seminar

This page lists recent talks in the Geometric Analysis Seminar at the University of Wollongong.

The aim is to keep talks understandable and useful to students and staff from a range of backgrounds.

The seminar is usually held in-person. If you would like to attend online, please email me and I can see whether a Zoom broadcast is possible.

Would you like to be added to the mailing list for the seminar? Are you interested in giving a talk yourself? Let me know!

Recent seminars

9 April 2026 — Poisson equation for the G_2-Laplace operator

Speaker: Stepan Hudecek (U Queensland) Time and location: 9:00 - 10:00 9th April 2026, 39C.174

Abstract. Riemannian manifolds whose holonomy group lies inside the exceptional Lie group G_2 are called G_2-manifolds. These manifolds have several interesting properties (they are Ricci-flat) and are of interest in geometric analysis as well as in mathematical physics and other fields. In this seminar, we will give an introduction to the theory of G_2-manifolds and discuss an associated non-linear Laplacian-type operator whose kernel essentially determines whether a compact manifold is G_2. We will present uniqueness and existence results for the Poisson’s equation of this operator on homogeneous and cohomogeneity-one manifolds.

24 March 2026 — Existence of heterogeneous elastic curves with non-classical shapes

Speaker: Prof Shinya Okabe (Tohoku U, Japan) Time and location: 13:30-14:30 24th March 2026, 6-210

Abstract. In this talk, we are interested in planar closed elastic curves with density-modulated stiffness. These heterogeneous elastic curves are considered to be critical points of a geometric functional, which is defined as the sum of a generalised bending energy with density-modulated stiffness and a Dirichlet energy for the density, under the length constraint. As any elastica with constant density is a trivial critical point in the model of density-dependent elastic curves, the functional can be considered a generalisation of the classical bending energy. The purpose of this talk is to prove that there exist infinitely many heterogeneous closed elastic curves with non-classical shapes. This talk is based on joint work with my PhD student, Masahiro Sakoda.

17 March 2026 — The Burnside Problem

Speaker: Anna Cascioli (Uni Munster, Germany)
Time and location: 11:30–12:30, 39C.174

Abstract. In 1902, William Burnside asked whether a finitely generated group in which every element has finite order must be finite. This question, now known as the Burnside Problem, is one of the oldest and most studied in group theory. Its investigation led to the study of free Burnside groups and surprising examples of infinite groups with strong algebraic constraints. In this talk, we present the main questions, the breakthrough result of Novikov and Adian from 1968, and outline recent developments and new approaches to groups of bounded exponent.

24 February 2026 — Jellyfish exist

Speaker: Glen Wheeler (UOW)
Time and location: 11:30–12:30, 39C.174

Abstract. The search for homothetic solutions is a classical pursuit in geometric flows. It has long been known that the lemniscate of Bernoulli is homothetic under the curve diffusion and elastic flows, however, further examples have proven elusive; indeed, it’s a common belief that other examples do not exist, and rigidity has been sought. In this talk, I describe recent exciting work that shows there is to the contrary a wealth of examples. We exhibit in particular the jellyfish and epicyclic families of self-similar solutions, covering the elastic flow, curve diffusion flow, and ideal flow. These provide infinitely many geometrically distinct examples, and we believe only scratch the surface of the rich dynamical picture for these flows. To describe the full landscape of asymptotic shapes appears to be an extremely ambitious task. This is joint work with Ben Andrews (ANU).

20 January 2026 — Curve diffusion flows in cones

Speaker: James McCoy (Newcastle U/RMIT)
Time and location: 11:30–12:30, 39C.174

Abstract. We study families of smooth, embedded, regular planar curves with generalised Neumann boundary conditions inside cones, satisfying three variants of the fourth-order nonlinear curve diffusion flow: curve diffusion flow with length penalisation and two forms of constrained curve diffusion flow with fixed length. Assuming neither end of the evolving curve reaches the cone tip, existence of smooth solutions for all time given quite general initial data is well known for the constrained flows, but classification of limiting shapes is generally not known. We prove for the constrained flows smooth exponential convergence of solutions in the $C^\infty$-topology to a circular arc centred at the cone tip with the same length as the initial curve. In the length penalised case, we show smooth exponential convergence under suitable rescaling to a circular arc centred at the cone tip. This is joint work with Mashniah Gazwani.

24 November 2025 — Curve shortening by Sobolev gradient flow

Speaker: Phil Schrader (Murdoch U)
Time and location: 11:30–12:30, 39C.174

Abstract. The classical curve shortening flow, or one-dimensional mean curvature flow, is the gradient descent of the length functional on curves when the gradient is taken with respect to a parametrisation invariant $L^2$ metric. In this talk I will discuss the gradient flows of length with respect to a family of parametrisation invariant $H^1$ Sobolev metrics with different degrees of homogeneity. The family of flows all turn out to be equivalent under time reparametrisations. Solutions preserve embeddedness, converge to points and appear to become round while converging, like the classical flow. But unlike the classical flow, we do not encounter singularities.