This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.

This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.

This volume contains nine survey articles based on the invited lectures given at the 24th British Combinatorial Conference, held at Royal Holloway, University of London in July 2013. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, matroid theory and automatic counting, as well as connections to coding theory and Bent functions. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of cutting-edge developments. The book provides a valuable survey of the present state of knowledge in combinatorics, and will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.

In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.

This book constitutes the proceedings of the 24th International Conference on Computing and Combinatorics, COCOON 2018, held in Qing Dao, China, in July 2018. The 62 papers presented in this volume were carefully reviewed and selected from 120 submissions. They deal with the areas of algorithms, theory of computation, computational complexity, and combinatorics related to computing.

Zusammenfassung: This book features selected papers from the 10th International Conference on Mathematics and Computing (ICMC 2024), held at Kalasalingam Academy of Research and Education (KARE), Krishnankoil, India during 2 - 7 January 2024. It covers recent advances in the field of mathematics, statistics, and scientific computing. The book presents innovative work by leading academics, researchers, and experts from industry in mathematics, statistics, cryptography, network security, cyber security, machine learning, data analytics and blockchain technology in computer science and information technology. The book is divided into two volumes

This two volume set LNCS 14422-14423 constitutes the refereed proceedings of the 29th International Conference, COCOON 2023, held in Hawaii, HI, USA, during December 2023. The 60 full papers were carefully reviewed and selected from 146 submissions. They are organized in the following topical sections: Part I : Combinatorics and Algorithms; Algorithmic Solution in Applications; and Algorithm in Networks. Part II: Complexity and Approximation; Graph Algorithms; and Applied Algorithms.

Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.