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Titles and abstracts:
Tuesday November 20th:
11:30 - 12:20 Alan McLeay: Mapping class groups, covers, and braids.
The mapping class group of a surface is the group of isotopy classes of boundary preserving homeomorphisms of the surface. Given a finite sheeted covering space between surfaces, we may ask what relationship, if any, exists between the two mapping class groups?
In joint work with Tyrone Ghaswala we investigate this question for surfaces with non-empty boundary. I will discuss a classical theorem of Birman-Hilden and give new insight into a family of covering spaces related to the Burau representation of braid groups.
14:00 - 14:50 Alfredo Hubard: The branch waist of two dimensional spheres
I will discuss several problems regarding extremal metrics on the 2-sphere. The main result I will discuss is that for every metric on the sphere, a variant of the waist inspired by a graph-minor concept called branch-width, equals the largest range of an antipodality. This is joint work with Arnaud de Mesmay and Francis Lazarus.
16:00 - 16:50 (General Math Seminar) Sergio Cabello: Interactions between geometry, graphs and algorithms
I will describe some of the interactions between graphs and geometry, many of them with an algorithmic slant. In particular, we will discuss the crossing number of graphs, properties and relations between different classes of graphs defined using the intersection of geometric objects in the plane, and some classical optimization problems for graphs defined geometrically.
Wednesday November 21st:
11:30 - 12:20 Binbin Xu: Geodesics in graphs associated to surfaces with marked points
Consider a surface with marked points. By considering different elementary objects on it, we can define different graphs, for example, the curve graph, the arc graph, the triangulation graph, etc. Given such a graph, by setting the edge length to be 1, we associate to it a metric. In the arc graph, Hensel-Przycycki-Webb used an idea considered by Hatcher to define the unicorn path connecting any two given vertices. In particular, this path is close to be a geodesic. The goal is to see whether the unicorn path can help us to find geodesics in any of the graphs mentioned above. In this talk I'll first define the objects mentioned above and then I'll discuss in details the case where the surface is a torus with one marked point as an example.
14:00 - 14:50 Funda Gultepe: Complexes related to surfaces
In this introductory talk we will introduce some of the simplicial complexes associated to a surface: the curve complex, the marking graph and the pants complex. We will give some basic examples and briefly mention some of the properties of these complexes which make them useful to study Teichmueller spaces and the mapping class group.