Hi! I am a fourth year PhD student (he/him) in homotopy theory under the supervision of Prof Marco SchlichtingLink opens in a new window. I'm currently on the job market! My research interests lie mainly in motivic homotopy and higher Grothendieck-Witt theory/ Hermitian $K$-theory.

I obtained a BA in Mathematics from Trinity Hall, University of Cambridge, and later an MSc at the University of Nottingham. During the latter I wrote a dissertation on A. Merkurjev's elementary proof of the norm residue isomorphism (in degree 2) under the supervision of Prof Alexander VishikLink opens in a new window.

Teaching and seminars

• Current TA for MA4J7 Cohomology and Poincaré Duality.
• Previously: TA for MA3G6 Commutative Algebra I and MA249 Algebra II: Groups and Rings 22-23, and MA268 Algebra III, Autumn term 23; and TA for MA4H8 Ring Theory, Spring 2024.
• I have contributed talks for reading groups on scheme theory, higher algebraic $K$-theory, $\infty$-categories, condensed mathematics, and stable homotopy groups of spheres (following Pstrągowski). In Winter term 2022, I co-organised (with Dhruva Divate and David Hubbard) a reading group on stacks and descent, following notes of Vistoli.

Contributed talks

• 03/05/23: Homotopy type theory and univalent foundations, Warwick Postgraduate Seminar.
• 05/10/23: Lindel's solution to the Bass-Quillen conjecture in the geometric case, ECHT reading seminar on algebraic vector bundles (see here for notes).
• 24/10/23: Theorem of the cube, square, and applications, reading group on abelian varieties (notes).
• 05/06/24: The universal property of motivic spectra, reading group on stable homotopy groups of spheres (notes).

Publications

Higher $K$-theory of forms III: from chain complexes to derived categories, joint w/ Marco Schlichting. Available on the arXiv. We exhibit a canonical equivalence between the hermitian $K$-theory (alias Grothendieck-Witt) spectrum of an exact form category, and that of its derived Poincaré $\infty$-category. Along the way, we add to the theory of complicial exact categories, and give an explicit model for the 2-excisive derived functor of a quadratic functor on an exact category.

Contact

Please feel free to reach out via email at dan [dot] marlowe [at] warwick [dot] ac [dot] uk.