108 research outputs found
On two topological cardinal invariants of an order-theoretic flavour
Noetherian type and Noetherian -type are two cardinal functions which
were introduced by Peregudov in 1997, capturing some properties studied earlier
by the Russian School. Their behavior has been shown to be akin to that of the
\emph{cellularity}, that is the supremum of the sizes of pairwise disjoint
non-empty open sets in a topological space. Building on that analogy, we study
the Noetherian -type of -Suslin Lines, and we are able to
determine it for every up to the first singular cardinal. We then
prove a consequence of Chang's Conjecture for regarding the
Noetherian type of countably supported box products which generalizes a result
of Lajos Soukup. We finish with a connection between PCF theory and the
Noetherian type of certain Pixley-Roy hyperspaces
Laver's results and low-dimensional topology
In connection with his interest in selfdistributive algebra, Richard Laver
established two deep results with potential applications in low-dimensional
topology, namely the existence of what is now known as the Laver tables and the
well-foundedness of the standard ordering of positive braids. Here we present
these results and discuss the way they could be used in topological
applications
The prospects for mathematical logic in the twenty-first century
The four authors present their speculations about the future developments of
mathematical logic in the twenty-first century. The areas of recursion theory,
proof theory and logic for computer science, model theory, and set theory are
discussed independently.Comment: Association for Symbolic Logi
Brill-Gordan Loci, Transvectants and an Analogue of the Foulkes Conjecture
Combining a selection of tools from modern algebraic geometry, representation
theory, the classical invariant theory of binary forms, together with explicit
calculations with hypergeometric series and Feynman diagrams, we obtain the
following interrelated results. A Castelnuovo-Mumford regularity bound and a
projective normality result for the locus of hypersufaces that are equally
supported on two hyperplanes. The surjectivity of an equivariant map between
two plethystic compositions of symmetric powers; a statement which is
reminiscent of the Foulkes-Howe conjecture. The nonvanishing of even
transvectants of exact powers of generic binary forms. The nonvanishing of a
collection of symmetric functions defined by sums over magic squares and
transportation matrices with nonnegative integer entries. An explicit set of
generators, in degree three, for the ideal of the coincident root locus of
binary forms with only two roots of equal multiplicity.Comment: This is a considerably expanded version of math.AG/040523
Mixed moduli in 3d N=4 higher-genus quivers
We analyze exactly marginal deformations of 3d N=4 Lagrangian gauge theories,
especially mixed-branch operators with both electric and magnetic charges.
These mixed-branch moduli are either single-trace (non-factorizable) or in
products of electric and magnetic current supermultiplets. Apart from some
exceptional quivers (which have additional moduli), 3d N=4 theories described
by genus g quivers with nonabelian unitary gauge groups have exactly g
single-trace mixed moduli, which preserve the global flavour symmetries. For
g>1, this implies that AdS_4 gauged supergravities cannot capture the entire
moduli space even if one takes into account the (quantization) moduli of
boundary conditions. Likewise, in a general Lagrangian theory, we establish
(using the superconformal index) that the number of single-trace mixed moduli
is bounded below by the genus of a graph encoding how nonabelian gauge groups
act on hypermultiplets.Comment: 39 pages, 1 figur
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