About

I am a third year Mathematics DPhil student at the University of Oxford, supervised by Lukas Brantner.

I am mostly interested in homotopy theory and derived algebraic geometry, especially in mixed characteristic or arithmetic situations.

Research

Characterising canonical lifts of ordinary Calabi–Yau varieties (Oct. '26). arXiv.

We study Brantner–Taelman's canonical lifts of ordinary Calabi–Yau varieties and characterise their (quasi)canonical lifts in terms of rational \(p\)-adic Hodge theoretic data. We also show that these canonical lifts need not be of CM type and that the associated local Galois representations need not split as sums of twists of unramified representations, in contrast to classical results for abelian varieties and K3 surfaces.

The period map from commutative to noncommutative deformations (Dec. '25). arXiv. Submitted.

We study the period map from infinitesimal deformations of a qcqs derived scheme \(X\) over a field \(k\) to those of the associated \(k\)-linear \(\infty\)-category \(\mathrm{QC}(X)\). We identify the corresponding map on tangent fibres with the dual HKR map \(\mathrm{R}\Gamma(X,\mathbf T_{X/k})[1] \longrightarrow \mathrm{HH}_{\bullet}(X/k)[2]\) and study its injectivity on homotopy groups. As applications, we show liftability of qcqs schemes along square-zero extensions to be a derived invariant, at least when \(\mathrm{char}(k) \ne 2\), and exhibit cases where the entire classical deformation functor of \(X\) is a derived invariant; this partially answers a question of Lieblich.

Talks

• Deformations of schemes and infinity categories. Warwick Junior Algebra seminar (Oct. ‘26)

• Deformations of schemes and derived categories. Oxford Algebraic and Symplectic Geometry seminar (Feb. ‘26)

• Deformations of schemes and infinity categories. Cambridge Junior Geometry seminar (Feb. ‘26)

Contact

Email: forename dot surname at maths.ox.ac.uk