Curriculum Vitae for Warwick Dumas 29th May 2010 of proficiency in C, C++, Windows C++; Oxford College of Further Ed., 1995. Professional experience 09/2005-01/2010 Studying for PhD.

Curriculum Vitae for Warwick Dumas Current address: 102 Grange Road, Wigston, Leicester, LE18 1JJ. Current telephone: (+44) 0116 288 7879 Email: [email protected] Qualifications Doctor of Philosophy in Applied Mathematics, University of Leicester, thesis submitted in January 2010. Postgraduate Diploma in Economics, University of Warwick, 2002. Bachelor of Arts (2:1 Honours) in Mathematics, University of Warwick, 2001. GCE A-Levels: At John Mason School, Abingdon: English (A,1998), Mathematics (A, 1997), Further Maths (B, 1998). At Oxford College of Further Education: Russian (C, 1998), Economics (C, 1998). OCEAC Step Paper 1 in Mathematics, Grade 1, 1998. Certificates of proficiency in C, C++, Windows C++; Oxford College of Further Ed., 1995. Professional experience 09/2005-01/2010 Studying for PhD. Department of Mathematics and Computer Science, University of Leicester. My thesis relates to computing expectations of functionals of conditional Wiener processes, and to the fermion sign problem which arises in performing certain path integral simulations. The main focus of the thesis is on developing high-performance numerical simulations of particular functional integrals, by employing a statistical perspective. This has involved stochastic numerical analysis, scientific programming, and the development of a novel solution to a long-standing and challenging problem. A certain piecewise constant method was demonstrated to be second-order for conditional Wiener integrals of functionals of a general form, by exploiting the fact that the Brownian bridge SDE is exactly soluble. It has also been shown that no linear integration methods are of higher order. Computational experiments were performed to illustrate the order of convergence of the piecewise constant method. A similar result is also developed for the more general case of a conditioned diffusion. An approach to the fermion sign problem in the case of finding the thermal density matrix of a canonical quantum system is then advanced. This is based on a resampling over paths which samples together those paths with countersigned, strongly covariant

contributions, ie those which otherwise give rise to the sign problem. This approach is applicable using Markov Chain Monte Carlo. Simulations are performed both to illustrate the nature of the sign problem and to investigate the efficacy of my approach to solving it. It is shown that an exact solution is possible for 2 2D particles. Most of the scientific programming has been in C. Mathematica and Excel VBA were also used as appropriate. In academic years 2005-06 and 2006-07, I taught undergraduate supervisions. In 2007-08 and 2008-09 Semester 1, I taught computer labs for MA1011 Methods of Applied Mathematics, using MATLAB. In 2008-09 Semester 2, I taught the course MA1061 Probability. 12/2003 – 08/2005 Strategic Analyst. Learning and Skills Council, LSC National Office, Quinton Road, Coventry. Main responsibilities: In this role I developed Bayesian hierarchical models of student attainment and institutional performance, and calibrated these models using Markov Chain Monte Carlo. The analysis related to attainment in A-Levels and vocational qualifications in the UK. I was also responsible for making presentations to colleagues and, occasionally, external stakeholders, about both modelling concepts and analysis results. I produced software that would allow the user to specify a highest-level subset of data and calculate posterior expectations and credibility intervals for coefficients describing a performance curve for this subset. In the case of Gaussian models, the formula for the joint posterior distribution of the coefficients was found directly. In the case of dichotomous regressands, Monte Carlo or another method of numerical integration was used. Exploratory analysis was performed on the full dataset using SPSS. 06/2001 - 06/2002 Research Assistant, part-time, Warwick Centre for Public Economics, University of Warwick Main responsibilities: This involved proof-reading economics papers, specifically with regard to the mathematical details.

06/2000 – 09/2000 Actuarial Analyst (summer internship), NPI Financial Services, Tunbridge Wells Main responsibilities: I reengineered existing pension benefit calculation codes to ensure exact compliance with Inland Revenue Rules. I also automated the premium calculation test procedures for life insurance products. Publications Computing conditional Wiener integrals of functionals of a general form W. M. Dumas and M. V. Tretyakov (accepted for IMA Journal of Numerical Analysis) From the abstract: A numerical method of second order of accuracy for computing conditional Wiener integrals of smooth functionals of a general form is proposed. The method is based on simulation of Brownian bridge via the corresponding stochastic differ- ential equations (SDEs) and on ideas of the weak-sense numerical integration of SDEs. A geometrical approach to the fermion sign problem W. M. Dumas (forthcoming) Based on the latter chapters of my PhD thesis, this paper will explain how to perform MCMC simulations of fermion systems in such a way as to create a strong covariance between the contributions from trajectories yielding positive and negative contributions. It shall be demonstrated that this allows numerical computations of functional integrals to be successfully performed.