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 as the self-linking number and regular isotopy class. One of the first connections between transverse links and quantum invariants was made by Plamenevskaya in 2006,…

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 quantitative isoperimetric inequality involving the scattering asymmetry and characterize the domains with vanishing scattering asymmetry by their rotational symmetry. We also give a new proof…

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 as a Jones polynomial analogue of the Seifert surface. The Turaev genus of a link is the minimum genus of the Turaev surface for any…

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 Lidman (tlid@math.ncsu.edu) Instructions to join: Zoom invitation is sent to the geometry and topology seminar list. If you are not on the list, please, contact the…

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 waves from the boundary of an open bounded domain. The waves propagate inside the domain and scatter from an unknown point scatterer. We measure the entering…

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 the non-zero level curves of this function are smooth Jordan curves. Whenever the origin is a Morse critical point, the sufficiently small levels become boundaries…

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 to the setting of Lie group valued time series while retaining their universal and characteristic properties. This talk will introduce these generalized path signatures on Lie groups and…

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 diagram: three sets of curves in a surface satisfying some properties. In general, it is not evident whether two trisection diagrams represent the same decomposition…

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 known to contain only 2-torsion. In this paper, we prove a local version of this result. If the Khovanov homology of a link is supported…

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 invariants from the package to give bounds for the four-ball genus of links in the three-sphere. We also give a family of links where the…

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 signatures must be used with caution by constructing 1-parameter families of non-congruent curves with degenerate vertices (curve segments of constant curvature) with identical signatures. We address the claim…

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, but also introduce the basic properties of the X-ray transform of higher order tensor fields. I give some unique continuation results for the normal operator…

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 it is conformally equivalent to the 2-sphere.  The method of proof is through harmonic maps, and we show that the conformal equivalence is achieved by…

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 surface of any given topology  be realised as an embedded free boundary minimal surface in the 3-dimensional Euclidean unit ball? We will answer this question…

This is a report on the joint work with Matthew Levy. We use surjection operations on integral cochains tof a topological space X (described by McClure-Smith and Berger-Fresse) to describe a complex computing (co)homology of the cartesian power of X with some diagonals removed. Host: Radmila Sazdanovic ZOOM link:  https://ncsu.zoom.us/j/97278681300

The Ricci curvature Ric(g) is a symmetric 2-tensor on a Riemannian manifold (M,g) that encodes curvature information. It features in several interesting geometric PDEs such as the Ricci flow and the Einstein equation. The nature of Ric(g) as a differential operator -- nonlinear and degenerate elliptic -- make these equations particularly challenging. Host: Peter McGrath Instructions to join: Zoom…

When is a function in the spacetime uniquely determined by its integrals over all light rays? I will introduce the problem, discuss why we might care about it, and how one might go about proving such uniqueness results. Depending on time and audience interest, I can also discuss proofs and tensor tomography.   Organizer: T.…

The question of measuring "handedness" is of some significance in both mathematics and in the real world. Propellors and screws, proteins and DNA, in fact *almost everything* is chiral.  Can we quantify chirality?  Or can we perhaps answer the question:  "Are your shoes more left-or-right handed than a potato?" We can begin with the hydrodynamic…

One approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular, one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings of Legendrian links in the standard contact 3-sphere, and one can use Floer theoretic…