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…
In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is links whose Khovanov homology is supported on two adjacent diagonals, are…
The Heegaard Floer homology introduced by Ozsvath and Szabo provides a lot of link invariants to study links in the three-sphere and its surgery manifolds. In this talk, we exact some…
This talk will focus on using the Euclidean Signature to determine whether two smooth planar curves are congruent under the Special Euclidean group. Work done by Emilio Musso and Lorenzo Nicolodi emphasizes that…
I give an introductory talk about geometric inverse problems and ray transforms (no proofs are involved). I mainly focus on the Euclidean X-ray transform of scalar fields and vector fields,…
Consider a metric space (S,d) with an upper curvature bound in the sense of Alexandrov (i.e.~via triangle comparison). We show that if (S,d) is homeomorphically equivalent to the 2-sphere, then…
The study of extremals for Steklov eigenvalues has revitalised the theory of free boundary minimal surfaces. One of the most basic open questions can be phrased as follows: Can a…