Triangulated surfaces are Riemann surfaces formed by gluing
together equilateral triangles. They are also the Riemann surfaces
defined over the algebraic numbers. Brooks, Makover, Mirzakhani and
many others proved results about the geometric...
To any unital, associative ring R one may associate a family of
invariants known as its algebraic K-groups. Although they are
essentially constructed out of simple linear algebra data over the
ring, they see an extraordinary range of information...
Structures which minimise area appear in numerous geometric
contexts often related to degeneration phenomena. In turn, in many
situations these structures also reflect the ambient geometry in
some way (they are ‘calibrated’) and so they may provide...
The Fourier uniformity conjecture seeks to understand what
multiplicative functions can have large Fourier coefficients on
many short intervals. We will discuss recent progress on this
problem and explain its connection with the distribution of...
The problem of control of large multi-agent systems, such as
vehicular traffic, poses many challenges both for the development
of mathematical models and their analysis and the application to
real systems. First, we discuss how conservation laws can...
I will discuss a result with Bonatti and Crovisier from 2009
showing that the C1 generic diffeomorphism f of a closed manifold
has trivial centralizer; i.e. fg = gf implies that g is a power of
f. I’ll discuss features of the C1 topology that enable...
Let G be an infinite discrete group. Finite dimensional unitary
representations of G are usually quite hard to understand. However,
there are interesting notions of convergence of such
representations as the dimension tends to infinity. One notion
—...
Translational tiling is a covering of a space (such as Euclidean
space) using translated copies of one building block, called a
"translational tile'', without any positive measure
overlaps.
Can we determine whether a given set is a translational...
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...
