Limit F-invariants of the ADE singularities and the Fermat hypersurfaces
Limits of the Hilbert–Kunz multiplicity and F-signature of the ADE singularities, generating functions and their combinatorics.
Research
My research has mainly focused on Singularity Theory in Positive Characteristic, which lies in the field of Commutative Algebra.
During my PhD, I have mostly been thinking about singularities and numerical invariants derived from the Frobenius endomorphism, also known as F-singularities and F-invariants, with a focus on various aspects of the Watanabe–Yoshida conjecture, one of the main driving questions in Hilbert–Kunz theory.
In this page, you can find a summary of some projects I have been working on, together with a brief explanation of some of the main results. Feel free to reach out if you have any comments!
On the Watanabe–Yoshida conjecture
The strong form of the Watanabe–Yoshida conjecture for complete intersections and dimensions 2 through 7, for every characteristic.