About

Hi! I am a third year PhD student (he/him) in homotopy theory under the supervision of Prof Marco SchlichtingLink opens in a new window. My research interests lie mainly in motivic/ $\mathbb{A}^1$-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 MA4H8 Ring Theory.
• Previously: TA for MA3G6 Commutative Algebra I and MA249 Algebra II: Groups and Rings 22-23, and MA268 Algebra III, Autumn term 23.
• I have contributed talks for reading groups on scheme theory, higher algebraic $K$-theory, $\infty$-categories, and condensed mathematics. 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).

Publications

In preparation: Higher $K$-theory of forms III: from chain complexes to derived categories, joint w/ Marco Schlichting.

Contact

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