Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (p. 45-46).

Symplectic cohomology is an algebraic invariant of filled symplectic cobordisms that encodes dynamical information. In this thesis we define a modified symplectic cohomology theory, called action-completed symplectic cohomology, that exhibits quantitative behavior. We illustrate the non-trivial nature of this invariant by computing it for annulus subbundles of line bundles over complex projective space. The proof relies on understanding the symplectic cohomology of the complex fibers and the quantum cohomology of the projective base. We connect this result to mirror symmetry and prove a non-vanishing result in the presence of Lagrangian submanifolds with non-vanishing Floer homology. The proof uses Lagrangian quantum cohomology in conjunction with a closed-open map.

Thesis (Ph. D.)--Duke University, 2007. / Includes bibliographical references.

Originally presented as the author's Thesis (Ph. D.)--Scuola normale superiore Pisa. / Includes bibliographical references (p. [125]-131) and index.

Thesis (Ph. D.)--University of Chicago, Dept. Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Oct. 31, 2008). PDF text: v, 54 p. : ill. ; 769 K. UMI publication number: AAT 3313102. Includes bibliographical references. Also available in microfilm and microfiche formats.

Let K be an imaginary quadratic field, with associated quadratic character α. We construct an analytic p-adic L-function interpolating the special values L(1, ad(f) ⊗ α) as f varies in a Hida family; these values are non-critical in the sense of Deligne. Our approach is based on Greenberg--Stevens' idea of Λ-adic modular symbols. By considering cohomology with values in a space of p-adic measures, we construct a Λ-adic evaluation map that interpolates Hida's integral expression as the weight varies. The p-adic L-function is obtained by applying this map to a cohomology class corresponding to the given Hida family.

In this thesis I will give a description of the Deligne–Mumford properad expressing it as the result of homotopically trivializing S¹ families of annuli (with appropriate compatibility conditions) in the properad of smooth Riemann surfaces with parameterized boundaries. This gives an analog of the results of Drummond-Cole and Oancea–Vaintrob in the setting of properads. We also discuss a variation of this trivialization which gives rise to a new partial compactification of Riemann surfaces relevant to the study of operations on symplectic cohomology.

No description available.

The dissertation uses a number of mathematical formula including de Rham cohomology with complex coefficients to state and prove extension of Brieskorn's Lemma theorem.