My Research
My research is in the area of algebraic topology known as stable homotopy theory, in connection with algebraic K-theory, higher category theory and theoretical computer science. I am particularly interested in showing how certain algebraic structures lead to new and effective computations. For instance, I have shown that model categories fail to accurately represent so-called coalgebraic structures in stable homotopy theory, and hence we need the language of ∞-categories to accurately capture homotopy coherent structures. More recently, I have studied trace methods to compute algebraic K-theory and introduced new variants of topological Hochschild homology. I have also extended my interests to theoretical computer science, applying methods of category theory and coalgebras to study algebraic data type interactions.
Publications &
Preprints
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Coalgebraic K-theory, with Teena Gerhardt and Hermann Soré, (submitted). (ArXiv)
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Topological ΔG homology of rings with twisted G-action, with Gabriel Angelini-Knoll and Mona Merling, (submitted). (ArXiv)
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Measuring data types, with Lukas Mulder and Paige Randall North, (submitted). (ArXiv)
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Equivariant algebraic K-theory of symmetric monoidal Mackey functors, with Maxine Calle and David Chan, (submitted). (ArXiv)
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Trace Methods for coHochschild homology, with Sarah Klanderman, to appear in Mathematische Zeitschrift. (ArXiv)
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Rigidification of Connective Comodules, to appear in Proceedings of American Mathematical Society. (ArXiv)
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A monoidal Dold-Kan correspondence for comodules, Journal of Pure and Applied Algebra 226 (2024), no.8. (ArXiv, Publication)
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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)
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Spanier-Whitehead duality for topological coHochschild homology, with Haldun Özgür Bayındır, Journal of the London Mathematical Society 107 (2023) no. 5. (ArXiv, Publication)
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Koszul Duality in Higher Topoi, with Jonathan Beardsley, Homology, Homotopy and Applications 25 (2023), no. 1. (ArXiv, Publication)
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Coalgebras in the Dwyer-Kan Localization of a Model Category, Proceedings of American Mathematical Society 150 (2022), no. 10. (ArXiv, Publication)
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The Coalgebraic Enrichment of Algebras in Higher Categories, Journal of Pure and Applied Algebra 226 (2022), no. 3. (ArXiv, Publication)
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Coalgebras in symmetric monoidal categories of spectra, with Brooke Shipley, Homology, Homotopy and Applications 21 (2019), no.1. (ArXiv, Publication)
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Highly Structured Coalgebras and Comodules, PhD thesis (Aug 2020).