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    • Deformation theory of nearly G₂-structures and nearly G₂ instantons 

      Singhal, Ragini (University of Waterloo, 2021-08-30)
      We study two different deformation theory problems on manifolds with a nearly G₂-structure. The first involves studying the deformation theory of nearly G₂ manifolds. These are seven dimensional manifolds admitting real ...
    • Derived Geometry and the Integrability Problem for G-Structures 

      McCormick, Anthony (University of Waterloo, 2017-08-24)
      In this thesis, we study the integrability problem for G-structures. Broadly speaking, this is the problem of determining topological obstructions to the existence of principal G-subbundles of the frame bundle of a manifold, ...
    • Differential Operators on Manifolds with G2-Structure 

      Suan, Caleb (University of Waterloo, 2020-12-16)
      In this thesis, we study differential operators on manifolds with torsion-free G2-structure. In particular, we use an identification of the spinor bundle S of such a manifold M with the bundle R ⊕ T*M to reframe statements ...
    • Topics in G₂ geometry and geometric flows 

      Dwivedi, Shubham (University of Waterloo, 2020-05-15)
      We study three different problems in this thesis, all related to G₂ structures and geometric flows. In the first problem we study hypersurfaces in a nearly G₂ manifold. We define various quantities associated to such a ...
    • Weak Moment Maps in Multisymplectic Geometry 

      Herman, Jonathan (University of Waterloo, 2018-07-04)
      We introduce the notion of a weak (homotopy) moment map associated to a Lie group action on a multisymplectic manifold. We show that the existence/uniqueness theory governing these maps is a direct generalization from ...


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