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Ilmar Gahramanov: *Witten index and applications*

In 1982 Witten suggested an elegant and effective way of characterizing spontaneous supersymmetry breaking in supersymmetric theories. He introduced a topological invariant of the theory which tells us whether supersymmetry is broken or not. This topological invariant, called the Witten index, computes the difference between the numbers of bosonic and fermionic ground states. In the lectures, we will review the Witten index and discuss its recent applications to supersymmetric gauge theories.