2013
15-19 April 2013, Common Themes in Financial and Actuarial Mathematics, Liverpool (Applications have now closed)
8-12 July 2013, Modern nonlinear PDE methods in fluid dynamics, Reading (Application Deadline: 27 May 2013)
8-12 July 2013, O-Minimality and Diophantine Geometry, Manchester (Application Deadline: 27 May 2013)
29 July - 2 August 2013, Computational Group Theory, St. Andrews (Application Deadline: 17 June 2013)
19-23 August 2013, Random Graphs, Geometry and Asymptotic Structure, Birmingham (Application Deadline: 8 July 2013)
26-30 August 2013, Topology in Low Dimensions, Durham (Application Deadline: 15 July 2013)
15-19 April 2013, Common Themes in Financial and Actuarial Mathematics, Liverpool
Financial and actuarial mathematics share the same mathematical foundations: probability theory, stochastic analysis and differential equations. Often, financial mathematics is studied and has developed separately from actuarial mathematics. This short course will cover topics of interest to both fields.
The proposed course will introduce students to derivative modelling with counterparty risk and life insurance modelling with particular focus on using advanced interest rate models. Having completed the course, participants should be familiar with basics of derivatives pricing including counterparty risk as well as life insurance modelling using advanced interest rate models.
The broad field of the course should appeal to students and postdoctoral researcher in financial and actuarial mathematics as well as researchers and students in probability theory, stochastic analysis, stochastic control theory or partial differential equations that are interested in applications of their respective, more theoretical, subjects. The course may also be of interest to practitioners in the financial and insurance industry.
The two main lecture course topics are:
· Counterparty risk and models of default time (Monique Jeanblanc, Université d’Evry)
· Life insurance and long term interest rate modelling (Nicole El Karoui, Ecole Polytechnique)
These lecture courses will be supplemented by tutorial sessions.
There will be guest speakers: Francesca Biagini (LMU Munich), José Manuel Corcuera Valverde (University of Barcelona), Angelos Dassios (London School of Economics), Henrik Hult (KTH Stockholm), Vladimir Kaishev (City University London), Goran Peskir (University of Manchester).
Course Website (external link)
Applications have now closed. (For further details, please email shortcourses@lms.ac.uk)
8-12 July 2013, Modern nonlinear PDE methods in fluid dynamics, Reading
The course aims to give the opportunity to a new generation of UK PhD students to attend high quality lectures on the analysis of PDE in fluid dynamics, delivered by leading international experts. The four courses are broadly divided in two strands. The first, containing the courses given by Luigi Ambrosio and Yann Brenier, deals with applications in fluid dynamics of optimal transport methods, more specifically the variational approach to the incompressible Euler equations, and the monotone rearrangement and convection theory for the Navier-Stokes and semi-geostrophic equations. The second, containing the courses of Adrian Constantin and Georg Weiss, deals with methods specific to free-boundary problems in fluid dynamics, addressing respectively the bifurcation theory approach to existence of large-amplitude steady water waves with vorticity, and the use of blow-up techniques in the study of regularity and behaviour at singularities in free boundaries.
The four main lecture course topics are:
Variational models for incompressible Euler equations(Luigi Ambrosio, Scuola Normale Superiore, Pisa)
Monotone rearrangement and convection theory (Yann Brenier, University of Nice)
Bifurcation theory in the context of steady water waves (Adrian Constantin, King’s College, London)
Analysis of singularities in free-boundary problems (Georg Weiss, Heinrich Heine University, Düsseldorf)
Guest lectures will be given by Mike Cullen (Met Office) and Camillo De Lellis (University of Zürich).
Course Website (external link)
Application Form Application Deadline 27 May 2013
8-12 July 2013, O-Minimality and Diophantine Geometry, Manchester
The last five years seen a surprising and fruitful interaction between o-minimality, a branch of model thoery, and diophantine geometry. The most spectacular outcome of this interaction is Pila's proof of the André-Oort conjecture for products of modular curves (Annals of Math., 2011). There have been further important developments by several mathematicians including Masser, Zannier, Ullmo, Yafaev, Habegger, and Pila.
