Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions.

In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level. Product details Format Paperback pages Dimensions x x 9.

Illustrations note VIII, p. Other books in this series. Gradient Flows Luigi Ambrosio. Add to basket. Singularit ten Daniel Battig.

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Cardinal Functions on Boolean Algebras J. Compact Riemann Surfaces R. Modules and Group Algebras Jon F.

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Topics in Disordered Systems Charles M. Splinefunktionen Carl de Boor. Introduction to Combinatorial Torsions Vladimir Turaev. Table of contents I History. The beginnings.

Finitely presented groups. More history. Higman's marvellous theorem. Varieties of groups. Small Cancellation Theory. The Grigorchuk-Gupta-Sidki groups. An application to associative algebras. Frobenius' representation. Semidirect products. Subgroups of free groups are free. The calculus of presentations.

## abstract algebra - Application of group theory to combinatorics - Mathematics Stack Exchange

The calculus of presentations continued. The Reidemeister-Schreier method. Generalized free products. Recursively presented groups. Some word problems. Groups with free subgroups. Some basic algebraic geometry. More basic algebraic geometry.

## Algebra and Combinatorics

Useful notions from topology. Representations of the free group of rank two in SL 2,C. Affine algebraic sets of characters. Back to basics. The calendar is published for the convenience of conference participants and we strive to support conference organisers who need to publish their upcoming events. Although great care is being taken to ensure the correctness of all entries, we cannot accept any liability that may arise from the presence, absence or incorrectness of any particular information on this website.

## Reading List

Always check with the meeting organiser before making arrangements to participate in an event! Search the calendar. Browse by subject. Kolkom - Colloquium on Combinatorics.

Event listing ID:. Event website:. Beyond spectral gaps — Pansu's Fest, for the 60th birthday of Pierre Pansu. University of Oxford, Mathematical Institute. The goal of this workshop is to bring to Oxford leading experts in the various areas of mathematics and theoretical computer science with an interest in the spectral analysis of graphs and its many applications within mathematics. The event is organised in partnership with the Clay Mathematics Institute.

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Related subject s :. Information Theory, Foundations of Computer Science. Software Engineering. Graph theory and combinatorics are closely related to many mathematical subjects, such as, topology, geometry and number theory and have a lot of applications in applied sciences, engineering and optimization problems.

The workshop focuses on all aspects of graph theory, combinatorics and their applications. Operational research. Symposium on Graphs, Informatics and Algebra. The purpose of this workshop is to bring together researchers from different areas in order to share different points of view and to make collaborations possible, with the ultimate aim that this will result in new connections and possibly unexpected breakthroughs. Dynamics, Geometry and Combinatorics. This workshop brings together dynamicists who use techniques from, and are motivated by, combinatorics, geometry, and number theory.

The topics cover a broad swath of dynamics, including ergodic theory, homogeneous dynamics, symbolic dynamics, Teichmuller theory, and billiards, and the aim of the workshop is to highlight the common features across these subjects. Part of the Semester : Dynamics with Structures. Numerical Analysis and Computational Mathematics. The thirteenth edition of the TextGraphs workshop aims to extend the focus on graph-based and graph-supported machine learning and deep learning methods. We encourage the description of novel NLP problems or applications that have emerged in recent years, which can be addressed with existing and new graph-based methods.

Natural Language Processing, Computational Linguistics. AIM Workshop: Rigidity and flexibility of microstructures.

- Interactions between group theory, number theory, combinatorics and geometry.
- Algebra, Number Theory and Combinatorics | Mathematics.
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This workshop, sponsored by AIM and the NSF, will be devoted to problems in combinatorial and geometric rigidity theory arising from modeling of microstructures. The overall goal of this workshop is to formalize and start working on a graded set of problems arising from the applications, framed by specific focus topics on flexibility, tunnelling, stresses and periodicity, while connecting them with existing techniques and already formulated open problems.

Kolkom — 38th Colloquium on Combinatorics. Triangle Lectures in Combinatorics. These are a series of combinatorial workshops, held once per semester, each on a Saturday. The series began with its first meeting in spring They rotate among the universities in and around the Research Triangle.

Participants come from numerous colleges and universities within a few hours drive, and some from even farther away. These workshops are funded by the National Science Foundation, in particular enabling us to bring in four exciting speakers to give one hour talks each time as well as funding travel expenses for participants. It also provides a premier interdisciplinary platform for researchers to present and discuss the most recent innovations as well as practical challenges encountered in the field of Graph Theory.

In the proposed conference, we have planned to conduct a symposium on graph decompositions. Graph decompositions have a wide variety of applications such as computer architecture, designing reliable communication networks. Hypercubes, Butterfly network, and de Bruijn network are proved to be good interconnection networks.