ACC Seminar: Linear Representations of Fundamental Groups and Applications

ABSTRACT

Let M be a compact manifold, possibly with boundary. Its fundamental group is a finitely presented group. In my research, I usually study the parameter spaces of linear representations of these fundamental groups, and their geometric meaning. Usually, I consider the case when dim M = 2, i.e. surface groups or free groups, where several powerful tools are available to study these questions. In this talk, I will discuss how to generalize some of these tools to higher dimension. This is especially interesting when dim M = 3 or dim M = 4. In dimension 3, there are applications to interesting geometric questions about hyperbolic 3-manifolds. Dimension 4 is particularly interesting because it includes all finitely presented groups, hence these tools might be used to answer group-theoretic questions involving linear representations.

BIOGRAPHY

Daniele Alessandrini is a Lecturer at Stevens Institute of Technology. He completed his PhD at Scuola Normale Superiore, Pisa, Italy under the supervision of Riccardo Benedetti. He held positions at the University of Heidelberg and Columbia University. Dr. Alessandrini’s research interests include Geometric Topology and Differential Geometry, usually in Higher Teichmüller Theory and surface group representations. 

Attendance: This is a technical talk open to all.
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