Braid groups belong to a broad class of groups known as Artin groups, which are defined by presentations of a particular form and have played a major role in geometric group theory and low-dimensional topology in recent years. These groups fall into two classes, finite-type and infinte-type Artin groups. The former come equipped with a powerful combinatorial structure, known as a Garside structure, while the latter are much less understood and present many challenges.
Disks are nice for many reasons. In this casual talk, I will try to convince you that it's even nicer than you think by presenting the Alexander's lemma. Just like in algebraic topology, we are going to rely on disks heavily to understand mapping class groups of surfaces. The particular method is called the Alexander's method. Twice the Alexander, twice the fun! No background in mapping class group is required.
Morse theory and Morse homology together give a method for understanding how the topology of a smooth manifold changes with respect to a filtration of the manifold given by sub-level sets. The Morse homology of a smooth manifold can be expressed using an algebraic object called a persistence module. A persistence module is a module graded by real numbers, and in this setup the grading on the module corresponds to the aforementioned filtration on the smooth manifold.
Morse theory and Morse homology together give a method for understanding how the topology of a smooth manifold changes with respect to a filtration of the manifold given by sub-level sets. The Morse homology of a smooth manifold can be expressed using an algebraic object called a persistence module. A persistence module is a module graded by real numbers, and in this setup the grading on the module corresponds to the aforementioned filtration on the smooth manifold.
We will talk a little about realizing automorphisms of a free group as graph maps and how to use Stallings folds to study them.
How good of an invariant is the Jones polynomial? The question is closely tied to studying braid group representations since the Jones polynomial can be defined as a (normalized) trace of a braid group representation.
Let M be the 3-manifold obtained by r-surgery on the right handed trefoil knot. Classification of contact structures on such manifolds have been mostly understood for r \geq 1 and r=0. Etnyre-Min-Tosun has an upcoming work on the classification of the tight contact structures for all r. The fillability of contact structures on M is mostly understood if r is not between 0 and 1/2. In this talk, we will discuss the fillability of the contact structures M for 0
Abstract: How big is a group? One possible notion of the size of the group is the cohomological dimension, which is the largest n for which a group G can have non—trivial cohomology in degree n, possibly with twisted coefficients. Following the work of Bestvina, Bux and Margalit, we compute the cohomological dimension of the terms Johnson filtration of a closed surface. No background is required for this talk.
I'll talk about some 2D billiards, the most visual class of dynamical systems, where orbits (rays) move along straight lines within a billiard table with elastic reflections off the boundary. Elliptic flowers are built “around" convex polygons, and the boundary of corresponding billiard tables consists of the arcs of ellipses.
