The C0 distance on the space of contact forms on a contact
manifold has been studied recently by different authors. It can be
thought of as an analogue for Reeb flows of the Hofer metric on the
space of Hamiltonian diffeomorphisms. In this talk, I...
A weighted pseudorandom generator (WPRG) is a generalization of
a pseudorandom generator (PRG) in which, roughly speaking,
probabilities are replaced with weights that are permitted to be
positive or negative. In this talk, we present new explicit...
In the study of Hamiltonian systems, integrable dynamics play a
crucial role. Integrability, however, appears to be a delicate
property that is not expected to persist under generic small
perturbations. Understanding the essence of this fragility...
Is randomness ever necessary for space-efficient computation? It
is commonly conjectured that L = BPL, meaning that halting decision
algorithms can always be derandomized without increasing their
space complexity by more than a constant factor. In...
The Higgs mechanism is a part of the Standard Model of quantum
mechanics that allows certain kinds of particles to have nonzero
mass. In spite of its great importance, there is no rigorous proof
that the Higgs mechanism can indeed generate mass in...
Results concerning rigidity of Lagrangian submanifolds lie at
the heart of symplectic topology, and have been intensively studied
since the 1990s. An example for this phenomenon is the concept of
Lagrangian Barriers, a form of symplectic rigidity...
Strong spatial mixing (SSM) is an important and widely studied
quantitative notion of "correlation decay" for a variety of natural
distributions arising in statistical physics, probability theory,
and theoretical computer science. One of the most...
A smooth, oriented n-manifold is called a homotopy sphere if it
is homeomorphic, but not necessarily diffeomorphic, to the standard
n-sphere. In dimensions n>4
, one often studies the group Θn of homotopy spheres up to
orientation-preserving...
