Seminars and Colloquia

The mathematics colloquium is held twice a term.

Mathematics Colloquium

During term time seminars are held by the different research groups in the School of Mathematics.

Pure Mathematics

Applied Mathematics

Events this week:

Applied Mathematics Seminar Series: A computational model of vascular regression

Jessica Crawshaw, University of Melbourne
Tuesday 10 December 2019, 13:00
Nuffield G17

Note date and place outside of usual slot.

Vascular regression refers to the pruning of superuous vessels from a capillary net-work. Whilst it is accepted that the local haemodynamic environment has some role inregression in the developing retinal vasculature, it is difficult to experimentally distinguishthe relative contribution of the haemodynamic forces from those of the cellular signallingpathways. As such, the development of computational models to analyse the relationshipbetween blood ow and vascular regression are invaluable.We are developing computational models to examine the relationship between endothe-lial cell migration and haemodynamic forces during vascular regression in the developingretinal network of neonatal mice (postnatal day 5). A cell-based model is used to de-scribe the endothelial cell population over a hyperelastic capillary network taken fromconfocal images of the retinal vasculature. Endothelial cell migration is regulated by thelocal haemodynamic environment, which is modelled using a computational uid dynam-ics tool. The subsequence vessel collapse, and evolution of the network will be simulatedover long time periods.These computational models will enable us to gain insight into the dynamic rela-tionship between the endothelial cells, the capillary wall and the local haemodynamicenvironment, as well as provide a framework to computationally analyse and interrogatethe relationship between mechanical forces and vascular regression.

Analysis Seminar: Perturbations of elliptic operators on non-smooth domains

Murat Akman (Essex)
Tuesday 10 December 2019, 14:00
Lecture Theatre B, Watson Building
Tea and coffee will be provided after the talk at the common room

In this talk, we study perturbations of elliptic operators on domains with rough boundaries. In particular, we focus on the following problem: suppose that we have ``good estimates’’ for the Dirichlet problem for a uniformly elliptic operator $L_0$, under what optimal conditions, are those good estimates transferred to the Dirichlet problem for uniformly elliptic operator L which is a ``perturbation’’ of L_0?

Geometry and Mathematical Physics seminar: Some homological algebra behind scattering diagrams

Hipolito Treffinger, University of Leicester
Tuesday 10 December 2019, 14:30
Poynting Small Lecture Theatre (S06)

The notion of scattering diagram arose in mirror symmetry and have shown to be a powerful tool in the study of cluster algebras, being used to prove a wide range of conjectures in the theory. Recently, Bridgeland showed that cluster scattering diagrams can be built using the representation theory of quivers using stability conditions and motivic Hall algebras. Moreover, he showed that his methods can be applied in a much more general setting, constructing a scattering diagram for every finite dimensional algebra over an algebraically closed field.

In this talk, after explaining briefly the construction by Bridgeland, I will show how the stability conditions used in his construction can be recovered by the homological properties of the module category the algebra. Time permitting, I will talk about some “toric” properties arising in the homological algebra of module categories.

Part of this work is joint with T. Brustle and D. Smith from the University of Sherbrooke.

Applied Mathematics Seminar Series: Structure, function and growth in asthmatic airways: towards integration of mechanistic models and experimental data

Bindi Brook, University of Nottingham
Thursday 12 December 2019, 13:00
Nuffield G13

Asthma is a chronic lung disease affecting approximately 5.4 million people in the UK. Severe asthmatics suffer frequent exacerbations requiring hospitalisation, and furthermore, there are 3 asthma-related deaths a day in the UK. There is no real cure and its pathogenesis is not clearly understood. The disease is characterised by inflammation, airway hyper responsiveness (excessive contraction of the airways) and remodelling (irreversible structural changes in the airway). While each of these hallmarks have been studied extensively, it is not clear whether they develop independently or if one is responsible for another. In this talk I will describe the mechanistic models we have developed to understand these characteristics and how they may be linked. In particular I will focus on (i) airway contraction models based on continuum descriptions of soft tissue mechanics coupled to biophysical models of protein interactions that generate contractile force in airway smooth muscle cells lining the airway and (ii) the consequences of mechanical stresses generated in the airway on remodelling, via feedback into airway smooth muscle cell functions such as proliferation and phenotype switching. I will describe how we intend to explore homoeostasis in the normal airway using these models together with extensive structure, function and remodelling data obtained from tailored mouse model experiments.

Combinatorics and Probability Seminar: Distinct degrees in induced subgraphs

Eoin Long (University of Birmingham)
Thursday 12 December 2019, 14:00
Watson LTB
Tea, coffee and biscuits will be provided after the talk at the common room

An important theme of recent research in Ramsey theory has been establishing pseudorandomness properties of Ramsey graphs. An N-vertex graph is called C-Ramsey if it has no homogeneous set of size Clog(N). A theorem of Bukh and Sudakov, solving a conjecture of Erdős, Faudree and Sós, shows that any C-Ramsey N-vertex graph contains an induced subgraph with Ω(N^1/2) distinct degrees. We improve this to Ω(N^2/3), which is tight up to the constant factor.

We also show that any N-vertex graph with N > (k−1)(n−1) and n=Ω(k⁹) either contains a homogeneous set of order n or an induced subgraph with k distinct degrees. The lower bound on N here is sharp, as shown by an appropriate Turán graph, and confirms a conjecture of Narayanan and Tomon.

Joint work with Matthew Jenssen, Peter Keevash and Liana Yepremyan.