Let SO(3,R) be the 3D-rotation group equipped with the
real-manifold topology and the normalized Haar measure \mu.
Confirming a conjecture by Breuillard and Green, we show that if A
is an open subset of SO(3,R) with sufficiently small measure,
The Toda lattice is one of the earliest examples of non-linear
completely integrable systems. Under a large deformation, the
Hamiltonian flow can be seen to converge to a billiard flow in a
simplex. In the 1970s, action-angle coordinates were...
Symmetric power functoriality is one of the basic cases of
Langlands' functoriality conjectures and is the route to the proof
of the Sato-Tate conjecture (concerning the distribution of the
modulo p point counts of an elliptic curve over Q, as the...
A large toolbox of numerical schemes for dispersive equations
has been established, based on different discretization techniques
such as discretizing the variation-of-constants formula (e.g.,
exponential integrators) or splitting the full equation...
Ruzsa asked whether there exist Fourier-uniform subsets of ℤ/Nℤ
with very few 4-term arithmetic progressions (4-AP). The standard
pedagogical example of a Fourier uniform set with a "wrong" density
of 4-APs actually has 4-AP density much higher than...
In the last few years, expanders have been used in fast graph
algorithms in different models, including static, dynamic, and
distributed algorithms. I will survey these applications of
expanders, explain the expander-related tools behind this...
In a vertex expanding graph, every small subset of vertices
neighbors many different vertices. Random graphs are near-optimal
vertex expanders; however, it has proven difficult to create
families of deterministic near-optimal vertex expanders, as...
A symplectic embedding of a disjoint union of domains into a
symplectic manifold M is said to be of Kahler type (respectively
tame) if it is holomorphic with respect to some (not a priori
fixed) integrable complex structure on M which is compatible...