Date: Tuesday February 14th 2023
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: Totally geodesic surfaces and subgroup separability.
Speaker: Sayantika Mondal (CUNY GC)
Abstract: In this talk we will look at immersions and embeddings of totally geodesic surfaces in hyperbolic 3-manifolds. In particular, when can such immersed surfaces be virtually embedded and how this relates to separability conditions on surface subgroups.
Date: Tuesday February 28th
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: The field of definition of a dessin
Speaker: Ajmain Yamin (CUNY GC)
Abstract: I will introduce dessins d'enfants which are topological/combinatorial objects, essentially just embeddings of graphs in surfaces. I will explain how they are relevant in number theory, and in particular explain Belyi's theorem and the field of definition of a dessin. This talk will have many examples including some examples that I have computed myself.
Date: Tuesday March 7th & 14th
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: Quasi-isometric classification of graph manifold groups
Speaker: Zhihao Mu
Abstract: A graph manifold is a 3-manifold that can be
decomposed along embedded tori and Klein bottles in to finitely many
Seifert pieces. Behrstock and Neumann showed that quasi-isometry types
of fundamental groups of graph manifolds can be classified in terms of
certain finite two-colored graphs. As an application, it implies that
any pair of right-angled Artin groups with defining graph as a tree
with diameter larger than 2 is quasi-isomorphic. In the first talk, I
will introduce some preliminaries about 3-manifolds including the
prime decomposition, JSJ decomposition and the definition of Seifert
fibered manifolds. In the second talk, I will sketch the proof of the
classification theorem and explain its application in the study of
Artin groups.
Date: Tuesday March 21st
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: Mapping class groups and finite presentability
Speaker: Yassin Chandran
Abstract: We'll introduce a useful topological criterion of
Brown to show a group is finitely presented. We'll then discuss some
applications. First to show that the mapping class group of a finite
type surface is finitely presented; then some surprising consequences
for (smooth) mapping class groups of some infinite type surfaces and
homeomophormisms of cantor sets. If time permits, we may discuss
further connections between mapping class groups, Thompson's groups,
and finiteness properties of groups.
Date: Tuesday April 18th
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: (Projectivized) geodesic currents, length function, and
intersection form: constructions and properties
Speaker: Weiyan Lin (CUNY GC)
Abstract: Bonahon’s foundational work on geodesic currents
play an important role in understanding the geometry of the
(compactified) Teichmuller space, and the dynamical properties of
mapping class group and its elements. Moreover, a central point of
Bonahon’s work on geodesic currents is the construction of the
intersection form. Here in the context of free group of finite rank,
we also have an analogous construction of geodesic currents.
Moreover, as an analogy of the Teichmuller space, Culler and Vogtmann
constructs the (projectivized) outer space, and it has been well
studied ever since. Ultimately, there is a “natural” construction of
the intersection form that arises in free groups. Throughout the talk,
I will demonstrate the construction of these geometric objects, and
present some important properties related to these objects.
Date: Tuesday April 25th
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: S^1 Action and Asymmetry of Topological Spaces (Especially 3-Manifolds)
Speaker: Yushan Jiang (CUNY GC)
Abstract: Asymmetry is a topological property. If a topological space X is asymmetric, then every “good” metric on X will always have discrete isometry group. For example, if M is a closed topological manifold which admits at least one Riemannian metric with negative sectional curvature, then any Riemannian metric on M will always have finite isometry group (hence discrete). This phenomenon is a corollary of Gromov and Yano's theorems which bring non-trivial smooth S^1 action, negative curvature and Gromov norm (on homology group with real coefficient) together. By these results, Gromov norm is a good way to detect asymmetry. However, there are some asymmetric closed manifolds with vanishing Gromov norm, e.g. nonpositively curved nontrivial graph 3-manifolds. In this talk, I will illustrate why they are still asymmetric and introduce other tools which might detect the asymmetry for more general topological spaces, e.g., the hyperbolicity of the fundamental group.
Date: May 9th
Tuesday, 1:30pm - 2:30 pm in Room 4214.03 (Math Thesis Room)
Title: Square peg problem and symplectic topology
Speaker: Susan Rutter (CUNY GC)
Abstract: The square peg problem, conjectured by Toeplitz in
1911, asks whether a square can be inscribed in a continuous simple
closed curve in the plane, and remains an open problem to this
day. This talk will discuss the result of the smooth case by Greene
and Lobb: that a rectangle of any ratio of sides can be inscribed in a
smooth simple closed curve. We will cover the topological ideas of the
proof and provide an introduction to symplectic topology for the
uninitiated.