*Jun 28 2021*

15:00 - 16:00

#### Organisers:

**Ana F. Loureiro**(University of Kent)**Thomas Bothner**(University of Bristol)**Adri Olde Daalhuis**(University of Edinburgh)**Walter Van Assche**(KU Leuven, Belgium)**Jani Virtanen**(University of Reading)

The seminars occur every two weeks, on a Monday, 15:00-16:00 BST, and will restart on Monday 17 May.

Each seminar we will present a seminar on the topics of orthogonal polynomials and special functions, operator theory and their remarkable applications to other fields of mathematics including analytic number theory, random matrix theory, numerical and computational methods and mathematical physics. The focus of discussion will be on the fruitful interactions between numerical analysis, approximation theory, operator theory, spectral methods, combinatorics and the modern theory of orthogonal polynomials and special functions.

The series is organised by the OPSFOTA research network group funded by LMS. Due to the funding limitations it was restricted to researchers that are based in geographically close institutions: in the UK, University of Kent, University of Reading, King’s College London, Imperial College, University of Sussex, University College London and elsewhere in Europe KU Leuven (Belgium), Radboud Universiteit (the Netherlands) and Université Lille (France). The current situation has given the us the opportunity to open the seminar series to anyone who would like to participate.

Registration will close at 12.00 on the day of the seminar. The meetings will be held using Zoom and joining details will be sent after 12.00 on the day of the seminar.

Future seminars

**Ester Pérez Sinusía** (Universidad de Zaragoza, Spain) - *Uniform convergent expansions of special functions in terms of elementary functions*

- Expansions of special functions in series with respect to different systems of functions are interesting representations from an analytical and numerical point of view. Usually, existing expansions for these functions are not simultaneously valid for small and large values of the variable. In this work, we face the problem of designing a general theory of uniform convergent expansions of special functions in terms of elementary functions valid in a large region of the complex plane that include small and large values of the variable. Error bounds and numerical experiments showing the accuracy of the approximations are given.

12 July**Mirta Castro** (Universidad de Sevilla, Spain) - tba

26 July - tba

Past seminars

14 June**Ahmad Barhoumi** (University of Michigan, USA) - *Asymptotics of Kissing Polynomials and their Recurrence Relations*

24 May **Alexander Stokes** (University College London – University of Warsaw) - *Identifying Painlevé equations related to orthogonal polynomials: the geometric approach*

17 May 2021

**Dan Dai**(City University of Hong Kong) -

*The distribution for the maximal height of non-intersecting Bessel paths*

19 April 2021**Alan Sokal**, University College London & New York University

*-**Multiple orthogonal polynomials and branched continued fractions: An unexpected connection*

- Abstract can be viewed here

29 March 2021**Kerstin Jordaan**, University of South Africa

**-**Generalised higher order Freud polynomials

- Abstract can be viewed here

- A recording of this talk is available here

15 March 2021**María Ángeles Garcia-Ferrero**, Universität Heidelberg

**- Exceptional Legendre polynomials and confluent Darboux transformations**- Abstract can be viewed here

- A recording of this talk is available here

1 March 2021**Anna Maltsev***, Queen Mary University - Covariance formulas for fluctuations of linear spectral statistics for Wigner matrices with few moments*

- Abstract can be viewed here

15 February 2021**Jose Luis Lopez**, Universidad Publica de Navarra

**-**Asymptotics of the canonical catastrophe integrals- Abstract can be viewed here

26 November 2020

**Benjamin Eichinger**, Johannes Kepler University** - **Stahl-Totik regularity for orthogonal rational functions with real poles and GMP matrices

29 October 2020

**Maxim Yattselev**, Indiana University-Purdue University** - **On Hermite–Padé approximants for a pair of Cauchy transforms with overlapping symmetric supports

- A recording of this talk is available here.

1 October 2020

**Diane Holcomb**, KTH**- **The stochastic Airy operator and an interesting eigenvalue process

- Abstract can be viewed here

17 September 2020

** Margit Rösler**, Paderborn University** - **Intertwining operators between Dunkl operators of type Bn

- Lecture slides can be found here

03 September 2020

**Giorgio Mantica**, Università Degli Studi Dell’insubria**- **Computing the isospectral torus of finite sets of intervals via mappings of polynomial

- A recording of this talk can be found here

27 August 2020

**W. Riley Casper**, California State University** - **Fourier Algebras for Orthogonal Matrix Polynomials

- A recording of this talk can be found here

20 August 2020

**Robert Buckingham**, University of Cincinnati** **and **Peter Miller**, University of Michigan** - **Large-degree asymptotics of rational Painleve-IV solutions by the isomonodromy method

- Part I - Robert Buckingham: recording here
- Part II - Peter Miller: recording here

13 August 2020

**Maurice Duits**, KTH** - **Limit shape fluctuations for q-distributions for boxed plane partitions via q-Hahn polynomials

- A recording of this talk can be found here

06 August 2020

**Robert Milson**, Dalhousie University** - **The adelic grassmannian and exceptional Hermite polynomials

- A recording of this talk can be found here

30 July 2020

**Manuela Girotti**, University of Montreal **- **Fredholm Determinant Solutions of the Painlevé II Hierarchy and Gap Probabilities of Determinantal Point Processes

- A recording of this talk can be found here

23 July 2020

**Roozbeh Gharakhloo**, Colorado State **- **A Riemann-Hilbert approach to asymptotic analysis of Toeplitz+Hankel determinants

- A recording of this talk can be found here

16 July 2020

**Sergey Denisov**, University of Wisconsin** - **Continuity of weighted operators, Muckenhoupt weights, and Steklov problem for orthogonal polynomials

- A recording of this talk can be found here

9 July 2020

**Fredrik Johansson**, INRIA Bordeaux** - **Special functions in Fungrim

- A recording of this talk can be found here

2 July 2020

**Emma Bailey**, University of Bristol** - **Moments of moments

- A recording of this talk can be found here

25 June 2020

**Grzegorz Swiderski**, KU Leuven** - **About essential spectra of unbounded Jacobi matrices

18 June 2020

**Håkan Hedenmalm**, KTH Stockholm** - **Gaussian analytic functions and operator symbols of Dirichlet type

- A recording of this talk can be found here

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