Mon, 03 Nov 2014
15:45
Oxford-Man Institute

Selection and dimension

Nic Freeman
(Bristol University)
Abstract

I will describe the Spatial Lambda-Fleming-Viot process, which is a model of evolution in a spatial continuum, and discuss the time and spatial scales on which selectively advantageous genes propagate through space. The appropriate scaling depends on the dimension of space, resulting in three distinct cases; d=1, d=2 and d>=3. In d=1 the limiting genealogy is the Brownian net whereas, by contrast, in d=2 local interactions give rise to a delicate damping mechanism and result in a finite limiting branching rate. This is joint work with Alison Etheridge and Daniel Straulino.

Thu, 13 Jun 2013

16:00 - 17:00
L3

Manin's conjecture for certain smooth hypersurfaces in biprojective space

Damaris Schindler
(Bristol University)
Abstract

So far, the circle method has been a very useful tool to prove
many cases of Manin's conjecture. Work of B. Birch back in 1961 establishes
this for smooth complete intersections in projective space as soon as the
number of variables is large enough depending on the degree and number of
equations. In this talk we are interested in subvarieties of biprojective
space. There is not much known so far, unless the underlying polynomials are
of bidegree (1,1). In this talk we present recent work which combines the
circle method with the generalised hyperbola method developed by V. Blomer
and J. Bruedern. This allows us to verify Manin's conjecture for certain
smooth hypersurfaces in biprojective space of general bidegree.

Thu, 26 Apr 2012

16:00 - 17:00
L1

Synchronization, Control and Coordination of Complex Networks via Contraction Theory

Mario di Bernardo
(Bristol University)
Abstract

In a variety of problems in engineering and applied science, the goal is to design or control a network of dynamical agents so as to achieve some desired asymptotic behaviour. Examples include consensus and rendez-vous problems in robotics, synchronization of generator angles in power grids or coordination of oscillations in bacterial populations. A pressing challenge in all of these problems is to derive appropriate analytical tools to prove convergence towards the target behaviour. Such tools are not only invaluable to guarantee the desired performance, but can also provide important guidelines for the design of decentralized control strategies to steer the collective behaviour of the network of interest in a desired manner. During this talk, a methodology for analysis and design of convergence in networks will be presented which is based on the use of a classical, yet not fully exploited, tool for convergence analysis: contraction theory. As opposed to classical methods for stability analysis, the idea is to look at convergence between trajectories of a system of interest rather that at their asymptotic convergence towards some solution of interest. After introducing the problem, a methodology will be derived based on the use of matrix measures induced by non-Euclidean norms that will be exploited to design strategies to control the collective behaviour of networks of dynamical agents. Representative examples will be used to illustrate the theoretical results.

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