Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
|February 2017||April 2017|
Events for 6 March 2017
The probabilistic modelling of observed phenomena sometimes require the introduction of (unobserved) latent variables, which may or may not be of direct interest. This is for example the case when a realisation of a Markov chain is observed in noise and one is interested in inferring its transition matrix from the data. In such models inferring the parameters of interest (e.g. the transition matrix above) requires one to incorporate the latent variables in the inference procedure, resulting in practical difficulties. The standard approach to carry out inference in such models consists of integrating the latent variables numerically, most often using Monte Carlo methods. In the toy example above there are as many latent variables as there are observations, making the problem high-dimensional and potentially difficult.
We will show how recent advances in Markov chain Monte Carlo methods, in particular the development of “exact approximations” of the Metropolis-Hastings algorithm (which will be reviewed), can lead to algorithms which scale better than existing solutions.
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The mean curvature flow is one of the most important geometric flows on Riemannian submanifolds. Translating solitons are special solutions, where the flow is along straight lines, and have particular importance since they exist for all time and are related to certain singularities (Type II) of the flow. We study translating solitons in a more general context than Eulidean space: the product of a (semi-)Riemannian manifold with the real line, and develop new tools to study them. Considering Riemannian submersions where the total space is a translating soliton, we show that under certain hypotheses involving the mean curvature of the fiber, this data is equivalent to a
certain type of object on the base manifold. In the case where the submanifold is a leaf of a codimension-one foliation by orbits of a Lie group of symmetries (such as SO(n) or SO(p,q) acting on Euclidean or Minkowski space), we reduce the existence of a translating soliton to an ODE that we explicitly solve in many examples.
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PLEASE NOTE that the visit of Prof. N. T. Wright is open only to members of the seminar.
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