The aim of the LMS-EPSRC Short Course is to introduce students in both model theory and number theory to these recent developments. The strategy underlying the diophantine applications will be introduced through a simple example accessible to first-year graduate students, and the key ingredients will each be discussed.
The three main lecture course topics are:
· Rational points on definable sets (Alex Wilkie, Manchester)
· Functional transcendence via o-minimality (Jonathan Pila, Oxford)
· Diophantine applications (Philipp Habegger, Frankfurt)
There will be guest lectures given by David Masser (Basel), Andrei Yafaev (UCL) and Gareth Jones (Manchester).
Application Form Application Deadline 27 May 2013
29 July - 2 August 2013, Computational Group Theory, St. Andrews
The course will introduce students to the four main areas of Computational Group Theory: permutation groups, soluble and p-groups, matrix groups and finitely presented groups. The course will cover typical problems and standard algorithms, along with the analysis of these algorithms and their practical use on a computer. In the practical sessions there will be some emphasis on using the computer algebra system GAP, a world wide open source project established in 1988. After this course the participants will have a good understanding of what computers can and cannot do with groups and will be able to use GAP to answer their own group theoretic questions. The course aims to appeal to a broad spectrum of students from areas such as Algebra, Topology, Combinatorics and Graph Theory.
The four main lecture course topics are:
Permutation Groups (Alexander Hulpke, Colorado State University)
Soluble Groups and p-Groups (Bettina Eick, Technische Universität Braunschweig)
Matrix Groups/Constructive Recognition (Derek Holt, University of Warwick)
Finitely Presented Groups (Max Neunhöffer, University of St Andrews)
These lecture courses will be supplemented by tutorial sessions.
Course Website (external link)
Application Form Application Deadline 17 June 2013
19 - 23 August 2013, Random Graphs, Geometry & Asymptotic Structure, Birmingham
The objectives of this course are two-fold:
1. to provide an introduction to recent developments and techniques for classical problems in the theory of random graphs;
2. to cover geometric and topological aspects of the theory of random graphs and introduce participants to the diversity and the depth of the combinatorial, probabilistic and analytical methods that have been invented in this context.
The three main lecture course topics are:
· Long paths and hamiltonicity in random graphs (M. Krivelevich, Tel Aviv University)
· Random graphs from restricted classes (K. Panagiotou, Ludwig-Maximilians-Universität)
· Random geometric graphs (M. D. Penrose, University of Bath)
There will also be a special guest lecture: Random planar graphs (C. McDiarmid, University of Oxford)
Course Website (external link)
Application Form Application Deadline 8 July 2013
26-30 August 2013, Topology in Low Dimensions, Durham
Low-dimensional topology has seen a proliferation of new invariants and techniques over the last decade or so which are intimately interrelated. The ideas behind them are approachable from a number of points of view: for example from algebraic geometry, differential geometry, algebraic topology, or from representation theory. The invariants include Khovanov homology and related constructions, Floer homologies, and various gauge theories.
The course aims to present a broad selection of these ideas, covering the construction, the properties, and applications.
The three main lecture course topics are:
· Heegaard-Floer homology (Matthew Hedden, Michigan State University)
· Khovanov homology and its offspring. (Jacob Rasmussen, Cambridge)
· Contact 3-manifolds and holomorphic curves. (Chris Wendl, UCL)
These lecture courses will be supplemented by tutorial sessions.
Course Website (external link)
Application Form Application Deadline 15 July 2013
Past Short Courses
| Year | Title | Institution |
| 2012 | Continuum Mechanics in Biology and Medicine | UCL |
| 2012 | Stochastic Modelling in Biological Systems | Oxford |
| 2011 | Theoretical Fluid Dynamics | Heriot-Watt |
| 2011 | Duality, Malliavin Calculus and BSDEs in Mathematical Finance | Oxford |
| 2011 | Symplectic Geometry | Aberdeen |
| 2011 | Spectral Analysis and its Applications | UCL |
| 2011 | Topics in Probability | Oxford |
| 2010 | Ergodic Theory and Arithmetic Dynamics | QMUL |
| 2010 | Computational Mathematics and Scientific Computing | Durham |
| 2010 | Classical and Quantum Integrable Models | Kent |
| 2010 | Model Theory | Leeds |
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