Identifier

etd-07032017-154047

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

A classical problem in the theory of differential equations is the classification of first-order singular differential operators up to gauge equivalence. A related algebro-geometric problem involves the construction of moduli spaces of meromorphic connections. In 2001, P. Boalch constructed well-behaved moduli spaces in the case that each of the singularities are diagonalizable. In a recent series of papers, C. Bremer and D. Sage developed a new approach to the study of the local behavior of meromorphic connections using a geometric variant of fundamental strata, a tool originally introduced by C. Bushnell for the study of p-adic representation theory. Not only does this approach allow for the generalization of diagonalizable singularities, but it is adaptable to the study of flat G-bundles for G a reductive group. In this dissertation, the objects of study are irregular singular flat GSp-bundles. The main results of this dissertation are two-fold. First, the local theory of fundamental strata for GSp-bundles is made explicit; in particular, the fundamental strata necessary for the construction of well-behaved moduli spaces are shown to be associated to uniform symplectic lattice chain filtrations. Second, a construction of moduli spaces of flat GSp-bundles is given which has many of the geometric features that have been important in the work of P. Boalch and others.

Date

2017

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Sage, Daniel S

DOI

10.31390/gradschool_dissertations.4416

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