1,093 research outputs found
Commuting-Liftable Subgroups of Galois Groups II
Let denote either a positive integer or , let be a fixed
prime and let be a field of characteristic different from . In the
presence of sufficiently many roots of unity in , we show how to recover
some of the inertia/decomposition structure of valuations inside the maximal
-abelian Galois group of using the maximal
-abelian-by-central Galois group of , whenever is sufficiently
large relative to .Comment: 62 pages; final version; NOTE: numbering has changed from previous
version
The Galois action on geometric lattices and the mod- I/OM
This paper studies the Galois action on a special lattice of geometric
origin, which is related to mod- abelian-by-central quotients of
geometric fundamental groups of varieties. As a consequence, we formulate and
prove the mod- abelian-by-central variant/strengthening of a conjecture
due to Ihara/Oda-Matsumoto.Comment: Final version. Minor changes/corrections, introduction expanded. Will
appear in Inventione
Almost-Commuting-Liftable Subgroups of Galois Groups
Let K be a field and \ell be a prime such that char K \neq \ell. In the
presence of sufficiently many roots of unity in K, we show how to recover some
of the inertia/decomposition structure of valuations inside the maximal
(\Z/\ell)-abelian resp. pro-\ell-abelian Galois group of K using its
(Z/\ell)-central resp. pro-\ell-central extensions.Comment: Version 2: updated two references, added a few words to the argument
in Theorem 3, fixed a few typos. All results and arguments are the same. 38
page
Gender Representation on Journal Editorial Boards in the Mathematical Sciences
We study gender representation on the editorial boards of 435 journals in the
mathematical sciences. Women are known to comprise approximately 15% of
tenure-stream faculty positions in doctoral-granting mathematical sciences
departments in the United States. Compared to this pool, the likely source of
journal editorships, we find that 8.9% of the 13067 editorships in our study
are held by women. We describe group variations within the editorships by
identifying specific journals, subfields, publishers, and countries that
significantly exceed or fall short of this average. To enable our study, we
develop a semi-automated method for inferring gender that has an estimated
accuracy of 97.5%. Our findings provide the first measure of gender
distribution on editorial boards in the mathematical sciences, offer insights
that suggest future studies in the mathematical sciences, and introduce new
methods that enable large-scale studies of gender distribution in other fields.Comment: 21 pages, 10 figure
A primer of swarm equilibria
We study equilibrium configurations of swarming biological organisms subject
to exogenous and pairwise endogenous forces. Beginning with a discrete
dynamical model, we derive a variational description of the corresponding
continuum population density. Equilibrium solutions are extrema of an energy
functional, and satisfy a Fredholm integral equation. We find conditions for
the extrema to be local minimizers, global minimizers, and minimizers with
respect to infinitesimal Lagrangian displacements of mass. In one spatial
dimension, for a variety of exogenous forces, endogenous forces, and domain
configurations, we find exact analytical expressions for the equilibria. These
agree closely with numerical simulations of the underlying discrete model.The
exact solutions provide a sampling of the wide variety of equilibrium
configurations possible within our general swarm modeling framework. The
equilibria typically are compactly supported and may contain
-concentrations or jump discontinuities at the edge of the support. We
apply our methods to a model of locust swarms, which are observed in nature to
consist of a concentrated population on the ground separated from an airborne
group. Our model can reproduce this configuration; quasi-two-dimensionality of
the model plays a critical role.Comment: 38 pages, submitted to SIAM J. Appl. Dyn. Sy
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