• Tuesday 29 May 2012
  Alastair Fletcher (Warwick)
  Decomposing diffeomorphisms of the sphere
   
• Tuesday 12 June 2012
  Katsutoshi Shinohara (Uni)
  On the (non)-minimality of free-semigroup actions on the interval C^1-close to the identity

  Abstract:
  We consider (attracting) free semigroup actions (with two generators) on an interval.
  It is known that, if those two maps are sufficiently C^2-close to the identity, then
  there is a restriction on the shape of the (forward) minimal set. Namely, it must be
  an interval. (This statement is not accurate. I will give the precise statement in my
  talk.) In this talk, I will explain that the similar argument fails in C^1-topology.
   

• Thursday 14 June 2012
  Arnaud Cheritat (Institut de Mathematique de Toulouse)
  The talk is moved to Friday!

• Wednesday 20 June 2012 - room MS.05
  Olga Lukina (University of Leicester)
  Hierarchy of graph matchbox manifolds
  Abstract:
  We study a class of graph foliated spaces, or graph matchbox manifolds, initially
  constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier
  of dynamical complexity which we call a level. We develop the fusion construction,
  which allows us to associate to every two graph foliated spaces a third one which
  contains the former two in its closure. Although the underlying idea of the fusion
  is very simple, it gives us a powerful tool to study graph foliated spaces.
  Using fusion, we prove that there is a hierarchy of graph foliated spaces at infinite
  levels. We also construct examples of graph foliated spaces at low levels.

Term 2

• Tuesday 17 January 2012
  Mark Pollicott (Warwick)
  The Schottky-Klein Function and Ergodic Theory
• Tuesday 24 January 2012
  Adam Epstein (Warwick)
  Quadratic Mating Discontinuity
  
  Abstract: Mating is a partially defined operation which sends pairs of normalized
  polynomials of the same degree to normalized rational maps of that degree.
  As proposed by Douady, the recipe is to glue filled-in Julia sets back-to-back along
  opposite prime ends, in the hope of obtaining a branched self-cover of a topological
  sphere which is suitably conjugate to a unique normalized endomorphism of the
  Riemann sphere. We will show that this procedure yields a highly discontinuous
  map between the relevant parameter spaces.
• Tuesday 31 January 2012
  Davoud Cheraghi (Warwick)
  Optimal estimates on perturbed Fatou coordinates
  
• Tuesday 7 February 2012
  Dimitry Turaev (Imperial College London)
  On stickiness and flicker-noise
• Tuesday 14 February 2012
  Peter Hazard (Warwick)
  Entropy without Periodic Points in Dimension Two
  
  Abstract: In 1980 A. Katok showed that if a $C^{1+\alpha}$-diffeomorphism $f$ of
  a compact surface has positive topological entropy then it has a homoclinic point.
  Consequently $f$ possesses a horseshoe, and hence infinitely many periodic orbits.
  It was asked if this held for $f$ with lower regularity. M. Rees later gave a counter-
  example, constructing a homeomorphism of the 2-torus with positive entropy which
  is minimal.
• Tuesday 21 February 2012
  James Langley (University of Nottingham)
  Non-real zeros of derivatives of real meromorphic functions
  
  Abstract: Around 1911 Wiman conjectured that if an entire function is real on the
  real axis and, together with its second derivative, has only real zeros, then the
  function belongs to the Laguerre-Polya class, from which it follows that all derivatives
  have only real zeros. This has now been proved via a combination of results by
  several authors including the speaker, as have some related conjectures advanced
  by Polya in the 1940s. The talk will survey results in this direction and report on
  recent progress towards an analogue of the Polya-Wiman conjectures for functions
  which are meromorphic rather than entire.
• Tuesday 28 February 2012
  Ian Morris (University of Surrey)
  Structure of extremal matrix products
  
  Abstract: The joint spectral radius of a finite or compact set of dxd matrices is the
  maximum possible exponential growth rate of long products of matrices drawn from
  that set. An influential conjecture of J. Lagarias and Y. Wang stated that for any
  finite set of matrices, this optimal rate of growth is achieved by a periodic product.
  We discuss counterexamples and describe the properties which must be satisfied
  by sequences of extremal growth.
• Tuesday 6 March 2012
  Boguslaw Zegarlinski (Imperial College London)
  TBA
• Tuesday 13 March 2012
  John Osborne (Open University)
  Spiders' webs and locally connected Julia sets of transcendental entire functions
  
  Abstract: In this talk, I will explore some links between the local connectedness of
  the Julia set of a transcendental entire function, and a particular geometric form
  of the Julia set known as a spider's web (first defined by Rippon and Stallard).