Misha Bialy (Tel Aviv University, Israel)
  New results on algebraic Birkhoff conjecture for convex billiards.

I shall discuss new results on polynomial integrals for Birkhoff billiards which we obtained recently with A.E. Mironov. Our main tool is a new, the so called Angular billiard. It enables us to get obstructions to integrability in terms of the dual curve, extending previous result by S. Bolotin of 1990. Our approach is inspired by recent paper of S. Tabachnikov on algebraic integrability of Outer billiards.