Research

Research interests

My main research interests are in equivariant homotopy theory. During my PhD studies I tried to answer the following question: Given a G-space X (where G is a finite group) and a real G-representation V, what can we say about Bredon homology of V-loops on X? Or V-loops of V-suspension of X? Motivation for this question lies in homotopy theory, but the actual calculations use various areas of topology - including homology of categories, configuration spaces, the action of operads and homological algebra over orbit category of G.

This led me to compute the coefficients of Eilenberg-MacLane spectra over the cyclic group of order 2. These computations relied heavily on the Tate square technique developed by J. Greenlees and P. May. Currently, I am working with G. Yan on the extension of these calculations to all cyclic 2-groups.

In my current work, we are focusing on the applications of algebraic topology in quantum computation. The projects I am involved in are applications of the group cohomology in Measurement-Based Quantum Computation (MBQC) and applying simplicial homotopy to the theory of linear constraint systems.

Papers

On the RO(Q)-graded coefficients of the Eilenberg-MacLane spectra. J. Homotopy Relat. Struct. 17, 525–568 (2022) (arxiv version)

Other publications

In March 2022 I wrote a microthesis for the LMS Newsletter, where I describe my research on an accessible level. You can find it in this issue.