Homological stability is now well established as an organizing
principle and computational tool in algebraic topology and other
areas. In many cases it is of interest to obtain homological
stability with twisted coefficients, and the standard choice...
The braid group B_{2g+1} has a description in terms of the
hyperelliptic mapping class group of a curve X of genus g.
This equips it with an action on V = H_1(X), and we may produce a
wealth of new representations S^{\lambda}(V) by applying
Schur...
A basic question in arithmetic statistics is: what does
the Selmer group of a random abelian variety look like? This
question is governed by the Poonen-Rains heuristics, later
generalized by Bhargava-Kane-Lenstra-Poonen-Rains, which predict,
for...
