Groups and group theory

Coclass is a powerful invariant that reveals patterns in the intricate landscape of finite p-groups.

This monograph provides the first comprehensive introduction to set-theoretic solutions of the Yang-Baxter equation and their deep connections with skew braces.

This monograph provides the first comprehensive introduction to set-theoretic solutions of the Yang-Baxter equation and their deep connections with skew braces.

The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type.

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Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration.

This volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the representations from the discrete and from the (full, non-unitary) series, or that between modular forms of the holomorphic and substitute for the usual Moyal-type brackets.

Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups.

Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field.

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks.

Hofstadter's Law: It always takes longer than you think it will take, even if you take into account Hofstadter's Law.

A self-contained introduction is given to J.

This book provides a definition of Green functors for a finite group G, and of modules over it, in terms of the category of finite G-sets.

This book provides a classification of all three-dimensional complex manifolds for which there exists a transitive action (by biholomorphic transformations) of a real Lie group.

The book describes some interactions of topology with other areas of mathematics and it requires only basic background.

Starting from basic knowledge of nilpotent (Lie) groups, an algebraic theory of almost-Bieberbach groups, the fundamental groups of infra-nilmanifolds, is developed.

The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions.

This research monograph introduces some new aspects to the theory of harmonic functions and related topics.

The theme of the monograph is an interplay between dynamical systems and group theory.

The book contains the first systematic exposition of the current known theory of K-loops, as well as some new material.

The aim of this work is the definition of the polyhedral compactification of the Bruhat-Tits building of a reductive group over a local field.

Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology.

The topic of this book, graded algebra, has developed in the past decade to a vast subject with new applications in noncommutative geometry and physics.

At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras.

This monograph develops the Grobner basis methods needed to perform efficient state-of- the-art calculations in the cohomology of finite groups.

The aim of this 1983 Yale graduate course was to make some recent results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians.

The Fourier transforms of invariant functions on finite reductive Lie algebras are due to T.

In my long professional life as a mathematician I have had to deliver various survey lectures.

Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems.

The theory of generalized functions is a general method that makes it possible to consider and compute divergent integrals, sum divergent series, differentiate discontinuous functions, perform the operation of integration to any complex power and carry out other such operations that are impossible in classical analysis.

by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule.

Compactness is related to a number of fundamental concepts of mathemat- ics.

This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity.

This book is devoted to an exposition of the theory of finite-dimensional Lie groups and Lie algebras, which is a beautiful and central topic in modern mathematics.

This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002.

The theory of elliptic functions and modular forms is rich and storied, though it has a reputation for difficulty.

This volume collects papers based on lectures given at the XLI Workshop on Geometric Methods in Physics, held in Bialystok, Poland in July 2024 as well as extended abstracts of minicourses presented during the XIII School on Geometry and Physics.