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Title:   Computing with Thurston maps
Speaker:   Laurent Bartholdi [Saarland University]

Abstract:   Thurston maps are branched coverings of the 2-sphere all of whose critical points have finite orbits. They admit an algebraic avatar, a set with two commuting actions of a free group. I will present some computer code that translates between these two worlds, and show its usefulness in studying twists, matings, obstructions etc.
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Title:   Near-Degenerate Regime in Transcendental Dynamics
Speaker:   Kostiantyn Drach [Universitat de Barcelona]

Abstract:   Near-Degenerate Regime, i.e., a collection of tools and ideas to control degeneration of Riemann surfaces endowed with dynamics, has been instrumental in the most recent progress towards the MLC Conjecture and understanding rigidity of quadratic polynomials. Likewise, it was one of the key ingredients of extending Yoccoz's results from quadratic polynomials to polynomials of higher degree. In this talk, based on joint work in progress with Dima Dudko, we introduce this set of ideas into Transcendental Dynamics (to Yoccoz-type maps in the Speiser class) and discuss possible applications to rigidity as well as to Thurston-type realization problems.
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