My Research
My research is in algebraic topology: in particular I study stable homotopy theory, in connection with algebraic K-theory, higher category theory and geometry. My work is organized into 3 main themes.
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Algebraic structures in topology and geometry: I use higher categorical methods to encode algebraic structures up to homotopy, aiming either to capture complex geometric information or to facilitate computations in the study of topological spaces.
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Trace methods for algebraic K-theory: I build frameworks to compute the algebraic K-theory of rings and its variants, introducing new approaches to trace methods and Hochschild homology.
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Applications to theoretical computer science and topological data analysis: I apply category theory and algebraic topology to problems outside pure mathematics, both in computer science and data analysis.
Publications &
Preprints
[15] On products of skeleta, with Liam Keenan, (submitted). (ArXiv)
[14] Topological ΔG-homology of rings with twisted G-action, with Gabriel Angelini-Knoll and Mona Merling, (submitted). (ArXiv)
[13] Equivariant algebraic K-theory of symmetric monoidal Mackey functors, with Maxine Calle and David Chan, (submitted). (ArXiv)
[12] Coalgebraic K-theory, with Teena Gerhardt and Hermann Soré, to appear in Journal of Pure and Applied Algebra. (ArXiv)
[11] Functoriality of enriched data types, with Lukas Mulder and Paige Randall North, to appear in the proceedings of CATMI 2023 (Category Theory at Work in Computational Mathematics and Theoretical Informatics). (ArXiv)
[10] Measuring data types, with Lukas Mulder and Paige Randall North, to appear in 41st Conference on the Mathematical Foundations of Programming Semantics (MFPS XLI). (ArXiv)
[9] Rigidification of connective comodules, to appear in Proceedings of American Mathematical Society. (ArXiv)
[8] Trace methods for coHochschild homology, with Sarah Klanderman, Mathematische Zeitschrift 310 (2025), no. 1. (ArXiv, Publication)
[7] A monoidal Dold-Kan correspondence for comodules, Journal of Pure and Applied Algebra 226 (2024), no.8. (ArXiv, Publication)
[6] Coinductive control of inductive data types, with Paige Randall North, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023) in Leibniz International Proceedings in Informatics (LIPIcs) 270 (2023). (ArXiv, Publication)
[5] Spanier-Whitehead duality for topological coHochschild homology, with Haldun Özgür Bayındır, Journal of the London Mathematical Society 107 (2023) no. 5. (ArXiv, Publication)
[4] Koszul duality in higher topoi, with Jonathan Beardsley, Homology, Homotopy and Applications 25 (2023), no. 1. (ArXiv, Publication)
[3] Coalgebras in the Dwyer-Kan localization of a model category, Proceedings of American Mathematical Society 150 (2022), no. 10. (ArXiv, Publication)
[2] The coalgebraic enrichment of algebras in higher categories, Journal of Pure and Applied Algebra 226 (2022), no. 3. (ArXiv, Publication)
[1] Coalgebras in symmetric monoidal categories of spectra, with Brooke Shipley, Homology, Homotopy and Applications 21 (2019), no.1. (ArXiv, Publication)
[0] Highly Structured Coalgebras and Comodules, PhD thesis (Aug 2020).