Registration is required for attendance (for catering and other purposes)!!!
Please register before 23:59 on 30/11/2025 by filling out THIS REGISTRATION FORM
Limited support available for travel and accommodation, please email lashi.bandara@deakin.edu.au with subject "AGD Support" to apply
When: Monday 8 December 2025
Where: Geelong Waterfront Campus, 1 Gheringhap St, Geelong VIC 3220
Note: This is not the Burwood, Warun Ponds (Geelong) or Deakin Downtown campus. This event is located in the city of Geelong.
How to get there: PTV (Public Transport Victoria) runs frequent trains from Melbourne to Geelong. Geelong Waterfront is a short walk from the train station
What?
This is a one day conference centred on analysis, geometry and their intersection.
Why?
Global analysis is the marriage of analysis, geometry and operator theory. Differential operators encode geometric and topological problems and the analysis of these operators yield powerful geometric results. It is an area of research recent to Deakin and the goal of the meeting is to bring together interested members of the Australian mathematical community to Deakin.
Who?
The aim of this meeting is to bring together participants with an interest in analysis and geometry from within Australia.
This event is open to everyone and in particular, Honours students, PhD students and Postdocs are welcome and invited to attend the event.
Please remember to register for this event by filling out THIS REGISTRATION FORM before 30/11/2025.
There will be three invited talks given in total. The host (Lashi Bandara) will give a short mathematical introduction to set the context, particularly for mathematics at Deakin. The invited speakers are:
Want to help advertise? Print the high-res poster: Poster-gab.pdf or Poster-agd.png
Event date
8 December 2025
Event location
The talks will be held at the Deakin Geelong Waterfront Campus, Room D2.104. Maps are available at [PDF] and [StudentVIP]
Timetable
| 09:00-09:30 | Opening Nick Birbilis |
| 09:30-10:00 | Coffee |
| 10:00-10:30 | Global Analysis at Deakin Lashi Bandara |
| 10:30-11:30 | Recent developments on stability for the elastic flow of curves Glen Wheeler |
| 11:30-13:00 | Lunch |
| 13:00-14:00 | TBA Galina Levitina |
| 14:00-15:00 | Coffee |
| 15:00-16:00 | The intermediate nonlinear Schrödinger equation Justin Forlano |
| 16:00- | Discussions, Pub, Dinner |
Talks
Global Analysis at Deakin
Lashi Bandara
In this short presentation, I will set the context by outlining some of the Global Analysis research being undertaken at Deakin. It will also set the context for the remaining external presentations.
The intermediate nonlinear Schrödinger equation
Justin Forlano
In this talk, I will discuss recent results regarding the intermediate nonlinear Schrödinger equation (INLS). Analytically speaking, INLS is a one-dimensional completely integrable nonlinear Schrödinger equation with a cubic derivative nonlinearity and is $L^2$-critical. A limiting form of INLS is the continuum Calogero-Moser equation (CCM), which is also completely integrable. Interestingly, CCM keeps the Hardy space $L^2_+$ invariant, and, under this assumption, tools from complete integrability have recently resolved the well-posedness problem for CCM in $L^2_+$. I will discuss progress on the well-posedness for INLS and CCM (not relying on complete integrability), outside of the Hardy space and in low-regularity. Our approach combines a gauge transformation, bilinear Strichartz estimates and a refined decomposition for smooth solutions. This is based on joint work with A. Chapouto (CNRS, UVSQ) and T. Laurens (UW-Madison).
Spectral shift function for Dirac operator in the presence of a constant magnetic field.
Galina Levitina
The spectral shift function (SSF) provides a powerful tool for quantifying the spectral response of quantum systems to perturbations. In the context of Dirac operators in the presence of a constant magnetic field, the unperturbed spectrum is characterized by sequences of threshold energies, commonly known as Landau levels, which correspond to eigenvalues of infinite multiplicity. In this talk, we investigate how these spectral thresholds are affected by the introduction of a short-range electric potential. Focusing on the three-dimensional Dirac operator, we will describe in detail the asymptotic behaviour of the SSF near the Landau levels.
Recent developments on stability for the elastic flow of curves
Glen Wheeler
The free elastic flow is the $L^2(ds)$ steepest descent gradient flow for Euler’s elastic energy defined on curves. Among closed curves, circles and the lemniscate of Bernoulli expand self-similarly under the elastic flow, and there are no stationary solutions. This means that any stabilising effect must be modulo a rescaling that fixes, for instance, length. This additional difficulty has led authors (following Euler) to introduce a constraint or a penalisation in the energy, which changes the dynamics substantially. In particular, there are a plethora of stability and convergence results in a variety of settings, both planar and space, and with a number of boundary conditions. The free elastic flow itself remained untouched, until recently: In 2024, joint with Miura, we were able to establish convergence of the asymptotic profile, through the use of a new quantity depending on the derivative of the curvature. Then, in 2025, joint with Andrews, this has been improved and a sharp convergence rate has been obtained. In this talk, I describe these new results, and also explain what more may be on the horizon for the free elastic flow. If time permits I will also talk about our initial work on the space curve case, where an unexpected phenomenon related to turning number appears.
This event is funded by the School of IT of Deakin University in which Mathematics sits. It is also connected to the DMG, a network of mathematicians working at Deakin.