Mathematics Colloquium

03 March 2010 at 5:00 p.m.

Attenborough Tower, ATT LT3

Peter Kloeden (University of Frankfurt)

The talk will be preceded by a drinks and snack reception at ATT SB0.03 starting at 4:00 p.m.

Random attractors and the preservation of synchronization in the presence of noise

Abstract:

The long term behaviour of dissipatively synchronized deterministic systems is determined by the system with the averaged vector field of the original uncoupled systems. This effect is preserved in the presence of environmental -- i.e., background or additive -- noise provided stochastic stationary solutions are used instead of steady state solutions. Random dynamical systems and random attractors provide the appropriate mathematical framework for such problems and require Ito stochastic differential equations to be transformed into pathwise random ordinary differential equations. An application to a system of semi-linear parabolic stochastic partial differential equations with additive space-time noise on the union of thin bounded tubular domains separated by a permeable membrane will be considered.

 

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19 February 2009 at 5:45 p.m.

Ken Edwards building, lecture theatre 3.

Stephen Hurder (University of Illinois in Chicago)

The talk will be preceded by a wine and cheese reception in the reading room of the Mathematics and Computer Science Building (F9) starting at 5:00 p.m.

 

Foliations, Fractals and Cohomology

Abstract:

In this talk, we will give a brief introduction to each of the three themes,"Foliations, Fractals and Cohomology".  By cohomology, we mean in particular the Cheeger-Simons classes of vector bundles. The goal of the talk will be to show how the combination of the three subjects leads to new questions about dynamics, and the "wild" topological sets that naturally arise in dynamical systems. This leads to a new understanding of one of the "mysterious" results of foliation theory, the so-called Bott-Heitsch Theorem which dates from 1972. This new understanding raises as many questions as it answers.


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January 22, 2008, 5:45 p.m.; Ken Edwards building, lecture theatre 3.

Caroline Series (Warwick)

 The talk will be preceded by a cheese and wine reception starting at 5:00 p.m.


Continued fractions and building hyperbolic manifolds.

 

Abstract:

 

The Farey tessellation of the upper half plane gives a beautiful geometrical representation of continued fractions which finds many applications in  hyperbolic geometry.

 

After introducing the tessellation, I will explain how it provides a guide for constructing hyperbolic manifolds which illustrate some of the most important developments of recent years.

 

 

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