Celebrating Women in Analysis and Partial Differential Equations
Miniworkshop
The aim of this one-day mini workshop is to celebrate the achievements of women in Analysis and Partial Differential Equations. The event brings together specialists, early career researchers, and PhD students working in related fields, both internationally and locally from the University of Sydney. We hope this workshop will provide a welcoming and inclusive platform to present research, foster collaboration, and spark new research initiatives among participants.
The mini workshop is supported by the School of Mathematics and Statistics and the Sydney Mathematical Research Institute (SMRI). All staff, visitors and students are warmly invited to attend. To register, please send an email to Jiakun Liu (jiakun.liu@sydney.edu.au) and indicate any dietary requirements for catering purposesProgram for 1 September 2025 at the University of Sydney
Venue:
University of Sydney (Camperdown Campus): See the information on how to get there.
Draft Program
The talks will be in Room 301, Level 4, Macleay Building (A12).
| Morning Session | ||
| Time | Speaker | Title of Talk | 09:00–09:10 | Opening (Dingxuan Zhou) |
|---|---|---|
| 09:10–09:55 | Nalini Joshi | Integrable dynamical systems on bi-elliptic surfaces |
| 09:55–10:25 | Morning tea | |
| 10:25–11:10 | Barbara Brandolini | Symmetrisation for singular problems |
| 11:15–12:00 | Elisa Tornatore | Degenerate Dirichlet Problems with unbounded coefficient in the principal part and convection term |
| 12:30–13:30 | Lunch break at Forum | |
| Afternoon Session | ||
| Time | Speaker | Title of Talk |
| 13:30–14:15 | Maria Fărcăşeanu | Nonlinear elliptic equations with singular potentials and gradient-dependent nonlinearities |
| 14:20–15:05 | Polina Vytnova | TBA |
| 15:05–15:30 | Afternoon Tea | |
| 15:30–16:15 | Caroline Wormell | Mixing of Cantor measures in chaotic dynamics |
| 16:15–17:00 | Free discussion and closing | |
Abstracts of Talks
Symmetrisation for singular problems
Barbara Brandolini (Università degli Studi di Palermo)
Abstract
We discuss Talenti-type symmetrisation results in the form of mass concentration (i.e. integral comparison) for both local and nonlocal singular problems, whose prototype is
The different approaches will be compared, highlighting the differences in the selection of the basic ingredients and in the outcomes. Then, the results will be extended from the elliptic setting to the parabolic one.
The results are contained in some papers written in collaboration with F. Chiacchio, I. de Bonis, V. Ferone, C. Trombetti and B. Volzone.
Nonlinear elliptic equations with singular potentials and gradient-dependent nonlinearities
Maria Fărcăà§eanu (University of Sydney)
Abstract
In this talk, we present recent classification results on the behaviour near the origin of all positive solutions to a broad class of nonlinear elliptic equations involving singular potentials and gradient-dependent nonlinearities. We also discuss sharp existence results for solutions to these problems.
This is joint work with Florica Cîrstea.
Integrable dynamical systems on bi-elliptic surfaces
Nalini Joshi (University of Sydney)
Abstract
The family of mappings of the plane possessing a biquadratic invariant, which is known as the QRT maps, is composed of two involutions, one preserving a vertical shift and the other preserving a horizontal shift in the plane. In this talk, we outline an extension when each shift is replaced by the group homorphism on each of two interlacing elliptic pencils.
Degenerate Dirichlet Problems with unbounded coefficient in the principal part and convection term
Elisa Tornatore (Università degli Studi di Palermo)
Abstract
A sub-supersolution method is used in the case of a quasilinear Dirichlet problem which exhibits convection, with an intrinsic operator, and whose principal part contains an unbounded coefficient \(G(u)\) depending on the solution \(u\). In particular a truncation technique leading to a priori estimates is developed, not only for the reaction term in the equation, but also for the unbounded coefficient. Then different truncation method is used to study a Dirichlet problem whose equation is driven by a degenerate \(p\)-Laplacian with a weight depending on \(x\) and on the solution and whose reaction term is a convection term. The existence of solutions is obtained together with uniform boundedness of the solution set.
This is joint work with D. Motreanu and R. Livrea.
TBA
Polina Vytnova (University of Surrey)
Abstract
TBA
Mixing of Cantor measures in chaotic dynamics
Caroline Wormell (University of Sydney)
Abstract
For many chaotic systems we know the following: sufficiently smooth measures, when advected by the dynamics, converge weakly to certain 'physical' invariant measures at a rate that is usually exponential. This is down to the quasi-compact structure of the advection operators in appropriate function spaces, and lets us show that chaotic systems exhibit many of the same statistical behaviours as, for example, SDEs.
However, outside some special types of chaos, this quasi-compactness property is not enough to get the same nice statistical stability properties SDEs have with respect to dynamical perturbations (the problem of 'linear response'). It turns out that convergence under advection of certain insufficiently smooth measures: in this talk I will give some numerical and theoretical evidence as to why we should believe this is true, and discuss why it is hard to prove.
Organisers
- Florica Cîrstea
- Daniel Daners (Website)
- Jiakun Liu