Alex Chandler, NC State, Spectral Sequences Working Seminar
Spectral sequences in Khovanov homology.
Spectral sequences in Khovanov homology.
The cosmetic surgery conjecture states that no two surgeries on a given knot produce the same 3-manifold (up to orientation preserving diffeomorphism). Floer homology has proved to be a powerful…
For an un-oriented link K, let L(K) be the ropelength of K. It is known that in general L(K) is at least of the order O((Cr(K))3/4), and at most of the…
The original construction of the Khovanov homology of a link can be seen as a formal complex in the category of flat tangles and surfaces between them. There is a way to…
In his monograph “Systèmes Orthogonaux” (Leçons sur les systèmes orthogonaux et les coordonnées curvilignes, Gauthier-Villars, Paris, 1910), Darboux stated three theorems providing local existence and uniqueness of solutions to first order systems of…
One way to effectively show a group is non-trivial is to find a non-trivial representation. A major open question in low-dimensional topology is whether the fundamental group of a closed…
In this talk I'll explain a surprising relationship between the objects in the title. Two n-dimensional polytopes, $P$, $Q$ are said to be scissors congruent if one can cut $P$…
The Penrose triangle, also known as the impossible tribar is an icon for cohomology. It is literally the icon for Cech cohomology on Wikipedia. The idea goes back to a…
Self-duality equations in gauge theory can be complexified in many inequivalent ways, but there are two obvious options: One can extend Hodge duality in either a complex linear fashion, or…
Topological Data Analysis (TDA) is a relatively young field in both algebraic topology and machine learning. Tools from TDA, in particular persistent homology, have proven successful in many scientific disciplines. Persistence…
A geometrically-exact beam is a nonlinear field-theoretic model for elongated elastic objects. It utilizes moving frames to reduce the number of system’s independent spatial variables, which is a further development…
A transverse link is a link in the 3-sphere that is everywhere transverse to the standard contact structure. Transverse links are considered up to transverse isotopy, with classical invariants such…
In this talk, we introduce a scattering asymmetry which measures the asymmetry of a domain on a surface by quantifying its incompatibility with an isometric circle action. We prove a…
The Turaev surface of a link diagram is a surface built from a cobordism between the all-A and all-B Kauffman states of the diagram. The Turaev surface can be seen…
Come chat with other geometers/topologists. This is a good chance for graduate students to meet the geometry/topology faculty, especially our newest members, Peter McGrath and Teemu Saksala. Host: Tye…
We consider a geometric inverse problem of recovering some material parameters of an unknown elastic body by probing with elastic waves that scatter once inside the body. That is we send elastic…
We consider a real bivariate polynomial function vanishing at the origin and exhibiting a strict local minimum at this point. We work in a neighbourhood of the origin in which…
Path signatures are powerful nonparametric tools for time series analysis, shown to form a universal and characteristic feature map for Euclidean valued time series data. The theory of path signatures can be lifted…
A trisection of a smooth, connected 4-manifold is a decomposition into three standard pieces. Like the case of Heegaard splittings in dimension three, a trisection is described by a trisection…