We prove ''reasonable'' quantitative bounds for sets in ℤ2
avoiding the polynomial corner configuration
(x,y),(x+P(z),y),(x,y+P(z)), where P is any fixed
integer-coefficient polynomial with an integer root of multiplicity
1. This simultaneously...
We will discuss recent results towards the quantum unique
ergodicity conjecture of Rudnick and Sarnak, concerning the
distribution of Hecke--Maass forms on hyperbolic arithmetic
manifolds. The conjecture was resolved for congruence surfaces
by...
In this talk we will discuss some aspects of the question: given
a group, what is the range of Furstenberg entropy of ergodic
stationary actions of it? For the special linear group and its
lattices, constraints on this spectrum come from Nevo-Zimmer...
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...
