# Browsing by Subject "Representation theory"

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Item Four dimensional N=2 theories from six dimensions(2014-08) Balasubramanian, Aswin Kumar; Distler, JacquesShow more By formulating the six dimensional (0,2) superconformal field theory X[j] on a Riemann surface decorated with certain codimension two defects, a multitude of four dimensional N=2 supersymmetric field theories can be constructed. In this dissertation, various aspects of this construction are investigated in detail for j=A,D,E. This includes, in particular, an exposition of the various partial descriptions of the codimension two defects that become available under dimensional reductions and the relationships between them. Also investigated is a particular observable of this class of four dimensional theories, namely the partition function on the four sphere and its relationship to correlation functions in a class of two dimensional non-rational conformal field theories called Toda theories. It is pointed out that the scale factor that captures the Euler anomaly of the four dimensional theory has an interpretation in the two dimensional language, thereby adding one of the basic observables of the 4d theory to the 4d/2d dictionary.Show more Item Some results in Iwasawa Theory and the p-adic representation theory of p-adic GL₂(2014-05) Kidwell, Keenan James; Ciperiani, Mirela, 1976-Show more This thesis is divided into two parts. In the first, we generalize results of Greenberg-Vatsal on the behavior of algebraic lambda-invariants of p-ordinary modular forms under congruence. In the second, we generalize a result of Emerton on maps between locally algebraic parabolically induced representations and unitary Banach space representations of GL₂ over a p-adic field.Show more Item Towards a self-dual geometric Langlands program(2018-06-15) Derryberry, Richard Thomas; Ben-Zvi, David, 1974-; Neitzke, Andrew; Blumberg, Andrew; Keel, Sean; Nadler, DavidShow more This thesis is comprised of two logically separate but conjecturally related parts. In the first part of the thesis I study theories of class S [32] via the formalism of relative quantum field theories [30]. From this physical formalism, and by analogy to the physical derivation of usual geometric Langlands [45, 86], I conjecture the existence of a self-dual version of the geometric Langlands program. In the second part of the thesis I study shifted Cartier duality for the moduli of Higgs bundles. The main results are: (1) a criteria for ramification of L-valued cameral covers, (2) a generalisation of the Langlands duality/mirror symmetry results for the moduli of Higgs bundles of [24, 37], and (3) the existence of a self-dual version of the moduli of Higgs bundles. This self-dual space is conjecturally the target space for a theory of class S compactified on a torus, and provides positive evidence for the self-dual geometric Langlands program.Show more