Suppose a light source is placed in a polygonal hall of mirrors (so
\nlight can bounce off the walls). Does every point in the room get
\nilluminated? This elementary geometrical question was open from the
\n1950s until Tokarsky (1995) found an example of a polygonal room in
\nwhich there are two points which do not illuminate each other.
\nResolving a conjecture of Hubert-Schmoll-Troubetzkoy, in joint work
\nwith Lelievre and Monteil we prove that if the angles between walls is
\nrational, every point illuminates all but at most finitely many other
\npoints. The proof is based on recent work by Eskin, Mirzakhani and
\nMohammadi in the ergodic theory of the SL(2,R) action on the moduli
\nspace of translation surfaces. The talk will serve as a gentle
\nintroduction to the amazing results of Eskin, Mirzakhani and Mohammadi.<\/p>\n","protected":false},"excerpt":{"rendered":"
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…
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