12,961 research outputs found
Unconditional convergence and invertibility of multipliers
In the present paper the unconditional convergence and the invertibility of
multipliers is investigated. Multipliers are operators created by (frame-like)
analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or
necessary conditions for unconditional convergence and invertibility are
determined depending on the properties of the analysis and synthesis sequences,
as well as the symbol. Examples which show that the given assertions cover
different classes of multipliers are given. If a multiplier is invertible, a
formula for the inverse operator is determined. The case when one of the
sequences is a Riesz basis is completely characterized.Comment: 31 pages; changes to previous version: 1.) the results from the
previous version are extended to the case of complex symbols m. 2.) new
statements about the unconditional convergence and boundedness are added
(3.1,3.2 and 3.3). 3.) the proof of a preliminary result (Prop. 2.2) was
moved to a conference proceedings [29]. 4.) Theorem 4.10. became more
detaile
Cohomological Donaldson-Thomas theory
This review gives an introduction to cohomological Donaldson-Thomas theory:
the study of a cohomology theory on moduli spaces of sheaves on Calabi-Yau
threefolds, and of complexes in 3-Calabi-Yau categories, categorifying their
numerical DT invariant. Local and global aspects of the theory are both
covered, including representations of quivers with potential. We will discuss
the construction of the DT sheaf, a nontrivial topological coefficient system
on such a moduli space, along with some cohomology computations. The
Cohomological Hall Algebra, an algebra structure on cohomological DT spaces,
will also be introduced. The review closes with some recent appearances, and
extensions, of the cohomological DT story in the theory of knot invariants, of
cluster algebras, and elsewhere.Comment: 33 pages, some references adde
Growth fluctuations in a class of deposition models
We compute the growth fluctuations in equilibrium of a wide class of
deposition models. These models also serve as general frame to several
nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero
range process, where our result turns to current fluctuations of the particles.
We use martingale technique and coupling methods to show that, rescaled by
time, the variance of the growth as seen by a deterministic moving observer has
the form |V-C|*D, where V and C is the speed of the observer and the second
class particle, respectively, and D is a constant connected to the equilibrium
distribution of the model. Our main result is a generalization of Ferrari and
Fontes' result for simple exclusion process. Law of large numbers and central
limit theorem are also proven. We need some properties of the motion of the
second class particle, which are known for simple exclusion and are partly
known for zero range processes, and which are proven here for a type of
deposition models and also for a type of zero range processes.Comment: A minor mistake in lemma 5.1 is now correcte
Enhanced gauge symmetry and braid group actions
Enhanced gauge symmetry appears in Type II string theory (as well as F- and
M-theory) compactified on Calabi--Yau manifolds containing exceptional divisors
meeting in Dynkin configurations. It is shown that in many such cases, at
enhanced symmetry points in moduli a braid group acts on the derived category
of sheaves of the variety. This braid group covers the Weyl group of the
enhanced symmetry algebra, which itself acts on the deformation space of the
variety in a compatible fashion. Extensions of this result are given for
nontrivial -fields on K3 surfaces, explaining physical restrictions on the
-field, as well as for elliptic fibrations. The present point of view also
gives new evidence for the enhanced gauge symmetry content in the case of a
local -configuration in a threefold having global monodromy.Comment: 16 pages, 5 figure
Some finiteness results for Calabi-Yau threefolds
We investigate the moduli theory of Calabi--Yau threefolds, and using
Griffiths' work on the period map, we derive some finiteness results. In
particular, we confirm a prediction of Morrison's Cone Conjecture.Comment: 15 pages LaTex, uses amstex, amscd. New title, paper completely
rewritten, results same as in previous version
Induced and non-induced forbidden subposet problems
The problem of determining the maximum size that a -free
subposet of the Boolean lattice can have, attracted the attention of many
researchers, but little is known about the induced version of these problems.
In this paper we determine the asymptotic behavior of , the maximum
size that an induced -free subposet of the Boolean lattice can have
for the case when is the complete two-level poset or the complete
multi-level poset when all 's either equal 4 or
are large enough and satisfy an extra condition. We also show lower and upper
bounds for the non-induced problem in the case when is the complete
three-level poset . These bounds determine the asymptotics of
for some values of independently of the values of and
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