Interests

Broadly, my interests lie in algebraic geometry: the geometry of solution sets of polynomial equations, studied through the language of schemes and sheaves. I am drawn to the classical end of the subject — concrete varieties, intersection-theoretic counts, and theorems whose statements would have made sense to Cayley or Salmon, even when the modern proofs are very different.

A particular fascination is the configuration of the twenty-seven lines on a smooth cubic surface, and more generally the way that small finite invariants — character tables, Weyl groups, marked configurations — arise from the geometry of low-dimensional varieties.

Currently reading

• Hartshorne, Algebraic Geometry, Chapters II–III.
• Eisenbud and Harris, 3264 and All That: Intersection Theory in Algebraic Geometry.
• Vakil, The Rising Sea: Foundations of Algebraic Geometry (used as a parallel text).

Projects

No standalone research projects to report yet. Working notes appear under notes; I expect this section to gain content over the first year of the BSc.

Applied: robustness of neural networks

Separately from the pure mathematics, I work on trustworthy machine learning — first as a research intern at the DLR Institute for AI Safety and Security, and from September 2026 as a student research assistant at the CAISA Lab (Lamarr Institute, Bonn).

The thread I find most mathematically interesting is certified robustness. A classifier f is robust at an input x if small perturbations do not change its decision; making this precise leads directly to the Lipschitz constant L, the smallest number for which

‖f(x) − f(y)‖ ≤ L ‖x − y‖   for all inputs x, y.

A good upper bound on L turns into a guaranteed radius around each input within which the prediction cannot flip. Computing it exactly is NP-hard, so the practical question is how tightly it can be approximated — via the product of layerwise spectral norms, semidefinite relaxations, or bound-propagation. That tension between a clean mathematical object and its hardness in practice is what drew me in.

I am at the start of my undergraduate studies; anything described here as “in progress” should be read accordingly. Corrections are very welcome — see contact.