Alexey GLUTSYUK, On projective billiards rationally integrable

A planar mathematical billiard is a field in the plane bounded by a smooth curve. The straight lines, which intersect it, reflect from the edge according to the classical law of reflection: the angle of incidence is equal to the angle of reflection. A caustic of a planar billiard table is a curve in which any tangent line is reflected to another tangent line. The famous conjecture of Birkhoff concerns the convex planar billiards bounded integrable to the sense of Birkhoff: that is, admitting a lamination in caustic closed near the border, on the interior side. She asserts, that the only billiards that can be integrated into Birkhoff’s sense are the ellipses.