Diss. (sammanfattning) Uppsala : Uppsala universitet, 2009. / Härtill 6 uppsatser.

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This essay examines the question whether the classical theory of electrodynamics can be extended to a spacetime which locally changes dimension and if such an endeavour is mathematically possible. Recent research has developed a new generalisation of smooth manifolds, the so called M-polyfolds, which constitutes a sufficient foundation to make this endeavour a physical plausibility. These M-polyfolds then facilitate the capability to define the velocity of a curve going through a dimensionally shifting spacetime. Moreover, necessary extensions to the theory of M-polyfolds is developed in order to tailor the theory to a more physically focused framework. Concluding the essay, Maxwell’s equations on M-polyfolds are defined. / Den här uppsatsen betraktar huruvida klassisk elektrodynamik kan generaliseras till en rumtid som lokalt byter dimension samt om detta är matematiskt möjligt. Nyligen har forskningen utvecklat en generalisering av släta mångfalder, så kallade M-polyfolds, vilka ger oss en tillräcklig grund för att göra detta till en fysikalisk möjlighet. Dessa M-polyfolds möjliggör förmågan att definiera hastigheten av en kurva som går igenom en dimensionellt varierande rumtid. Därutöver utvecklas vissa nödvändiga förlängningar av teorin om M-polyfolds, detta för att skräddarsy teorin till ett mer fysikaliskt ramverk. Därefefter avslutas uppsatsen genom att definiera Maxwells ekvationer på M-polyfolds.

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For an aspherical symplectic manifold M, closed or with convex contact boundary, and with vanishing first Chern class, a Floer chain complex is defined for Hamiltonians linear at infinity with coefficients in the group ring of the fundamental group of M. For two non-degenerate Hamiltonians of the same slope continuation maps are shown to be simple homotopy equivalences. As a corollary the number of contractible Hamiltonian orbits of period 1 can be bounded from below.

The reason I am writing this essay is due to my curiosity on how children are interested in and how their understanding in geometry is at preschool years. My interest lies in children and arithmetic and especially geometry, which is something I belive that children deal with a great deal in their everyday routines, both in school and at home. What do children do when they work with geometry, and are they aware of what they do? To figure this out, I have taken my findings from three different interviews that I have done atmy preschool with a group of children that have been preselected. I am also curious about whether there is a difference in different types of schools. In this essay I have compared the preschool I work with a Montessori school and a third type of schoolwhere the children spends most of their day´s outdoors called “Ur och Skur” In my results I can not see any major differences in these three preschools work with mathematics. The childrens knowledge is at a similar level and the work with geometry hasbeen implemented in a similar way.

Diss. (sammanfattning) Stockholm : Univ., 2004. / Härtill 6 uppsatser. Titel från s. 1. På titelsida och omslag felaktigt: Intersections of the moduli space of curves.

Diss. (sammanfattning) Uppsala : Uppsala universitet, 2007. / Härtill 2 uppsatser.

Diss. (sammanfattning) Stockholm : Stockholms universitet, 2008. / Härtill 7 uppsatser.

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