Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [117]-121).

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 91-93).

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Computer Science." Includes bibliographical references (p. 103-108).

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1992. / Includes bibliographical references (p. 91-93).

Thesis (doctoral)--Universität Bonn, 1993. / Includes bibliographical references (p. 68-71).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 52-55).

No description available.

We propose a coherent analogue of the non-archimedean case of Venkatesh's conjecture on the cohomology of locally symmetric spaces for Shimura varieties coming from unitary similitude groups. Let G be a unitary similitude group with an indefinite signature at at least one archimedean place. Let Π be an automorphic cuspidal representation of G whose archimedean component Π∞ is a non-degenerate limit of discrete series and let 𝑊 be an automorphic vector bundle such that Π contributes to the coherent cohomology of its canonical extension. We produce a natural action of the derived Hecke algebra of Venketesh with torsion coefficients via cup product coming from étale covers and show that under some standard assumptions this action coincides with the conjectured action of a certain motivic cohomology group associated to the adjoint representation Ad𝜌π of the Galois representation attached to Π. We also prove that if the rank of G is greater than two, then the classes arising from the \'etale covers do not admit characteristic zero lifts, thereby showing that previous work of Harris-Venkatesh and Darmon-Harris-Rotger-Venkatesh is exceptional.

Pure mathematics is often classified as continuous or discrete, that is into topology and combinatorics. Classical topology is the study of spaces in the small, modern topology or homology theory is the study of their large scale structure. The latter and its applications to General Systems Theory and implications on computer programming are the subject of our investigations. A general homology theory includes boundary and adjoint operators defined over a graded category. Singular homology theory describes the structure of high dimensional Simplicial complexes, and is the basis of Kron's tearing of electrical networks. De ~ham Cohomology Theory describes the structure of exterior differential forms used to ~nalyse distributed fields in high dimensional spaces. Likewise optimal control ~roblems can be described by abstract homology theories. Ideas from tensor theory are ~sed to identify the homological structure of Leontief's economic model as a real ~xample of an optimal control system. The common property of each of the above ~ystems is that of optimisation or equivalently the mapping of an error to zero. The ~~iterion may be a metric in space, or energy in an electrical or mechanical network ~~ system, or an abstract cost function in state space or money in an economic system ~~d is always the product of a covariant and a contravariant variable. ~e axiomatic nature of General Homology Theory depends on the definition of an ~~missable category, be it group, ring or module structure. Similarly real systems ~~e analysed in terms of mutually recursive algebras, vector, matrix or polynomial. ~~rther the group morphisms or mode operators are defined recursively. An orthogonal ~~mputer language, Algo182, is proposed which is capable of manipulating the objects ~~scribed by homological systems theory, thus alleviating the tedium and insecurity t~curred in iDtplementing computer programs to analyse engineering systems.

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / Microfiche copy available in Archives and Science. / Vita. / Bibliography: leaves 184-186. / by David Vogan. / Ph.D.