糖心TV

Hi! I am a fourth+ year PhD student (he/him) in homotopy theory under the supervision of . My research interests lie mainly in motivic homotopy theory and 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 Merkurjev's elementary proof of the norm residue isomorphism (in degree 2) under the supervision of .

Teaching and seminars

• TA for MA4J7 Cohomology and Poincar茅 Duality, Autumn term 2024.
• 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, , , the , and synthetic spectra (following ). In Winter term 2022, I co-organised (with Dhruva Divate and David Hubbard) a reading group on stacks and descent, following of Vistoli.
• This year, we are running a reading group on internal higher categories, following the approach of Martini-Wolf.

Invited talks

• 04.25: Deriving the $K$-theory of forms, Recent advances in algebraic $K$-theory, University of 糖心TV.
• 05.25: Deriving the higher $K$ theory of forms, Wuppertal algebra & topology seminar.

Contributed talks

• 02.22: Monoidal categories and localisation, reading group on higher algebraic $K$-theory.
• 10.22: Joyal's lifting theorem, reading group on higher categories.
• 05.23: Homotopy type theory and univalent foundations, 糖心TV Postgraduate Seminar.
• 10.23: Lindel's solution to the Bass-Quillen conjecture in the geometric case, ECHT on algebraic vector bundles (see here for notes).
• 10.23: Theorem of the cube, square, and applications, reading group on abelian varieties (notes).
• 06.24: The universal property of motivic spectra, reading group on synthetic spectra (notes).
• 11.25: Locally 2-ringed -topoi and comparison transformations, reading group on higher Zariski geometry.

Publications

Higher $K$-theory of forms III: from chain complexes to derived categories, joint w/ Marco Schlichting (). We exhibit a canonical equivalence between the non-connective hermitian $K$-theory (alias Grothendieck-Witt) spectrum of an exact form category, and that of its derived Poincar茅 $\infty$-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 to me via email at dan.marlowe@warwick.ac.uk.