Beyond Poncelet porism

Poncelet porism is one of the deepest and most beautiful results from the classical XIX-th century projective geometry. Having one closed polygon inscribed in a given conic and circumscribed about another one, the Poncelet porism states that there are infinitely many such polygons, all having the same number of sides. Notable great mathematicians, such as Jacobi, Cayley, Darboux, Lebesgue were interested in this beautiful theorem and gave their own contributions there. The interest in Poncelet porism revived in recent decades. In this talk, we present historical overview and recent advances, such as higher-dimensional generalisations, applications in mathematical billiards, connections with algebraic geometry, extremal functions and Pell equations.