Mathematics and Statistics (R0)

This volume collects papers based on lectures given at the XL Workshop on Geometric Methods in Physics, held in Białowieża, Poland in July 2023. These chapters provide readers an overview of cutting-edge research in infinite-dimensional groups, integrable systems, quantum groups, Lie algebras and their generalizations and a wide variety of other areas. Specific topics include:

• Yang-Baxter equation
• The restricted Siegel disc and restricted Grassmannian
• Geometric and deformation  quantization
• Degenerate integrability
• Lie algebroids and groupoids
• Skew braces

Geometric Methods in Physics XL will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.

This edited volume introduces undergraduate students to several diverse and emerging research topics in three major areas of risk management: actuarial science, mathematical finance, and sports analytics. Each chapter is self-contained and provides students with the required background knowledge, context, and relevant references to motivate students and to enable them to successfully undertake research in these areas.  A variety of accessible research projects are included that can be conducted independently or in collaboration with a mentor. Throughout, emphasis is placed on the importance and advantages of interdisciplinary thinking in developing innovative approaches to problem-solving. This volume will also serve as a valuable resource to faculty mentors, graduate students, and others who are interested in supervising undergraduate research.

This is an open access book. Probabilistic tsunami hazard and risk assessment (abbreviated as PTHA and PTRA, respectively) has evolved quickly over the past 10 to 15 years and now forms the basis of many risk mitigation efforts. Methods are largely based on those used for probabilistic hazard and risk assessment for earthquakes. However, while seismic risk can be represented by a single workflow, tsunami risk is characterized by a number of different and cascading workflows. Funded in parts by the COST Action CA18109 AGITHAR (2019-2023), a group of more than 120 experts gathered to advance the scientific basis for PTHA and PTRA. Amongst them were over 50 volunteering to contribute to this so-called “cookbook” for PTHA and PTRA.

The aim of our cookbook is to give an overview of existing methods for PTHA and PTRA, to unify the description of named workflows, and to make best practices examples available to a wider community. We use the analogy of a cookbook, because we strive to describe the ingredients, i.e., the basic building blocks of PTHA and PTRA, and give examples of good recipes, i.e., well-designed workflows for concrete application fields. Furthermore, a cookbook gives inspiration but does not necessarily standardize methods. So, while this effort aims at some standardization of methodology, it gives enough freedom to build on this knowledge to further develop the field. The book is intended for scientists, but also practitioners and decision-makers in tsunami hazard and risk mitigation.

This contributed volume provides an integrated perspective on modern mathematical and computational techniques for addressing complex problems in networks, control systems, learning, and game theory. It encompasses state-of-the-art research from a diverse range of disciplines, including dynamical systems, stochastic analysis, optimization, game theory, machine learning, and transportation theory. Particular emphasis is placed on connecting rigorous theoretical developments with real-world applications.

This volume is organized into twelve chapters. The first part (Chapters 1-6) addresses the optimal transportation problem in traffic networks. The second part (Chapters 7-11) investigates Markov chains with memory by examining the geometric, algebraic, dynamical, and ergodic properties of quadratic (polynomial) stochastic operators associated with cubic stochastic hypermatrices. Finally, Chapter 12 illustrates how methods from stochastic analysis and dynamical systems can be applied to lattice models of statistical mechanics defined on a Cayley tree.

Intended to serve as a comprehensive reference for academics and researchers, this volume may also benefit practitioners and anyone interested in exploring the interplay among these fields.

Within the past few decades, there has been an accelerating development of methods for studying nonlinear equations. Nonlinear analysis offers exciting prospects for certain specific areas of nonlinear problems with continuum mechanics. The objective of this book is to carry out such studies for problems in nonlinear elasticity. This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is directed toward the scientist, engineer, and mathematician who wish to see careful treatments of precisely formulated problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.