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Durham University

Research & business

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.


April 2019
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Events for 29 April 2019

Alexandros Beskos : Geometric MCMC for infinite-dimensional inverse problems

12:00pm, CM221

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank–Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.

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Dr TJ Lang: A Multiplied Self: Divine Doubles and the Apostle Paul’s Anagogical Realism

3:30pm, Seminar Room C (D/TH107), Dept. of Theology & Religion, Abbey House, DH1 3RS, Durham

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Richard Webb: Topology, Groups and Complexity

4:00pm, CM219

I will start with some history about decision problems coming from group theory and from topology, including problems that are "easy" (can be solved in polynomial time), "hard" (or even undecidable), and problems whose complexity we still do not understand. I will then move on to current research at the intersection of group theory and topology, namely the mapping class groups of surfaces, which includes the braid groups. The so-called conjugacy problem for the mapping class group is related to several problems in topology of unknown complexity. I will discuss a polynomial-time solution for the conjugacy problem which emulates the solution provided by geometric group theory for "most" finitely presented groups. Joint work with Mark Bell.

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