# Calogero–Moser Systems and Representation Theory

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*Pavel Etingof*

A publication of the European Mathematical Society

Calogero–Moser systems, which were originally discovered by
specialists in integrable systems, are currently at the crossroads of
many areas of mathematics and within the scope of interests of many
mathematicians. More specifically, these systems and their
generalizations turned out to have intrinsic connections with such
fields as algebraic geometry (Hilbert schemes of surfaces),
representation theory (double affine Hecke algebras, Lie groups,
quantum groups), deformation theory (symplectic reflection algebras),
homological algebra (Koszul algebras), Poisson geometry, etc.

The goal of the present lecture notes is to give an introduction to
the theory of Calogero–Moser systems, highlighting their
interplay with these fields. Since these lectures are designed for
non-experts, the author gives short introductions to each of the subjects
involved and provides a number of exercises.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in representation theory, noncommutative algebra, algebraic geometry, and related areas.