# Spring 2019

Date Speaker Title Abstract
Jan 15 Alex Casella Let’s Talk! Communication is a fundamental skill in life. Whether you are professor, a scientist or a salesman, you will often find yourself talking in front of an audience. In this talk I will present my own experience regarding the preparation and execution of a scientific talk, covering most common DOs and DON’Ts.
Jan 22 Lorenzo Ruffoni Strict hyperbolization and its applications Gromov introduced some procedures to turn a given polyhedron into a new one endowed with a piecewise Euclidean metric of non-positive curvature, while preserving some of its original topological features. In this talk we will describe a refinement of Gromov's construction due to Charney and Davis, in which the new space carries a strictly negatively curved metric, and thus has hyperbolic fundamental group. Some applications will be discussed
Jan 29 Ettore Aldrovandi Homotopy theoretic aspects of central extensions The classification of central extensions of a group $$G$$ by a (necessarily abelian) group $$A$$ is very well understood from both the Algebra and Geometry viewpoints. Indeed, one of the most interesting aspects is the interplay between the two.
A much more interesting situation is when the topology is directly part of the structure, for example if $$G$$ and $$A$$ are topological groups. Alternatively, since the category of topological spaces and that of simplicial sets have equivalent homotopy theories, we can assume they are simplicial groups. I will discuss some of the aspects of the classification of central extensions in this context, centered around the statement that such classification is given by homotopy classes of maps $$BG \to B^2A$$ between classifying spaces.
This is work in progress in collaboration with Niranjan Ramachandran (UMD) and my student Michael Niemeier.
Feb 5 John Bergschneider Finite 2-Stratifold Groups 2-Stratifolds are a generalization of closed surfaces in that they contain simple closed curves where several sheets meet. Currently, there is no general classification of these spaces or their fundamental groups. Most finitely generated Fuchsian Groups and some generalized triangle groups can be realized as the fundamental of a 2-stratifold. We explore a possible solution on how to classify finite 2-stratifold groups and how Fuchsian groups and generalized triangle groups are involved.
Feb 12
Feb 19
Feb 26 Kate Petersen Representations and Hyperbolic structures on knot complements Thurston’s hyperbolic Dehn surgery theorem gives a geometric picture of many (mostly incomplete) hyperbolic structures on a knot complement. I’ll discuss how this can be used to define representations of the knot group into SL(2,C) in a completely diagrammatic way.
Mar 5
Mar 12 Woojin Kim Persistent homology for time-evolving metric/network data Characterizing the dynamics of time-evolving data within the framework of topological data analysis has been attracting increasingly more attention. Popular instances of time-evolving data include flocking/swarming behaviors in animals and social networks in the human sphere. A natural mathematical model for such collective behaviors is a dynamic metric space (DMS)/dynamic network (DN). We will discuss (1) how to induce a multiparameter/zigzig persistent homology as an invariant of a DMS/DN, and (2) stability of these invariants. In order to address the stability, we extend the Gromov-Hausdorff distance on metric spaces to the setting of DMSs/DNs. This is a joint work with Facundo Memoli and Zane Smith
Mar 26 Anindya Chanda Classification of Partial Hyperbolic Automorphisms on 3-Manifolds The notion of hyperbolicity of a Automorphisms on a Riemannian Manifold and it's properties were introduced around 1960-70. But the idea of partial hyperbolicity was not much explored at that time. After 1995, it was proven that partial hyperbolic systems satisfy some very strong and exceptional properties in the field of Dynamical Systems and Ergodic Theory and those results greatly motivated the study of partial hyperbolicity. But till today it is a largely open area of research and the field is not discovered in great details, specially very little is known about the dimensions greater or equal to 4. In this talk we will try to present a (partial) classification of Partial Hyperbolic Automorphisms over the dimension 3.
Apr 2 Sam Ballas Gluing equations for projective structures on 3-manifolds One of Thurston’s many amazing ideas are his hyperbolic gluing equations. Roughly speaking, given an ideally triangulated 3-manifold M, one can construct a set of complex polynomial equations whose solutions correspond to hyperbolic structures on M. In this talk I will describe some work in progress (joint with Alex Casella) on generalizing these equations in the context of real projective structures. After describing our parameters and equations, I will describe how a solution enables one to build a developing map, find a holonomy representation for a real projective structure and draw some nice pictures of the developing image.
Apr 9
Apr 16 Aamir Rasheed Surface subgroups of 3-manifold groups. A closed irreducible 3-manifold M with infinite fundamental group is uniquely determined up to homeomorphism by its fundamental group. One can understand the topology of M by studying its group structure and conversely the group structure can be understood by studying the topology. One important tool in this study is the study of embedded surfaces. The image of the fundamental groups of these surfaces (surface subgroups) in the fundamental group of M encode a lot of useful information about the topology and geometry of M. In this talk we will discuss this relationship further. In particular, we will see, how various properties such as malnormality and maximality of surface subgroups give us information about the 3-manifold itself.
Apr 23 Daniel Hartman Anosov flows and contact surgery Until a few years ago, the only know examples of contact Anosov flows were geodesic flows of Riemannian manifolds. In 2013, Patrick Foulon and Boris Hasselblatt gave a surgery method which, when performed along an E-transverse link, results in a new contact Anosov flow. This surgery method subsumes the Handel-Thurston and Goodman surgeries. The goal of the talk will be to outline the surgery

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