Colloquium: Tuesday March 24, 2pm. Speaker: Barak Weiss (Tel Aviv). Title: Everything is Illuminated (Except for at Most Finitely Many Points)
Suppose a light source is placed in a polygonal hall of mirrors (so
light can bounce off the walls). Does every point in the room get
illuminated? This elementary geometrical question was open from the
1950s until Tokarsky (1995) found an example of a polygonal room in
which there are two points which do not illuminate each other.
Resolving a conjecture of Hubert-Schmoll-Troubetzkoy, in joint work
with Lelievre and Monteil we prove that if the angles between walls is
rational, every point illuminates all but at most finitely many other
points. The proof is based on recent work by Eskin, Mirzakhani and
Mohammadi in the ergodic theory of the SL(2,R) action on the moduli
space of translation surfaces. The talk will serve as a gentle
introduction to the amazing results of Eskin, Mirzakhani and Mohammadi.