case where 2 singularities merge into 1 singularity, and the case where a singularity emerges from an analytic potential. We obtain a formula for the correlation kernel and the partition function in terms of a special form of Painlevé V. The research is in collaboration with Tom Claeys at UC Louvain.
05/06/2015 Jenny Ashcroft

Topological Solitons

Topological solitons are stable, finite energy solutions to nonlinear field equations found in a variety of physical systems. Examples include vortices in superconductors, baby Skyrmions in condensed matter systems and the infamous Skyrmions of nuclear physics. In this talk, I will provide an introduction to topological solitons, with a particular focus on the solitons of the sine-Gordon and baby Skyrme models. Both of these theories can be considered as lower dimensional analogues of the Skyrme model.
12/06/2015 Alex Cockburn Durham University

Vortices and magnetic impurities

The vortex is a fascinating example of a topological soliton in two spatial dimensions, with many applications in both mathematics and physics. I will review basic facts about vortices, with emphasis on a particularly interesting limit where the space of static vortex solutions assumes the form of a curved manifold whose geodesics correspond to vortex scatterings. At the end I will also briefly discuss my own work on introducing impurities into the vortex system.
19/06/2015 Su Wang

Decode place cells – a filtering approach

In a typical place cell decoding experiment, a population of neurons is recorded while an animal (typically a rat) is moving in a field. The movements of the animal are recorded using a camera. The decoder is then trained using a dataset containing fully observed data (both spikes and positions). Typically the problem is solved by continuous state-space methods involving recursive filtering like the Kalman filter or more generally sequential Monte Carlo methods.

Archive of previous PGR talks.