The NASA Kepler Mission has demonstrated that planets with radii
larger than Earth yet smaller than Neptune are common around
Sun-like stars. Although Kepler has determined the physical sizes
of hundreds of such planets, we know virtually nothing...
Let \(Y\) be a smooth rational surface and let \(D\) be an
effective divisor linearly equivalent to \(-K_Y\), such that \(D\)
is a cycle of smooth rational curves. Such pairs \((Y,D)\) arise in
many contexts, for example in the study of...
A folded symplectic form on a manifold is a closed 2-form with the
mildest possible degeneracy along a hypersurface. A special class
of folded symplectic manifolds are the origami manifolds. In the
classical case, toric symplectic manifolds can...
Groups are Gromov-hyperbolic when all geodesic triangles in their
Cayley graphs are close to being tripods. Despite being tree-like
in this manner, they can harbour extreme wildness in their
subgroups. I will describe examples stemming from a re...
We discuss the universal triviality of the \(\mathrm{CH}_0\)-group
of cubic hypersurfaces, or equivalently the existence of a
Chow-theoretic decomposition of their diagonal. The motivation is
the study of stable irrationality for these varieties...
Hydrogen recombination at redshifts z ~ 1100 - 1500 leads to the
rapid decrease of the optical depth of the Universe due to Thomson
scattering. As a result CMB photons previously strongly coupled
with baryonic matter become free and able to reach...
Tate's conjecture for divisors on algebraic varieties can be
rephrased as a finiteness statement for certain families of
polarized varieties with unbounded degrees. In the case of abelian
varieties, the geometric part of these finiteness statements...
In its simplest form, the central limit theorem states that a sum
of n independent random variables can be approximated with error
\(O(n^{-1/2})\) by a Gaussian with matching mean and second moment
(given these variables are not too dissimilar). We...
