2025 MATRIX Annals Part II

The 2025 MATRIX Annals Part II, the tenth book in the MATRIX Book Series, documents scientific activities at MATRIX in the second half of 2025. Pre-publication versions of the articles in the book are posted below.

We expect that the 2025 MATRIX Annals Part II will be indexed by zbmath and mathscinet.

Preface

MATRIX Research Programs

Bayesian Learning of Very High-Dimensional Physical Process Models
Slow Viscous Flows with Interfaces (Guest editor: Michael Dallaston)
Integrable Geometry: Smooth and Discrete (Guest editor: Albert Chern)
Log-gases in Caeli Australi: Recent Developments in and around Random Matrix Theory (Guest editors: Lucas Hackl and Anas Rahman)
Mathematics of Risk – 2025 (Guest editor: Stuart Hawkins)
Theoretical and Computational Foundations of Sequential Learning (Guest editors: Sahani Pathiraja and Tiangang Cui)
Enumerative Geometry, Integrability, and Topological Recursion (Guest editor: Norman Do)

MATRIX-MFO Tandem Workshop

Machine Learning and AI for Mathematics

MATRIX-AMSI PhD Student Symposium

Integrable Systems with respect to Geometry and Quantum Mechanics
Dynamical Systems Student Symposium

Refereed Articles

MATRIX Program: Slow Viscous Flows with Interfaces

Caitriona K. Lightbody, Tharindi T. Amarathunge Achchige, Kara L. Maki
Mathematical Model of the Effectiveness of Contact Lens Wetting Agents

Raja Venkata Satya Saikumar Bheemarasetty
Two dimensional model of Marangoni convection of a droplet on a heated superhydrophobic surface

Rodney Dharma, Michael C. Dallaston, Marco A. Fontelos, Bronwyn H.Bradshaw-Hajek, Scott W. McCue
Self-similar rupture of a thin viscous filament in a Hele-Shaw cell

Fiaz Ur Rehman, Stephen K. Wilson
The effect of a pressure-dependent viscosity on the viscous scraper problem

Matthew Walker, Josephine Hoesel
Slumping of a thin viscous shell

Xinyi Yang, John R. Lister, Anette Hosoi
Wicking yarn problem

R.C. Ward, A.E. Hosoi
Hairy Hele-Shaw Cells

MATRIX Program: Integrable Geometry: Smooth and Discrete

Emma Carberry
Universal Deformations of Spectral Curve Data

Albert Chern, John Rice
Geometric invariants of curves and integrable systems

Joseph Cho, Katrin Leschke, Yuta Ogata
Monodromy of discrete curves under Darboux transformations

Ross Ogilvie
Weakly conformal maps into R3 and R4

Joseph Cho, Mason Pember, Wayne Rossman
Special cases of the discretization principle via permutability

MATRIX Program: Log-gases in Caeli Australi: Recent Developments
in and around Random Matrix Theory

Sung-Soo Byun, Peter J. Forrester
Electrostatic Computations for Statistical Mechanics and Random Matrix Applications

Peter J. Forrester and Fei Wei
A Note on “Higher Order Linear Differential Equations for Unitary Matrix Integrals: Applications and Generalisations

Anas A. Rahman, Daniel Munoz George, and James A. Mingo
Corrections to Classical Matrix Ensemble Moments, NonCrossing Annular Pairings, and Ribbon Graphs

Peter J. Forrester, Anas A. Rahman, and Bo-Jian Shen
A Note on Optimal Soft Edge Expansions for Gaussian β Ensembles

Arno Kuijlaars, Erwin Miña-Díaz, Aron Wennman, Eui Yoo
Bergman Polynomials on a Half Lemniscate

MATRIX Program: Mathematics of Risk — 2025

Joshua J. Y. Chan, Nicolas Privault
Probabilistic representation and classical solutions of wave equations with complex polynomial nonlinearities

Huan Chen, Jie Yen Fan, Kais Hamza, Fima C. Klebaner
Mimicking Brownian martingales

Dan Crisan, Arturo Kohatsu-Higa
On the effect of boundary perturbations on the derivative of a killed diffusion semigroup

MATRIX Program: Theoretical and Computational Foundations of Sequential
Learning

Francesca Romana Crucinio, Sahani Pathiraja
Numerical Approximation of Splitting Schemes for the Wasserstein–Fisher–Rao Gradient Flow

Matthew T. Moores, Kirsten Gracie, Jake Carson, Karen Faulds, Duncan Graham, and Mark Girolami
Bayesian Modelling and Quantification of Raman Spectroscopy

Emma Hannula, Jana de Wiljes, Matthew T. Moores, Heikki Haario, Lassi Roininen
Identifiability and amortized inference limitations in Kuramoto models

MATRIX Program: Enumerative Geometry, Integrability, and Topological Recursion

Reinier Kramer
Explicit formulas and topological recursion for leaky Hurwitz numbers

Other Contributed Articles

MATRIX Program: Integrable Geometry: Smooth and Discrete

Masaya Hara, Denis Polly
On Weierstrass-type representations for timelike surfaces

MATRIX Program: Log-gases in Caeli Australi: Recent Developments
in and around Random Matrix Theory

Fu-Hsuan Ho and Justin Ko
Conjecture on an Enriched Continuous Random Energy Model

Mario Kieburg, Noriyoshi Sakuma, and Jiyuan Zhang
Connections Between Free Probability, Pólya Ensembles and Finite Free Convolutions

Mario Kieburg, Thomas Wolfs, and Jiyuan Zhang
The Charlier Ensemble as a Discrete Pólya Ensemble

MATRIX Program: Mathematics of Risk — 2025

Alex Novikov
Yet Another Look at Martingale Identities and Inequalities, and Their Applications to First Passage Times

MATRIX Program: Theoretical and Computational Foundations of Sequential
Learning

Utku Erdogan, Gabriel J. Lord, Joaquin Miguez
On a class of constrained particle filters for continuous-discrete state space models