*Jan 27 2021*

13:30 - 15:00

#### Organisers:

**Peter Clarkson**, University of Kent**Ian Strachan,**University of Glasgow

These seminars will be held on Wednesdays at 1.30pm (unless stated otherwise).

Joining details will be sent on the morning of the seminar.

Seminars will continue to run until March 2021. Details will be posted here in due course.

If you are interested in giving a seminar, please contact the organisers directly.

If you have any technical questions regarding the use of Zoom (the platform used for these meetings) please email ICMS.

### Upcoming Seminars

27 January 2021

**Andrea Brini** (Sheffield) - **Geometry and integrability from affine Weyl groups**

- Frobenius manifolds were introduced by Boris Dubrovin in the early nineties as an axiomatic framework to encode the properties of chiral rings of 2D topological field theories, and at the same time provide a natural stepping stone for the classification of KdV-type, local bihamiltonian integrable hierarchies in one space dimension. While traditional constructions of Frobenius manifolds are given in the quantum co-homology of symplectic manifolds and in singularity theory, a somewhat lesser studied source of Frobenius manifolds and its associated integrable hierarchies arise in Lie theory: in a seminal 1995 paper, Dubrovin and Zhang propose a construction of Frobenius manifolds on the orbits of certain extensions of affine Weyl groups, and propose a Landau--Ginzburg formulation in type A. In this talk I will give a unified picture Landau--Ginzburg description for all Dynkin types. I will also explain how this unlocks simultaneous applications to Frobenius manifolds, topology, integrable systems, Gromov--Witten theory, and five-dimensional gauge theory. This is joint work with K. van Gemst (Sheffield).

3 February 2021

**Jonatan Carl Anders Lenells** (KTH Royal Institute of Technology) - **A new approach to integrable evolution equations on the circle**

- I will describe recent work with B. Deconinck and A. S. Fokas, where we propose a new approach for the solution of an integrable evolution equation on the circle, i.e., for the periodic problem. The new approach provides a solution of the problem on the circle which is conceptually analogous to the solution of the problem on the line via the inverse scattering transform.

10 February 2021

**Theo Assiotis** (Edinburgh) – **On the joint moments of characteristic polynomials of random unitary matrices **

- I will talk about the joint moments of characteristic polynomials of random unitary matrices and their derivatives. In joint work with Jon Keating and Jon Warren we establish the asymptotics of these quantities for general real values of the exponents as the size N of the matrix goes to infinity. This proves a conjecture of Hughes from 2001. In subsequent joint work with Benjamin Bedert, Mustafa Alper Gunes and Arun Soor we focus on the leading order coefficient in the asymptotics, we connect this to Painleve equations for general values of the exponents and obtain explicit expressions corresponding to the so-called classical solutions of these equations.

17 February 2021

**Arno Kuijlaars** (KU Leuven) – **TBA**

24 February 2021

**Martin Hallnäs** (Chalmers University of Technology) - **TBA**

### Previous Seminars

20 January 2021

**Karima Khusnutdinova**(Loughborough)

**- Ring waves, singular solutions and hypergeometric functions**

- Recording is available here

13 January 2021**Tamara Grava** (Bristol/SISSA) - **Correlation functions for unitary invariant ensembles and Hurwitz numbers**

9 December 2020

**Davide Masoero** (Lisbon)** - Counting Monster Potentials**

- Recording is available here

2 December 2020

**Cornelia Schiebold** (Mid Sweden University)** - On particle-like solutions of the two-dimensional Toda lattice**

- Slides are available here

25 November 2020

**Laszlo Feher** (University of Szeged and Wigner RCP, Hungary) **- Trigonometric real form of the spin RS model of Krichever and Zabrodin**

- Recording is available here

18 November 2020

**Patrick Dorey** (Durham) **- Breaking integrability in classical field theories**

- Recording is available here

11 November 2020

**Claire Gilson** (Glasgow University) **- Soliton Solutions of noncommutative anti self dual Yang Mills equations**

- Recording is available here

4 November 2020

**Beatrice Pelloni** (Heriot-Watt University) **- The phenomenon of dispersive revivals**

- Recording is available here

28 October 2020

**Walter Van Assche **(KU Leuven) **- Orthogonal Polynomials and Random Matrices**

- Recording is available here

21 October 2020

**Raffaele Vitolo **(University of Salento) **- Homogeneous Hamiltonian operators, projective geometry and integrable systems**

- Recording is available here

14 October 2020

**Vincent Caudrelier **(Leeds)** - Covariant Poisson bracket and r-matrix structure for an integrable hierarchy: role of Lagrangian and Hamiltonian multiforms**

- Recording is available here

30 September 2020

**Misha Feigin** (Glasgow University) **- The Saito determinant for Coxeter discriminant strata**

- Recording is available here

23 September 2020

**Matteo Casati** (Kent/Ningbo) **- Nonabelian Hamiltonian (integrable) systems: double, lambda and Schouten brackets**

- Recording is available here

15 July 2020

**Thomas Bothner** (KCL)** - A threefold way to integrable probabilistic models**

- Recording is available here

1 July 2020

**Daniele Valeri **(University of Glasgow)** - Deformations of W-algebras and differential-difference equations**

- Recording is available here

24 June 2020

**Marco Bertola **(SISSA, Italy) **- Tyurin data, non-Abelian Cauchy kernels and the Goldman bracket**

- Recording is available here

17 June 2020

**Marta Mazzocco **(University of Birmingham) **- Quantum uniformisation and CY algebras**

- Recording is available here

10 June 2020

**Alfredo Deano** (University of Kent) **- Painlevé transcendents in non-Hermitian random matrix ensembles**

- Recording is available here

3 June 2020

**A.P. Veselov** (Loughborough)** - Geometrization, integrability and knots**

- Recording is available here

**Rod Halburd**(University College London)

**- Elementary calculations of complexity growth for solutions of discrete equations**

20 May 2020

**Antonio Moro** (Northumbria University) -** Integrability and complexity in statistical mechanics: thermodynamic limit vs viscous/dispersive regularisation**

- Recording is available here

13 May 2020

**Paolo Rossi** (University of Padova) -** Givental theory for F-manifolds and non-Hamiltonian integrable PDEs **

6 May 2020

**Clare Dunning **(University of Kent)** - Wronskian Hermite polynomials **

** **

29 April 2020

**Frank Nijhoff **(University of Leeds)

22 April 2020

**Nikita Nikolaev **(University of Geneva) **- Abelianisation of Meromorphic SL(2)-Connections and the Hitchin Integrable Systems**

- Recording is available here

1 April 2020

**Peter Clarkson **(University of Kent) **- Generalised Freud Weights **

25 March 2020

**Ian Strachan** (University of Glasgow) **- Miura Transformations from Novikov Algebras **

**This seminar series is supported as part of the ICMS Online Mathematical Sciences Seminars.**