Homological mirror symmetry has its origins in theoretical physics
but is now of great interest in mathematics due to the deep
connections it reveals between different areas of geometry and
algebra. This book offers a self-contained and accessible
introduction to the subject via the representation theory of
algebras and quivers. It is suitable for graduate students and
others without a great deal of background in homological algebra
and modern geometry. Each part offers a different perspective on
homological mirror symmetry. Part I introduces the A-infinity
formalism and offers a glimpse of mirror symmetry using
representations of quivers. Part II discusses various A- and
B-models in mirror symmetry and their connections through toric and
tropical geometry. Part III deals with mirror symmetry for Riemann
surfaces. The main mathematical ideas are illustrated by means of
simple examples coming mainly from the theory of surfaces, helping
the reader connect theory with intuition.
General
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