The classical Rokhlin Lemma asserts that for an aperiodic
measure-preserving transformation $T$ of a probability space, one
can find a "tower" of sets on which $T$ acts by translation and
which covers almost all of the space. This result is a basic...
In 2003, Bressan proposed a conjecture on the mixing efficiency
of incompressible flows, which remains open. This talk surveys
progress toward resolving Bressan’s mixing conjecture and presents
a new result confirming its asymptotic validity for...
A line of work has shown how nontrivial uniform algorithms for
analyzing circuits can be used to derive nonuniform circuit lower
bounds. In this talk, I will show in depth how the nonexistence of
nontrivial circuit-analysis algorithms can also imply...
Given a symplectic 4-manifold it may admit multiple toric
fibrations. These can be seen as boundary points of the moduli
space of almost toric fibrations. We will sketch that all toric
fibrations are in the same connected component of this
moduli...
I'll introduce the genus zero open Gromov-Witten invariants for
even-dimensional Lagrangians. The definition relies on a canonical
family of bounding cochains satisfying the point-like condition of
Solomon-Tukachinsky, with non-commutative...
A translation surface is a closed surface that is obtained by
gluing edges of a polygon in parallel. The group GL2(R) acts on the
collection translation surfaces of a fixed genus g. For a fixed
translation surface S and t greater than 0, we obtain a...
Cryptographic primitives have been used for various
non-cryptographic objectives, such as eliminating or reducing
randomness and interaction. We show how to use cryptography to
improve the time complexity of solving computational
problems...
The All-Pairs Min-Cut problem (APMC) asks to compute the minimum
cut (or equivalently, the maximum flow) between all pairs of nodes
in a graph.1 The naive solution of making n^2 calls to a
single-pair min-cut algorithm was surpassed in 1961 by a...
Helicity is an invariant of divergence free vector fields on a
three-manifold. One of its fundamental properties is invariance
under volume preserving diffeomorphisms. Arnold, having derived an
ergodic interpretation of helicity as an asymptotic...
