Teichmuller dynamics give us a nonhomogeneous example of an
action of SL_2(R) on a space H_g preserving a finite measure. This
space is related to the moduli space of genus g curves. The SL_2(R)
action on H_g has a complicated behavior: McMullen...
For every surface S, the pure mapping class group G_S acts on
the (SL_2)-character variety Ch_S of a fundamental group P of S.
The character variety Ch_S is a scheme over the ring of integers.
Classically this action on the real points Ch_S(R) of...
The Arithmetic Quantum Unique Ergodicity (AQUE) conjecture
predicts that the L2 mass of Hecke-Maass cusp forms on an
arithmetic hyperbolic manifold becomes equidistributed as the
Laplace eigenvalue grows. If the underlying manifold is
non-compact...
