Research

My research interests lie at the intersection of algebraic geometry and algebraic topology with higher category theory and homotopical algebra.
If you are interested in doing a PhD with me, or working with me as a Masters student or postdoc, send me an email!
Here is a list of my papers and preprints in reverese chronological order:
 Analytification of mapping stacks examines the interplay between the analytification functor and the mapping stack functor in derived geometry. In particular we show that in good cases the mapping stack between two analytifications is the analytification of the mapping stack. Along the way we prove a number of very useful technical results about analytic perfect complexes, analytic Tannaka duality and working with the derived analytification functor. This is joint work with Mauro Porta.
 Homotopy theory of monoids and derived localization derives a number of interesting consequences from the close relationship between the algebraic bar construction and the nerve construction on monoids. We prove that Adams' cobar construction is the analogue of the loop space even for nonsimply connected spaces, and we model topological spaces by an infinity category of discrete monoids. This is joint work with Joe Chuang and Andrey Lazrev.
 MaurerCartan moduli and theorems of RiemannHilbert type considers different notions of equivalence for MaurerCartan elements in dg algebras. As an application we compute some categories of twisted modules and give new descriptions of infinity local systems. This is joint work with Joe Chuang and Andrey Lazrev.
 The global derived period map c
onstructs an analogue of Griffiths' period map in derived geometry.
This is joint work with Carmelo di Natale.
Published in Advances in Mathematics, Volume 353 (2019).
 Explicity homotopy limits of dgcategories and twisted complexes constructs some explicit homotopy limits of dgcategories and thus gives a description of the twisted complexes of Toledo and Tong. This is joint work with Zhaoting Wei and Jonathan Block.
Published in Homology, Homotopy ond Applications, Volume 19 (2017), Number 2.
 Morita Cohomology constructs cohomology of a topological space X with coefficients in the dgcategory of perfect complexes in two different ways. The results agree and may be characterized as the dg category of infinity local systems on X.
Published in
Mathematical Proceedings of the Cambridge Philosophical Society, Volume 158, Issue 01.
 Morita Cohomology and homotopy locally constant presheaves shows that Morita cohomology is moreover equivalent to the dgcategory of homotopy locally constant sheaves of perfect complexes on X.
Published in
Mathematical Proceedings of the Cambridge Philosophical Society, Volume 158, Issue 01.
 Properness and simplicial resolutions for the model category dgCat proves two technical results about the category of dgcategories. When defined over a ring of flat dimension 0 dgCat is a left proper model category. Simplicial resolutions in dgCat are explicitly given by categories of MaurerCartan elements.
Published in Homology, Homotopy ond Applications, Volume 16 (2014), Number 2.
The paper title links to the arxiv, the journal title links to the published versions; there are no differences in content.
The last three papers are based on my PhD thesis Morita Cohomology.
My advisor was Ian Grojnowski.
