Modern Trends in Algebra and Representation Theory

Aimed at graduate students and non-experts, this text gives a guided tour of modern developments in algebra and representation theory.

Expanding on lectures given at the LMS Autumn Algebra School 2020, this text gives a guided tour of modern developments in algebra and representation theory. It includes many worked examples and applications, providing graduate students and researchers in related disciplines with a springboard into the vast literature in each area.Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.