Lecture by Mahdi Yazdi (Oxford) at IPM, Wednesday, 2 pm

[Meysam Nassiri]

Title: Stretch factors of surface homeomorphisms 

Abstract: Given a closed, orientable, hyperbolic surface S of genus g, the mapping class group of S is the group of orientation preserving homeomorphisms of S up to isotopy. A ‘generic’ element in the mapping class group is pseudo-Anosov. Given such a map f, one can assign an algebraic integer to f that measures how much the map stretches/shrinks in canonical directions. From a different perspective, the logarithm of this number is equal to the topological entropy of the map, hence a dynamical quantity. This number is called the stretch factor. We will discuss the following two open questions and state some of the known facts about them. 

1) Which algebraic integers arise as stretch factors of pseudo-Anosov maps (allowing the genus to vary)? 

2) Fixing the genus g, what is the smallest stretch factor? 

This talk is expository. 

Venue: IPM Niavaran bldg., Lecture Hall 1

Time: Wednesday, July 18, 2018, 14:00-15:00  

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