A day of ... Analysis & Geometry

Registration

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

Where and when?

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

Poster

What, Why, Who...

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:

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Event info!

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
Executive Dean of the Faculty of Science, Engineering, and Built Environment

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.

Funding and acknowledgements

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.