All talks will be in the Mathematics Seminar Room (Room 103, first floor of the Mathematical Sciences Building)
This is part of a series of collaborative meetings between Liverpool University, Manchester University, Queen Mary, and Surrey University, supported by a Scheme 3 grant from the London Mathematical Society.
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11.30-12.30
C. Liverani (IHES / Roma Tor Vergata)
Title: "Ruelle-Perron-Frobenius spectrum for Anosov maps"
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2.30-3.30pm
M. Pollicott (Manchester)
Title: "Ergodic properties of linear actions of 2 \times 2 matrices on the plane"
Abstract (see also picture ): Consider a discrete group G of 2 x 2 real matrices with determinant 1 and fix a non-zero point (x,y) in the plane. It is interesting to look at the orbit G(x,y) = {A(x,y) : A in G} of (x,y) under the natural linear action A: (x,y) -> (A[1,1]x + A[1,2]y, A[2,1]x + A[2,2]y). If G is a cocompact group then the orbit G(x,y) is dense and the action is ergodic, as was shown by Hedlund (1936). Ledrappier (1997) extended the ergodicity result to groups G' < G with G/G' an infinite abelian group. A simple example is the commutator subgroup G' = [G,G]. Francois Ledrappier and I have generalized these results to 2 x 2 real matrices with entries in the complex numbers, quarternions or the very general Clifford numbers.
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4-5pm
W. Tucker (Cornell)
Title: "The Lorenz attractor exists"
Abstract: We present an algorithm for computing rigorous solutions to a large class of ordinary differential equations. The main algorithm is based on a partitioning process and the use of interval arithmetic with directed rounding. As an application, we prove that the Lorenz equations support a strange attractor, as conjectured by Edward Lorenz in 1963. We also prove that the attractor is robust, i.e., it persists under small perturbations of the coefficients in the underlying differential equations. The proof is based on a combination of normal form theory and rigorous computations.
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5pm onwards : Drinks and restaurant meal