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Klinefelter syndrome (47, XXY) is a sex chromosome aneuploidy associated with mild deficits in cognitive and language functions. Dysfunctions have also been reported in performance of tasks which examine executive functions. However, it is unclear whether the impaired performance is caused or accentuated by problems with semantic processing and information… (More)

Let k be a field, let I be an ideal generated by monomials in the polynomial ring k[x

We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. Specifically, for an op-erad O, we define the notion of an 'O-algebra contraction' and we prove that the formulas of the Basic Perturbation Lemma preserve O-algebra contractions. Over a ground ring containing the rational numbers, we give explicit… (More)

- CASPER GULDBERG, Casper Guldberg, Alexander Berglund, Kathryn Hess, Pascal Lambrechts
- 2015

In this thesis we study the rational homotopy theory of the spaces of self-equivalences of Koszul spaces-that is, of simply connected spaces which are simultaneously formal and coformal in the language of rational homotopy theory. The primary tool to do so is the Homotopy Transfer Theorem for L ∞-algebras. We begin with a Lie model for the universal cover… (More)

Backelin proved that the multigraded Poincaré series for resolving a residue field over a polynomial ring modulo a mono-mial ideal is a rational function. The numerator is simple, but until the recent work of Berglund there was no combinatorial formula for the denominator. Berglund's formula gives the denominator in terms of ranks of reduced homology groups… (More)

In classical homological algebra one defines the derived functor of an additive covariant functor F : Mod Λ → Mod Λ. Our goal is to generalize this such that F need not be additive. In order to do this we introduce the ordinal number category ∆, the category of simplicial objects sC induced by the category C , and we define the functors N : sMod Λ → Ch Λ +… (More)

Shellability is a well-known combinatorial criterion on a simplicial complex ∆ for verifying that the associated Stanley-Reisner ring k[∆] is Cohen-Macaulay. A notion familiar to commutative algebraists, but which has not received as much attention from combinatorialists as the Cohen-Macaulay property, is the notion of a Golod ring. Recently, Jöllenbeck… (More)

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