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Full-Text Articles in Science and Mathematics Education
Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, Mu-Wan Huang
Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, Mu-Wan Huang
Department of Mathematics: Dissertations, Theses, and Student Research
Toric varieties are varieties equipped with a torus action and constructed from cones and fans. In the joint work with Suanne Au and Mark E. Walker, we prove that the equivariant K-theory of an affine toric variety constructed from a cone can be identified with a group ring determined by the cone. When a toric variety X(Δ) is smooth, we interpret equivariant K-groups as presheaves on the associated fan space Δ. Relating the sheaf cohomology groups to equivariant K-groups via a spectral sequence, we provide another proof of a theorem of Vezzosi and Vistoli: equivariant K …
Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au
Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au
Department of Mathematics: Dissertations, Theses, and Student Research
Mu-Wan Huang, Mark Walker and I established an explicit formula for the equivariant K-groups of affine toric varieties. We also recovered a result due to Vezzosi and Vistoli, which expresses the equivariant K-groups of a smooth toric variety in terms of the K-groups of its maximal open affine toric subvarieties. This dissertation investigates the situation when the toric variety X is neither affine nor smooth. In many cases, we compute the Čech cohomology groups of the presheaf KqT on X endowed with a topology. Using these calculations and Walker's Localization Theorem for equivariant K-theory, we give explicit formulas …
Combinatorial And Commutative Manipulations In Feynman's Operational Calculi For Noncommuting Operators, Duane Einfeld
Combinatorial And Commutative Manipulations In Feynman's Operational Calculi For Noncommuting Operators, Duane Einfeld
Department of Mathematics: Dissertations, Theses, and Student Research
In Feynman's Operational Calculi, a function of indeterminates in a commutative space is mapped to an operator expression in a space of (generally) noncommuting operators; the image of the map is determined by a choice of measures associated with the operators, by which the operators are 'disentangled.' Results in this area of research include formulas for disentangling in particular cases of operators and measures. We consider two ways in which this process might be facilitated. First, we develop a set of notations and operations for handling the combinatorial arguments that tend to arise. Second, we develop an intermediate space for …