Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
Roger Penrose

A dedicated search of the CMB sky, driven by implications of conformal
cyclic cosmology (CCC), has revealed a remarkably strong signal, previously
unobserved, of numerous small regions in the CMB sky that would appear to be
individual points on CCC's crossover 3-surface from the previous aeon, most
readily interpreted as the conformally compressed Hawking radiation from
supermassive black holes in the previous aeon, but difficult to explain in
terms of the conventional inflationary picture.

  • Quantum Field Theory Seminar
Maria del Rio Chanona

In this work, study the mean first saturation time (MFST), a generalization to the mean first passage time, on networks and show an application to the 2015 Burundi refugee crisis. The MFST between a sink node j, with capacity s, and source node i, with n random walkers, is the average number of time steps that it takes for at least s of the random walkers to reach a sink node j. The same concept, under the name of extreme events, has been studied in previous work for degree biased-random walks [2]. We expand the literature by exploring the behaviour of the MFST for node-biased random walks [1] in Erdős–Rényi random graph and geographical networks. Furthermore, we apply MFST framework to study the distribution of refugees in camps for the 2015 Burundi refugee crisis. For this last application, we use the geographical network of the Burundi conflict zone in 2015 [3]. In this network, nodes are cities or refugee camps, and edges denote the distance between them. We model refugees as random walkers who are biased towards the refugee camps which can hold s_j people. To determine the source nodes (i) and the initial number of random walkers (n), we use data on where the conflicts happened and the number of refugees that arrive at any camp under a two-month period after the start of the conflict [3]. With such information, we divide the early stage of the Burundi 2015 conflict into two waves of refugees. Using the first wave of refugees we calibrate the biased parameter β of the random walk to best match the distribution of refugees on the camps. Then, we test the prediction of the distribution of refugees in camps for the second wave using the same biased parameters. Our results show that the biased random walk can capture, to some extent, the distribution of refugees in different camps. Finally, we test the probability of saturation for various camps. Our model suggests the saturation of one or two camps (Nakivale and Nyarugusu) when in reality only Nyarugusu camp saturated.

[1] Sood, Vishal, and Peter Grassberger. ”Localization transition of biased random walks on random
networks.” Physical review letters 99.9 (2007): 098701.
[2] Kishore, Vimal, M. S. Santhanam, and R. E. Amritkar. ”Extreme event-size fluctuations in biased
random walks on networks.” arXiv preprint arXiv:1112.2112 (2011).
[3] Suleimenova, Diana, David Bell, and Derek Groen. ”A generalized simulation development approach
for predicting refugee destinations.” Scientific reports 7.1 (2017): 13377.

Jon Cockayne

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is employed. However, for more challenging systems a substantial error can be present even after many iterations have been performed. The estimates obtained in this case are of little value unless further information can be provided about the numerical error. In this paper we propose a novel statistical model for this numerical error set in a Bayesian framework. Our approach is a strict generalisation of the conjugate gradient method, which is recovered as the posterior mean for a particular choice of prior. The estimates obtained are analysed with Krylov subspace methods and a contraction result for the posterior is presented. The method is then analysed in a simulation study as well as being applied to a challenging problem in medical imaging.

  • Numerical Analysis Group Internal Seminar
Alexei Gazca

In the classical theory of fluid mechanics, a linear relationship between the stress and rate of strain is often assumed. Even when this relationship is non-linear, it is typically formulated in terms of an explicit relation. Implicit constitutive theories provide a theoretical framework that generalises this, allowing a, possibly multi-valued, implicit constitutive relation. Since it is not possible to solve explicitly for the stress in the constitutive relation, a more natural approach would be to include the stress as a fundamental unknown in the formulation of the problem. In this talk I will present a formulation with this feature and a proof of convergence of the finite element approximations to a solution of the original problem.

  • Numerical Analysis Group Internal Seminar
Alexander Ivanov

We study continuous theories of classes of finite dimensional Hilbert spaces expanded by 
a finite family (of a fixed size) of unitary operators. 
Infinite dimensional models of these theories are called pseudo finite dimensional dynamical Hilbert spaces. 
Our main results connect decidability questions of these theories with the topic of approximations of groups by metric groups. 

Benjamin Brück

"Fibre theorems" in the style of Quillen's fibre lemma are versatile 
tools used to study the topology of partially ordered sets. In this 
talk, I will formulate two of them and explain how these can be used to 
determine the homotopy type of the complex of (conjugacy classes of) 
free factors of a free group.
The latter is joint work with Radhika Gupta.

  • Junior Topology and Group Theory Seminar
25 October 2018
Shengguo Zhu

We will talk about the Cauchy problem of the three-dimensional isentropic compressible Navier-Stokes equations. When viscosity coefficients are given as a constant multiple of density's power, based on some analysis  of  the nonlinear structure of this system, by introducing some new variables and the initial layer compatibility conditions, we identify the class of initial data admitting a local regular solution with far field vacuum and  finite energy  in some inhomogeneous Sobolev spaces, which solves an open problem of degenerate viscous flow partially mentioned by Bresh-Desjardins-Metivier (2006, Anal. Simi. Fluid Dynam.),  Jiu-Wang-Xin (2014, JMFM) and so on. Moreover, in contrast to the classical well-posedness theory in the case of  the constant viscosity,   we show   that one can not obtain any global classical solution whose $L^\infty$  norm of $u$ decays to zero as time $t$ goes to infinity under the assumptions on the conservation laws of total mass and momentum.

  • PDE CDT Lunchtime Seminar
Add to My Calendar