37,775 research outputs found
Recent progress on truncated Toeplitz operators
This paper is a survey on the emerging theory of truncated Toeplitz
operators. We begin with a brief introduction to the subject and then highlight
the many recent developments in the field since Sarason's seminal paper in
2007.Comment: 46 page
Regularity of Edge Ideals and Their Powers
We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals
of graphs and their powers. Our focus is on bounds and exact values of and the asymptotic linear function , for in terms of combinatorial data of the given graph Comment: 31 pages, 15 figure
New mathematical structures in renormalizable quantum field theories
Computations in renormalizable perturbative quantum field theories reveal
mathematical structures which go way beyond the formal structure which is
usually taken as underlying quantum field theory. We review these new
structures and the role they can play in future developments.Comment: 26p,4figs., Invited Contribution to Annals of Physics, minor typos
correcte
Failure of Brown representability in derived categories
Let T be a triangulated category with coproducts, C the full subcategory of
compact objects in T. If T is the homotopy category of spectra, Adams proved
the following in [Adams71]: All contravariant homological functors C --> Ab are
the restrictions of representable functors on T, and all natural
transformations are the restrictions of morphisms in T.
It has been something of a mystery, to what extent this generalises to other
triangulated categories. In [Neeman97], it was proved that Adams' theorem
remains true as long as C is countable, but can fail in general. The failure
exhibited was that there can be natural transformations not arising from maps
in T. A puzzling open problem remained: Is every homological functor the
restriction of a representable functor on T? In a recent paper, Beligiannis
made some progress. But in this article, we settle the problem. The answer is
no. There are examples of derived categories T = D(R) of rings, and
contravariant homological functors C --> Ab which are not restrictions of
representables.Comment: 22 pages, to appear in Topology. http://jdc.math.uwo.ca Lots of minor
revisions. This version should closely match the published versio
Regularity of squarefree monomial ideals
We survey a number of recent studies of the Castelnuovo-Mumford regularity of
squarefree monomial ideals. Our focus is on bounds and exact values for the
regularity in terms of combinatorial data from associated simplicial complexes
and/or hypergraphs.Comment: 23 pages; survey paper; minor changes in V.
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