September 27th: Ara Basmajian (CUNY Graduate Center and Hunter College)
Title: Conformal scatterings as subsets of the Cantor set
Abstract: A set is said to be scattered if every non-empty subset has an isolated point. Using a recursively defined sequence of derived sets, Akin showed that there exist uncountably many topologically distinct compact countable scattered subsets of the Cantor set. In this talk, we investigate such problems in the category of conformal mappings.
October 4th: No meeting
October 11th: Harold Sultan (Columbia University)
Title: The mapping class group and natural combinatorial complexes
Abstract: In geometric group theory combinatorial complexes are often used as models to study the large scale geometry of groups or spaces of interest. Notably, the marking complex and the pants complex, both natural analogues of the curve complex, have proven to be useful in studying the mapping class group and Teichmüller space, respectively. In this talk, we will discuss some of the properties of the mapping class group and and Tiechmüller space as viewed from the perspective of the aforementioned combinatorial complexes.
October 18th: Viveka Erlandsson (CUNY Graduate Center)
Title: The Margulis region in hyperbolic 4-space
Abstract: Let G be a discrete subgroup of the isometry group of hyperbolic space containing a parabolic element. There is a region precisely invariant under the stabilizer of the parabolic fixed point in G, called the Margulis region. Perry Susskind has given an explicit description for the boundary of this region in hyperbolic 4-space when the parabolic element is screw parabolic with an irrational rotational part. Here we further describe the shape of this boundary when the irrational rotation is of bounded type. We describe the asymptotic behavior of the boundary and show that the Margulis regions corresponding to two such elements are quasi-isometric.
October 25th: Viveka Erlandsson (CUNY Graduate Center)
Title: The Margulis region in hyperbolic 4-space (continued)
November 1st: Gregory Fein (Rutgers University)
Title: Generalizing the recognition theorem for Out(Fn)
Abstract: The Recognition Theorem for Out(Fn), as laid out in the paper by Feighn and Handel, applies only to outer automorphisms which have no periodic behavior. I will demonstrate what can go wrong when that restriction is lifted by offering some rather problematic examples. If there is time, I will provide proofs of some lemmas I have come up with as ways to work around these issues. I will start with some background to get you all up to speed on the definitions, though many of these definitions will be familiar to anyone who has seen my talks before.
March 21st: Timothy Susse (CUNY Graduate Center)
Title: The action of the mapping class group on the curve complex
Abstract: The Mapping Class Group does not act on the Curve Complex properly discontinuously, however we will show that it satisfies a weaker condition called WPD. To prove the action has this property we will study stabilizers of curves and the action of the group on the Thurston boundary of Teichmüller space. We can then use this property to discern some algebraic properties of the group, including the structure of centralizers of pseudo-Anosovs, the structure of its second bounded cohomology and find geometric conditions to determine when one pseudo-Anosov is conjugate to a power of another.
November 15th: Ozgur Evren (CUNY Graduate Center)
Title: Two metrics on the Teichmüller space of flute surfaces
Abstract: A flute surface is defined to be an infinite type surface of genus zero which has a pants decomposition {Pn} such that Pn∩Pn+1 is a simple closed geodesic. We compare the topologies defined by Teichmüller metric and the length spectrum metric on the Teichmüller space of a flute surface. Namely, we give a sufficient condition for these two metrics to define different topologies, a phenomenon observed only on surfaces of infinite type.
November 22nd: No meeting
April 4th: Andrew Silverio (Rutgers University)
Title: Primitive words in rank 2 free group
Abstract: A primitive word is an element of a generating set of a group. In case of rank 2 free group, the primitive elements have a well-known form. I will discuss two ways to list all these primitive words using Keen-Series's Farey words and Gilman-Keen's palindromic words. The Gilman-Maskit algorithm produces Farey words as shown by Gilman-Keen. We make a slight modification to this algorithm to produce and study palindromic words. At some points of the talk, I will make dubious connections to mapping class groups and hyperbolic geometry.
April 11th: Hengyu Zhou (CUNY Graduate Center))
Title: Envelopes of horospheres in hyperbolic 3-space
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