Research

Here are my past and current research projects.

Current

• Synthetic isotropy separation

  We lift the familiar technique of isotropy separation from genuine equivariant spectra to the synthetic setting, in accordance similar constructions in equivariant motivic homotopy theory. In particular, we lift the tom Dieck splitting to a splitting on the level of Adams–Novikov spectral sequences and exhibit a vanishing line in the integer-graded equivariant ANSS.

Past

• Synthetic equivariant spectra for finite abelian groups and motivic homotopy theory (j/w Keita Allen)

  We analyse an appropriate cellular subcategory of equivariant motivic spectra over the complex numbers and show that (after completion at an arbitrary prime) this is equivalent to a suitable category of synthetic equivariant spectra, which categorifies an equivariant version of the perfect even filtration which we further relate to the Adams–Novikov spectral sequence. The key input in this motivic comparison argument is a description of the homotopy groups of torus-equivariant algebraic cobordism which we deduce using global methods. arXiv. An early research poster with a more accessible discussion can be found here

• 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. Here’s a pdf (contains outdated results, some redundant exposition, and some mistakes so beware!)