Research

Here are my past and current research projects.

Current

• An equivariant motivic reconstruction theorem at cyclic groups

  Gheorghe—Isaksen—Krause—Ricka construct a filtered model for (cellular, p-complete) motivic spectra over the complex numbers, showing that the latter are intimately related to the even filtration and the Adams—Novikov spectral sequence. We investigate whether an analogous comparison result holds in the equivariant setting, where on the motivic side we start with smooth schemes over the complex numbers with an action of the group scheme of n-th roots of unity as described in work of Hoyois and Gepner—Heller. This filtered model relies critically on the good behaviour of the spectrum representing equivariant algebraic cobordism and its “global” functoriality in the choice of group scheme.

• An equivariant Adams spectral sequence based on MO

  My current PhD project. The global spectrum MO for elementary abelian 2-groups represent the universal equivariant 2-torsion global group law. Further, at the trivial group its associated Hopf algebroid is equivalent to the classical dual Steenrod algebra. Their respective Adams spectral sequences are related by a series of Bockstein spectral sequences, which give us a systematic way to produce classes in an equivariant analogue of the Adams spectral sequence. A poster with a broad discussion of this project can be found here.

Past

• Deformations of stable homotopy theory

  This was my master’s thesis in which I looked at a filtered model for synthetic spectra, and its interpretation as a relative affineness result. The thesis further attempts to construct a partial universal property for synthetic spectra as a deformation of spectra with a given algebraic fibre, in terms of this filtered characterisation. (pdf forthcoming)