Talk
In this talk, I will discuss the ideas of ergodic theory of a dynamical system under the nonlinear expectation space/nonadditive probabilities. Ergodicity is defined as any invariant set or its complement having upper probability of 0 (Feng-Zhao (SIMA 2021)). It was proved that the ergodicity is equivalent to irreducibility, the eigenvalue 1 of the Koopman operator being simple and Birkhoff’s law of large numbers with a single value. For a stochastic system under a sublinear Markov setup, the theory was also developed via lifting to canonical dynamical systems. Following this initial work, many progresses have been made recently. One work is Zhao-Zhao (Preprint 2025) on the existence of invariant expectations of G-SDEs. Another work is Feng-Huang-Liu-Zhao (AAP 2026 and Preprint 2024) on the equivalence of the ergodicity of upper probability §with the ergodicity of the invariant skeleton measure. If time permits, I will also talk about mixing and discuss a weaker regime that any invariant set has upper probability 0 or 1 of Cerreia-Vioglio, Maccheroni and Marinacci (2016). We prove that this case does not give irreducibility but is equivalent to a decomposition of finite ergodic components.

Bio
Huaizhong Zhao is currently a Professor in Probability at Durham University. He graduated from Shandong University with BSc in Mathematics, Ph.D. in Dynamical Systems from the Institute of Applied Mathematics, Chinese Academy of Sciences, and Ph.D. in Stochastic Analysis from the Institute of Mathematics, University of Warwick. He held positions at the Institute of Applied Mathematics, Chinese Academy of Sciences, and University of California, Irvine, among others. He was formerly a Professor at Loughborough University and a Visiting Professor at Shanghai Jiaotong University and is a Visiting Professor at Shandong University. He was awarded an EPSRC Established Career Fellowship that enabled him to concentrate on his research in a full-time term for 6 years from January 2019-December 2024. He has published over 70 papers in journals such as Mem. Amer. Math. Soc., Comm. Math. Phys., J. Funct. Anal., J. Differ. Equ., and Ann. Appl. Probab. His main research interests lie in stochastic analysis, particularly the theory of stochastic dynamical systems, and ergodic theory.

Email
huaizhong.zhao@durham.ac.uk

Talk
This talk will be devoted to the role of pi in mathematics, probability and stochastic processes, as the title says. After short introduction about the role pi in mathematics, Dr. Anatoliy will share some results in probability associated with pi. Then he will discuss several results in stochastic processes related to pi and their applications in finance and insurance. Some recent results in those areas will be discussed as well as methodology to unstructured grids, electromagnetic wave scattering off curved conductors with corners, and the Poisson–Nernst–Planck ion channel model.

Bio
Prof. Dr. Anatoliy Swishchuk is a professor in mathematical finance at the Department of Mathematics and Statistics, University of Calgary, Calgary, Canada. He attained his B.Sc. and M.Sc. degrees from Kyiv State University, Kyiv, Ukraine. He is a holder of two doctorate degrees in Mathematics and Physics (Ph. D. and D. Sc.) from the prestigious National Academy of Sciences of Ukraine (NASU), Kiev, Ukraine, and is a recipient of NASU award for young scientist with a gold medal for series of research publications in random evolutions and their applications. Dr. Swishchuk is a chair and organizer of finance and energy finance seminar ’Lunch at the Lab’ at the Department of Mathematics and Statistics. Dr. Swishchuk is a Director of Mathematical and Computational Finance Laboratory at the University of Calgary. He was a steering committee member of the Professional Risk Managers International Association (PRMIA), Canada (2006-2015), and is a steering committee member of Global Association of Risk Professionals (GARP), Canada (since 2015). Dr. Swishchuk is a creator of mathematical finance program at the Department of Mathematics and Statistics. He is also a proponent and creator for a new specialization “Financial and Energy Markets Data Modelling” in the Data Science and Analytics program. His research areas include financial mathematics, random evolutions and their applications, insurance, energy markets modelling, biomathematics, stochastic calculus, and he serves on editorial boards for several research journals. He is the author of more than 200 publications, including 17 books and more than 150 articles in peer-reviewed journals. In 2018 he received a Peak Scholar award.

Email
aswish@ucalgary.ca

Talk
We present new results on reflection-positivity (Osterwalder–Schrader positivity, O.S.-p. and Markov transition systems) as they are used in the study of renormalization questions in physics; and in diverse subjects in mathematics, especially operator theory, and the theory of representations of Lie groups. A classification is given. And concrete cases are presented referring to specific Hilbert spaces that arise before and after the reflection arising in quantum field theory.

Bio
Jorgensen is a Professor of mathematics at the University of Iowa. He is also a Fellow of the American Math Society. Before University of Iowa, he taught at Stanford University, and at the University of Pennsylvania. His research has received funding from the Natl. Sci. Foundation—his research papers are highly cited, and they have appeared in top international scientific journals, both in pure and applied math—operator algebras, harmonic analysis, probability, stochastic analysis, dynamics, machine learning, and mathematical physics (quantum information). His recent research includes wavelet theory, multi-resolution, subdivision algorithms, image-processing, spectral-tile duality, scaling and fractals.

Email
palle-jorgensen@uiowa.edu

Talk
We obtain necessary and sufficient conditions for the uniform stability of a system of Volterra integro-dynamical equations on time scales. Our work will rely on the notion of the resolvent and Lyapunov functionals. The results of this work provide improvements for its counterparts in particular time scales. The theory is illustrated with several examples.

Bio
Dr. Youssef Raffoul holds the rank of Professor and is the Graduate Program Director in the Department of Mathematics at the University of Dayton. He joined the faculty in 1999. Dr. Raffoul obtained a B.S. and M.S. from the University of Dayton in mathematics in 1987 and 1989, respectively. After receiving his Ph.D. in mathematics from Southern Illinois University at Carbondale in 1996, he joined the faculty of the Mathematics Department at Tougaloo College in Mississippi, where he became the department chair for two years until he came to Dayton. Professor Raffoul has published extensively (more than 160 papers) in the area of functional differential and difference equations and has won several awards for his research, most recently, the Career in Science Award from the Lebanese Government.

Email
Yraffoul1@udayton.edu