About
I am a National Science Foundation (NSF) Postdoctoral Fellow at the Utrecht Geometry Center at Universiteit Utrecht working with Lennart Meier. From January 2023 through May 2024, I was a Postdoctoral researcher (Onderzoeker) at Universiteit Utrecht. From September 2022 through December 2022, I was at the Hausdorff Institute in Bonn for the trimester on Spectral Methods in Algebra, Geometry, and Topology. I received my Ph.D. in Mathematics in June 2022 from UCLA, where my advisor was Mike Hill. My CV is here.
My research is in equivariant, chromatic, synthetic, and motivic homotopy. I am particularly interested in (connective) higher real $K$-theories and relating the various computations one can perform with these theories (e.g. their slice, homotopy fixed points, Adams, Adams-Novikov, etc. spectral sequences) to moduli problems in algebraic geometry via the language of stacks. See my Research page for more.
Publications
- The descent spectral sequence for topological modular forms, with Jack Davies and Sven van Nigtevecht, arxiv, submitted.
- On MU homology of connective models of higher real K-theories, with Mike Hill, arxiv, submitted.
- Nonvanishing of products in v_2 periodic families at the prime 3, with Jack Davies, arxiv, submitted.
- Descent spectral sequences through synthetic spectra, with Jack Davies and Sven van Nigtevecht, arxiv, submitted.
- Chromatic defect, Wood's theorem, and higher real K-theories, arxiv, submitted.
- A synthetic approach to detecting v_1 periodic families, with Jack Davies, arxiv, submitted.
- The homological slice spectral sequence in motivic and Real bordism, with Mike Hill and Doug Ravenel, arxiv, Advances in Mathematics, Volume 458, Part A, 2024.
- Cofreeness in Real bordism theory and the Segal conjecture, arxiv, Proceedings of the American Mathematical Society, Volume 150(7), July 2022, 3161-3175.
- Smashing localizations in equivariant stable homotopy, arxiv, Journal of Homotopy and Related Structures, 17, 355-392 (2022).
Contact
- Email: c.d.carrick@uu.nl
- Office: Hans Freudenthalgebouw 521