For additional information see Michael Broshi's Personal Page.
Research Interests
I study number theory, in particular p-adic Galois representations and p-adic Hodge theory. In modern number theory, classical objects such as Diophantine equations are viewed through the guise of the representations of the absolute Galois group over number fields and p-adic fields.
I am interested in studying infinitesimal deformations of Galois representations, which in many concrete cases are representable by complete local rings, the so-called deformation rings. The singularities of deformation rings dictate whether Galois representations over finite fields can be lifted to integral representations with certain prescribed properties. In my thesis I study the singularities of the deformation ring of flat symplectic representations by building a sort of projective resolution over this ring. More recently, I have been studying the deformation ring of automorphic Galois representations into GSp(4).
Please direct questions and comments to: broshi.1@nd.edu
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