4,302 research outputs found
Essential cohomology for elementary abelian p-groups
For an odd prime p the cohomology ring of an elementary abelian p-group is
polynomial tensor exterior. We show that the ideal of essential classes is the
Steenrod closure of the class generating the top exterior power. As a module
over the polynomial algebra, the essential ideal is free on the set of Mui
invariants.Comment: 10 page
Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
This paper is a survey of the subject of variations of Hodge structure (VHS)
considered as exterior differential systems (EDS). We review developments over
the last twenty-six years, with an emphasis on some key examples. In the
penultimate section we present some new results on the characteristic
cohomology of a homogeneous Pfaffian system. In the last section we discuss how
the integrability conditions of an EDS affect the expected dimension of an
integral submanifold. The paper ends with some speculation on EDS and Hodge
conjecture for Calabi-Yau manifolds
-groups with maximal elementary abelian subgroups of rank
Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2. It follows that if G has rank greater than p, then the poset of elementary abelian subgroups of G of rank at least 2 is connected and the torsion-free rank of the group of endotrivial kG-modules is one, for any field k of characteristic p. We also verify the class-breadth conjecture for the p-groups G whose poset has more than one component
The Mod-2 Cohomology Ring of the Third Conway Group is Cohen-Macaulay
By explicit machine computation we obtain the mod-2 cohomology ring of the
third Conway group Co_3. It is Cohen-Macaulay, has dimension 4, and is detected
on the maximal elementary abelian 2-subgroups.Comment: 12 pages; writing style now more concis
On the boundary of moduli spaces of log Hodge structures, II: nontrivial torsors
This is a continuous work of our previous paper. In the previous work we
showed a triviality of the torsors in the case where period domains are
Hermitian symmetric and a non-triviality for one-example. In this paper we
determine whether the torsors are trivial or not for any period domains for
pure Hodge structures. We also show a generalization of a previous result which
gives a non-triviality on some open sets connecting to cycle spaces.Comment: 14 page
“The first man on the street” - tracing a famous Hilbert quote (1900) back to Gergonne (1825)
A short, catchy, and in its content somewhat exaggerated, quote allows us to draw a connection through three-quarters of a century between two leaders of mathematics who apparently held somewhat similar philosophical, pedagogical, and political views. In addition to providing some new facets to the biographies of Gergonne and Hilbert, our article relates to increasing demands for the dissemination of mathematical knowledge and to corresponding structural changes within mathematics during the 19th century
An exploratory study of the association between reactive attachment disorder and attachment narratives in early school-age children
To explore attachment narratives in children diagnosed with reactive attachment disorder (RAD). Method: We compared attachment narratives, as measured by the Manchester Child Attachment Story Task, in a group of 33 children with a diagnosis of RAD and 37 comparison children. Results: The relative risk (RR) for children with RAD having an insecure attachment pattern was 2.4 (1.4-4.2) but 30% were rated as securely attached. Within the RAD group, children with a clear history of maltreatment were more likely to be Insecure-Disorganised than children without a clear history of maltreatment. Conclusions: Reactive attachment disorder is not the same as attachment insecurity, and questions remain about how attachment research informs clinical research on attachment disorders
Arithmetically Cohen-Macaulay Bundles on complete intersection varieties of sufficiently high multidegree
Recently it has been proved that any arithmetically Cohen-Macaulay (ACM)
bundle of rank two on a general, smooth hypersurface of degree at least three
and dimension at least four is a sum of line bundles. When the dimension of the
hypersurface is three, a similar result is true provided the degree of the
hypersurface is at least six. We extend these results to complete intersection
subvarieties by proving that any ACM bundle of rank two on a general, smooth
complete intersection subvariety of sufficiently high multi-degree and
dimension at least four splits. We also obtain partial results in the case of
threefolds.Comment: 15 page
New & Noteworthy, June 2018
Contents include: Letters from the past and current presidents; ECD Travel Grant Recipients: Responses from their first conference; Conference Spotlights: Dramaturgs & #METOO: A Conference Report; Call for translators.https://soundideas.pugetsound.edu/lmdanewsletter/1001/thumbnail.jp
Large-N phase transition in lattice 2-d principal chiral models
We investigate the large-N critical behavior of 2-d lattice chiral models by
Monte Carlo simulations of U(N) and SU(N) groups at large N. Numerical results
confirm strong coupling analyses, i.e. the existence of a large-N second order
phase transition at a finite .Comment: 12 pages, Revtex, 8 uuencoded postscript figure
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