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…

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…

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.…

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…

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…

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…

Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary…

In order to explain the bi-concave shape of red blood cells, Helfrich proposed to study the minimisation of a bending energy amongst closed surfaces with given fixed area and volume.…

I will give a brief introduction to Heegaard Floer homology and survey what's known about its "extended" structure via Lipshitz-Ozsvath-Thurston's bordered Floer homology and Douglas-Lipshitz-Manolescu's cornered Floer homology. Then I will sketch…

In the 1980s Xavier proved that a complete non-planar minimal surface with bounded curvature of $\mathbb{R}^{3}$ can not lie in half-space. In 1990, Hoffman-Meeks proved that this half-space property holds…