The workshop will feature two mini-courses, each consisting of five lectures of ninety minutes:

Graphical probability and disordered systems

Prof. Geoffrey Grimmett (University of Cambridge)

Spanning trees, self-avoiding walks, connected clusters, entanglements: these are classes of graphs which, when chosen randomly, possess especially rich probabilistic structure. Their study impacts on such topics as combinatorics, geometry, and interacting systems in probability and physics. Some of their basic theory will be developed in these lectures, including introductions to percolation and the Ising model.

Introductory online text appears here. Other material discussed appears in here.

Topics in branching processes

Prof. John Biggins (University of Sheffield)

This series of lectures will use the results and techniques in three recent papers as the motivation to describe and develop key results in their hinterland. The current plan is to spend two sessions on introduction and general background, and then one session each on using these to explore more specifically topics from the following three papers:

Biggins J.D., Hambly B.M. and Jones, O.D., Multifractal spectra for random self-similar measures via branching processes. Adv. Appl. Probab 43 (2011), 1-39.

Alsmeyer, G, Biggins, J.D. and Meiners, M., The functional equation of the smoothing transformation. Ann. Probab., to appear.

Biggins J.D., Spreading speeds in reducible multi-type branching random walk. Ann. Appl. Probab., to appear.

There will be some time in the afternoons for the participants to think about issues arising from the lecture courses. These sessions will be run by Warwick staff/postdocs.

Participants are encouraged, but by no means obliged, to present their own work in one of the afternoon sessions. Speakers may choose to give an informal introduction to an area of interest, or to present a more detailed account of their research (subject to timetabling constraints). If you would be interested in presenting some work, please indicate this when completing your registration form.

The timetable is available here. All talks will take place in B3.02. The titles of participant talks are as follows:

Session 1 (Tuesday 24th July, 16.00-18.00)

• Peter Arzt, University of Siegen, Asymptotic behaviour of the eigenvalues of the Laplacian on random Cantor-like fractals
• Ksenia Chernysh, Heriot-Watt University, Optimal algorithms for the infinite bin model
• Marion Hesse, University of Bath, Branching Brownian motion in a strip: Survival near criticality
• Piotr Milos, University of Bath, Alpha-stable branching motion in inhomogenous potential
  
• Bati Sengul, University of Cambridge, Small time behaviour of coalescent processes
• Stephen Tate, University of Warwick, Tree-graph identities and the cluster expansion

Session 2 (Wednesday 25th July, 14.00-16.00)

• Tilman Bohl, Friedrich Schiller University Jena, Fractal curvature of self-conformal sets
• Fraser Daly, University of Bristol, Size biasing and stochastic ordering: three applications
• Martin Huesmann, University of Bonn, Optimal transport between the Lebesgue measure and a point process
• Simon Weber, University of Warwick, The sharp interface limit of the stochastic Allen-Cahn equation in one space-dimension
• Iulia Stanciu, Goethe University Frankfurt am Main, The external length of the evolving Kingman coalescent
• Sebastian Vollmer, University of Warwick, Sampling, MCMC and spectral gaps in infinite dimensions

Session 3 (Thursday 26nd July, 16.00-18.00)

• Joe Chen, Cornell University, Gaussian free fields on self-similar fractals
• Maren Eckhoff, University of Bath, Surviving near criticality in a preferential attachment network
• Naotaka Kajino, Bielefeld University, Non-regularly varying and non-periodic oscillation of the on-diagonal heat kernels on self-similar fractals
• Michael Scott, University of Warwick, The stochastic heat equation on an evolving curve with finite time singularity
• Tamas Szabo, University of Szeged, Change detection in INAR(p) processes