Computing the EHZ capacity is 𝑁𝑃-hard

The Ekeland–Hofer–Zehnder capacity (EHZ capacity) is a fundamental symplectic invariant of convex bodies. We show that computing the EHZ capacity of polytopes is <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N upper P"> <mml:semantics> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>P</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">NP</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-hard. For this we reduce the feedback arc set problem in bipartite tournaments to computing the EHZ capacity of simplices.