Seminars and Colloquia by Series

Groups as geometric objects

Series
Geometry Topology Seminar Pre-talk
Time
Monday, October 21, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jacob RussellCUNY Graduate Center

Gromov revolutionized the study of finitely generated groups by showing that an intrinsic metric on a group is intimately connected with the algebra of the group. This point of view has produced deep applications not only in group theory, but also topology, geometry, logic, and dynamical systems. We will start at the beginning of this story with the definitions of these metrics on groups and how notions from classical geometry can be generalized to this context.  The focus will be on how the "hyperbolic groups" exhibit geometric and dynamical feature reminiscent of the hyperbolic plane and its isometries.

Geometry Topology Seminar Pre-talk: Fundamental groups of projective varieties by Corey Bregman

Series
Geometry Topology Seminar Pre-talk
Time
Monday, September 30, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Corey BregmanBrandeis University

A question going back to Serre asks which groups arise as fundamental groups of smooth, complex projective varieties, or more generally, compact Kaehler manifolds.  The most basic examples of these are surface groups, arising as fundamental groups of 1-dimensional projective varieties.  We will survey known examples and restrictions on such groups and explain the special role surface groups play in their classification. Finally, we connect this circle of ideas to more general questions about surface bundles and mapping class groups. 

An Introduction to Braids and Complex Polynomials

Series
Geometry Topology Seminar Pre-talk
Time
Monday, September 23, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael DoughertyColby College

In this informal chat, I will introduce the braid group and several equivalent topological perspectives from which to view it. In particular, we will discuss the role that complex polynomials play in this setting, along with a few classical results.

Topology in complex dynamics

Series
Geometry Topology Seminar Pre-talk
Time
Monday, August 26, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jasmine PowellUniversity of Michigan

The field of complex dynamics melds a number of disciplines, including complex analysis, geometry and topology. I will focus on the influences from the latter, introducing some important concepts and questions in complex dynamics, with an emphasis on how the concepts tie into and can be enhanced by a topological viewpoint.

High-dimensional knots, and rho-invariants by Patrick Orson

Series
Geometry Topology Seminar Pre-talk
Time
Monday, April 15, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Patrick OrsonBoston College

I will give a brief survey of concordance in high-dimensional knot theory and how slice results have classically been obtained in this setting with the aid of surgery theory. Time permitting, I will then discuss an example of how some non-abelian slice obstructions come into the picture for 1-knots, as intuition for the seminar talk about L^2 invariants.

Seifert fibered manifolds

Series
Geometry Topology Seminar Pre-talk
Time
Monday, April 8, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tye LidmanNCSU

In this talk, we will study Seifert fibered three-manifolds. While simple to define, they comprise 6 of the 8 Thurston geometries, and are an important testing ground for many questions and invariants. We will present several constructions/definitions of these manifolds and learn how to work with them explicitly.

Classical knot invariants and slice surfaces by Peter Feller

Series
Geometry Topology Seminar Pre-talk
Time
Wednesday, April 3, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Peter FellerETH Zurich

In the setup of classical knot theory---the study of embeddings of the circle into S^3---we recall two examples of classical knot invariants: the Alexander polynomial and the Seifert form.

We then introduce notions from knot-concordance theory, which is concerned with the study of slice surfaces of a knot K---surfaces embedded in the 4-ball B^4 with boundary the knot K. We will comment on the difference between the smooth and topological theory with a focus on a surprising feature of the topological theory: classical invariants govern the existence of slice surfaces of low genus in a way that is not the case in the smooth theory. This can be understood as an analogue of a dichotomy in the study of smooth and topological 4-manifolds.

Doubly slice Montesinos links

Series
Geometry Topology Seminar Pre-talk
Time
Monday, April 1, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ahmad IssaUniversity of Texas, Austin

A link in the 3-sphere is doubly slice if it is the cross-section of an unknotted 2-sphere in the 4-sphere. The double branched cover of a doubly slice link is a 3-manifold which embeds in the 4-sphere. For doubly slice Montesinos links, this produces embeddings of Seifert fibered spaces in S^4. In this pre-talk, I'll discuss a construction and an obstruction to being doubly slice.

Spheres in 4-manifolds

Series
Geometry Topology Seminar Pre-talk
Time
Monday, March 11, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 257
Speaker
Hannah SchwartzBryn Mawr
In this talk, we will examine the relationship between homotopy, topological isotopy, and smooth isotopy of surfaces in 4-manifolds. In particular, we will discuss how to produce (1) examples of topologically but not smoothly isotopic spheres, and (2) a smooth isotopy from a homotopy, under special circumstances (i.e. Gabai's recent work on the ``4D Lightbulb Theorem").

A partial order on nu+ equivalence classes

Series
Geometry Topology Seminar Pre-talk
Time
Monday, March 4, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 257
Speaker
Kouki SatoUniversity of Tokyo
I will review the definition of nu+ equivalence, which is an equivalence relation on the knot concordance group, and introduce a partial order on the equivalence classes. This partial order is preserved by all satellite maps and some concordance invariants. We also consider full-twist operations and its relationship to the partial order.

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