We discuss a local to global profinite principle for being a
commutator in some arithmetic groups. Specifically we show that
SL2(Z) satisfies such a principle, while it can fail with
infinitely many exceptions for SL2(Z[1/p]). The source of
the...
Motivated by counting problems for closed geodesics on
hyperbolic surfaces, I will present a family of new results
describing the dynamics of mapping class groups on Teichmüller
spaces and spaces of closed curves of closed surfaces.
New kinds of vortex sheets with vorticity confined to the
boundary layer are proposed and investigated in detail. Exact
solutions of the steady Navier-Stokes equations for a planar vortex
sheet in arbitrary background strain are found in terms of...
A binary code is simply any subset of 0/1 strings of a fixed
length. Given two strings, a standard way of defining their
distance is by counting the number of positions in which they
disagree. Roughly speaking, if elements of a code are
sufficiently...
A binary code is simply any subset of 0/1 strings of a fixed
length. Given two strings, a standard way of defining their
distance is by counting the number of positions in which they
disagree. Roughly speaking, if elements of a code are
sufficiently...
We will discuss the existence of rational (multi)sections and
unirulings for projective families f:X→CP1 with at most two
singular fibres. In particular, we will discuss two ingredients
that are used to construct the above algebraic curves. The...
The spread of a matrix is defined as the diameter of its
spectrum. This quantity has been well-studied for general matrices
and has recently grown in popularity for the specific case of the
adjacency matrix of a graph. Most notably, Gregory...
The ABNNR encoding is a classical encoding scheme that amplifies
the distance of an error correcting code. The encoding takes an
error correcting code with a small distance and constructs an error
correcting code with distance approaching one, by...
We explain our proof of the unbounded denominators conjecture.
This talk will require the main theorem of the lecture on Nov. 17,
2021, as a “black box” but otherwise be logically independent of
that talk.
In this talk, we discuss the Diophantine study of relative
SL2-character varieties of surfaces. In particular, we prove that
the integral points on these varieties are effectively finitely
generated in a precise sense, and in particular their...
