Geometric Group Theory and Low-Dimensional Topology: Recent Connections and Advances

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This NSF award provides partial support for U.S. based mathematicians to participate in an advanced school and workshop on "Geometric Group Theory and Low-Dimensional Topology: Recent Connections and Advances," to be held at ICTP, Trieste, Italy, 23 May - 3 June 2016. The proposed activity is a mix of "hot topics" that would afford tremendous opportunities to mathematicians at all career stages to interact and generate new ideas. The advanced school will expose graduate students to a diverse array research topics. Introducing both US based and international students to leading experts from across the globe should have a profound effect on cultivating mathematics in the US and in the developing world. The potential for fostering initial contacts and interactions that lead to closer connections between US based mathematicians and those in the developing world is a long term benefit for faculty and students.The main topics to be covered at this advanced school and workshop include character varieties and deformation of geometric structures, effective geometry and topology of hyperbolic 3-manifolds, left orderability and Heegaard Floer theory, the mapping class group action on Teichmuller space and the curve complex, dynamics on these spaces and virtually special cube complexes and groups. There have been important developments in these areas recently, for example: the impact of geometric group theory in the work of Wise and subsequently Agol's resolution of the famous "virtual conjectures" in 3-manifold topology. The event website is: http://indico.ictp.it/event/7646/.