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You searched for +publisher:"University of Michigan" +contributor:("Pixton, Aaron"). Showing records 1 – 2 of 2 total matches.

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University of Michigan

1. Webb, Rachel. Functoriality and the Moduli of Sections, With Applications to Quasimaps.

Degree: PhD, Mathematics, 2020, University of Michigan

Motivated by Gromov-Witten theory, this thesis is about moduli of maps from curves to algebraic stacks, the obstruction theories of those moduli, and the functoriality of the stacks and their obstruction theories. The first part discusses the moduli of sections S of a map Z → C from an artin stack Z to a family of twisted curves C over a base algebraic stack. The existence and basic properties of S are due to Hall-Rydh; the new result in this thesis is that S has a canonical obstruction theory (not necessarily perfect), generalizing known constructions on Deligne-Mumford substacks of S. We also work out basic functoriality properties of S and its obstruction theory. The second part proves an abelianization formula for the quasimap I-function. That is, if Z is an affine l.c.i. variety with an action by a complex reductive group G such that the quotient Z//θG is a smooth projective variety, we relate the quasimap I-functions of Z//θG and Z//θ T where T is a maximal torus of G. With the mirror theorems of Ciocane-Fontantine and Kim, this computes the genus-zero Gromov-Witten invariants of Z//θG in good cases. Advisors/Committee Members: Pixton, Aaron (committee member), Pando Zayas, Leopoldo A (committee member), Bhatt, Bhargav (committee member), Fulton, William (committee member), Janda, Felix (committee member).

Subjects/Keywords: quasimaps; Gromov-Witten invariants; moduli of stable maps; deformation theory of algebraic stacks; abelianization; I-functions; Mathematics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Webb, R. (2020). Functoriality and the Moduli of Sections, With Applications to Quasimaps. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/155204

Chicago Manual of Style (16th Edition):

Webb, Rachel. “Functoriality and the Moduli of Sections, With Applications to Quasimaps.” 2020. Doctoral Dissertation, University of Michigan. Accessed November 29, 2020. http://hdl.handle.net/2027.42/155204.

MLA Handbook (7th Edition):

Webb, Rachel. “Functoriality and the Moduli of Sections, With Applications to Quasimaps.” 2020. Web. 29 Nov 2020.

Vancouver:

Webb R. Functoriality and the Moduli of Sections, With Applications to Quasimaps. [Internet] [Doctoral dissertation]. University of Michigan; 2020. [cited 2020 Nov 29]. Available from: http://hdl.handle.net/2027.42/155204.

Council of Science Editors:

Webb R. Functoriality and the Moduli of Sections, With Applications to Quasimaps. [Doctoral Dissertation]. University of Michigan; 2020. Available from: http://hdl.handle.net/2027.42/155204


University of Michigan

2. Chen, Ruian. E_?-Rings and Modules in Kan Spectral Sheaves.

Degree: PhD, Mathematics, 2020, University of Michigan

This thesis sets up the foundations of a theory of rings and modules on sheaves of spectra over topological spaces. The theory is based on Kan spectra, which is better behaved sheaf-theoretically, and a rigid smash product on Kan spectra is constructed, and is well-behaved enough for discussing E_∞-rings and their modules. Moreover, this thesis also develops localization on the homotopy category of sheaves of Kan spectra. Using the machinery of localization, the derived category of Kan spectral sheaves is defined and is compatible with the smash product. The main result of the thesis is building a symmetric monoidal structure on the derived category of modules over an E_∞-ring in Kan spectral sheaves. Advisors/Committee Members: Kriz, Igor (committee member), Merlin, Roberto D (committee member), Burns Jr, Daniel M (committee member), Pixton, Aaron (committee member), Wilson, Jennifer Catherine Hinton (committee member).

Subjects/Keywords: spectra; sheaves; sheaves of spectra; spectral algebra; smash product; rings and modules; Mathematics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Chen, R. (2020). E_?-Rings and Modules in Kan Spectral Sheaves. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/155195

Chicago Manual of Style (16th Edition):

Chen, Ruian. “E_?-Rings and Modules in Kan Spectral Sheaves.” 2020. Doctoral Dissertation, University of Michigan. Accessed November 29, 2020. http://hdl.handle.net/2027.42/155195.

MLA Handbook (7th Edition):

Chen, Ruian. “E_?-Rings and Modules in Kan Spectral Sheaves.” 2020. Web. 29 Nov 2020.

Vancouver:

Chen R. E_?-Rings and Modules in Kan Spectral Sheaves. [Internet] [Doctoral dissertation]. University of Michigan; 2020. [cited 2020 Nov 29]. Available from: http://hdl.handle.net/2027.42/155195.

Council of Science Editors:

Chen R. E_?-Rings and Modules in Kan Spectral Sheaves. [Doctoral Dissertation]. University of Michigan; 2020. Available from: http://hdl.handle.net/2027.42/155195

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