Ross building, Hebrew University of Jerusalem, (Room 70)
Abstract:
Borel studied the topological group actions that are
possible on locally symmetric manifolds. In these two talks, I will
explain Borel's work and interpret these results as a type of rigidity
statement very much related to the well-known Borel conjecture of high
dimensional topology. In particular, I will give the characterization
of locally symmetric manifolds (of dimension not 4) which have a
unique maximal conjugacy of finite group of orientation preserving
homeomorphisms, due to Cappell, Lubotzky and myself. We will then
In this talk I will provide some counter-examples for quantitative multiple
recurrence problems for systems with more than one transformation. For
instance, I will show that there exists an ergodic system
$(X,\mathcal{X},\mu,T_1,T_2)$ with two commuting transformations such that
for every $\ell < 4$ there exists $A\in \mathcal{X}$ such that
\[ \mu(A\cap T_1^n A\cap T_2^n A) < \mu(A)^{\ell} \]
for every $n \in \mathbb{N}$.
The construction of such a system is based on the study of ``big'' subsets
Abstract:
In 2009 the speaker and Vladimir Markovic constructed nearly geodesic surfaces in a given closed hyperbolic 3-manifold M. The construction proceeded by taking all "good pants" in M and matching them at their boundaries to produce a closed surface. I will describe this construction, as well as a new construction with Alexander Wright, of a nearly geodesic surface in the case where M has a cusp. If time permits, I will discuss the potential applications of this construction to higher rank nonuniform lattices and mapping class groups.
Ross building, Hebrew University of Jerusalem, (Room 70)
Abstract
Borel studied the topological group actions that are
possible on locally symmetric manifolds. In these two talks, I will
explain Borel's work and interpret these results as a type of rigidity
statement very much related to the well-known Borel conjecture of high
dimensional topology. In particular, I will give the characterization
of locally symmetric manifolds (of dimension not 4) which have a
unique maximal conjugacy of finite group of orientation preserving
homeomorphisms, due to Cappell, Lubotzky and myself. We will then
A sequence of Picard/Galois orbits of special points in a product of arbitrary many modular curves is conjectured to equidistribute in the product space as long as it escapes any closed orbit of an intermediate subgroup. This conjecture encompasses several well-known results and conjectures, including Duke's Theorem, the Michel-Venkatesh mixing conjecture and the equidistribution strengthening of André-Oort in this setting.
This talk is devoted to the "Kac-Rice formula", which is an explicit way to compute
the expected number of zeroes of a random series with independent Gaussian coefficients.
We will discuss the original proofs of Kac and Rice (1940's),
an elegant geometrical proof due to Edelman and Kostlan (1995), some interesting examples,
and extensions to complex zeroes and eigenvalues of random matrices.
Here is a title and abstract for the lunch seminar:
Rigidity sequences for weakly mixing transformations
Abstract: I will present a recent result of Bassam Fayad
and Jean-Paul Thouvenot that shows that any rigidty
sequence for an irrational rotation is also a rigidity
sequence for some weakly mixing transformation.
