Maximilien Péroux

My research is in algebraic topology, category theory and its connections with K-theory and computer science. I explore stable homotopy theory, which involves algebraic structures on topological spaces. I investigate the coherence of these structures when defined up to homotopy. This leads to the concept of ∞-loop spaces and their connection to spectra, representing homology and cohomology theories. I utilize model categories and ∞-categories to study these structures. Additionally, I examine coalgebraic structures, their encoding of algebraic structures, and their applications in theoretical computer science. I also explore new trace methods to approximate algebraic K-theory using variants of topological Hochschild homology.