###### Organisers | Talks |Schedule | Discussions | Registration | Zoom

COVID-19 advisory: we will be holding this year’s workshop via Zoom.

We are hosting our eighth annual Workshop on Integrable Systems on

**3 – 4 December 2020**

at the School of Mathematics and Statistics, the University of Sydney.

#### Organisers

This workshop is being organised by Sean Gasiorek, Nalini Joshi, and Milena Radnovic.

#### Talks

In this talk, we consider the Fredholm determinant $\det\left(I-\gamma K^{\mathrm{Pe}}_{s,\rho}\right)$, where $0 \leq \gamma \leq 1$ and $K^{\mathrm{Pe}}_{s,\rho}$ stands for the trace class operator acting on $L^2\left(-s, s\right)$ with the classical Pearcey kernel. Based on a steepest descent analysis for a $3\times 3$ matrix-valued Riemann-Hilbert problem, we obtain asymptotics of the Fredholm determinant as $s\to +\infty$, which is also interpreted as large gap asymptotics in the context of random matrix theory.

This is a joint work with Shuai-Xia Xu and Lun Zhang.

[1] “Two-component Yang-Baxter maps associated to integrable quad equations”, https://arxiv.org/abs/1910.03562

[2] “Interaction-round-a-face and consistency-around-a-face-centered-cube”, https://arxiv.org/abs/2003.08883

First Reinout will give a brief introduction to Darboux Polynomials, and then discuss their application to some low dimensional integrable systems of Lotka-Volterra equations.

Then Peter will take over and extend the discussion to Lotka-Volterra equations in dimensions that can be arbitrarily large. The emphasis will be on establishing the superintegrability/Liouville integrability of these equations.

This is joint work with Asaki Saito (Future University, Hakodate) and Franco Vivaldi (Queen Mary). A preprint with the same title will be posted to arXiv soon.

self-dual Einstein spaces with the underlying governing equation being revealed as the general heavenly equation. The formalism developed here may be used to link algorithmically a variety of known heavenly equations. We isolate a large class of self-dual Einstein spaces governed by a compatible system of dispersionless Hirota equations which is genuinely four-dimensional in that the metrics do not admit any conformal Killing vectors. In addition, Legendre transformations and connections with travelling wave reductions of the recently introduced TED equation which constitutes a 4+4-dimensional integrable generalisation of the general heavenly equation are discussed.

#### Schedule (AEDT = GMT + 11)

**Thursday, 3 December**

**10:30 – 11:00** Roberts

**11:00 – 11:30** Carberrry

**12:00 – 13:00** Post

Lunch

**14:00 – 15:00** Discussion #1

**15:30 – 16:30** Kels

**16:30 – 17:00** Dullin

**Friday, 4 December**

**08:00 – 09:00** Dunning

**09:00 – 10:00 ** Quispel & Van Der Kamp

**10:30 – 11:30** Discussion #2

**11:30 – 12:00** de Gier

Lunch

**13:00 – 14:00** Dai

**14:30 – 15:30** Iwaki

**15:30 – 16:00** Schief

#### Discussions

If you are interested in participating in either of the discussion sessions, please email Sean Gasiorek directly to RSVP.

#### Registration

Register by emailing the organisers at: integrable@maths.usyd.edu.au

Registrations close on 1 November 2020.

#### Zoom Information

Please email the organisers directly for the Zoom link.