This workshop is part of the Bernoulli Center programme at EPFL, to be held from 28 September to 02 October 2026.

Numerical invariants, such as the Hilbert-Kunz multiplicity and F-signature, encoding dynamical properties of the Frobenius endomorphism play a crucial role in prime characteristic singularity theory of algebraic varieties. Yet the nature of the generating functions of the Hilbert-Kunz and F-signature function remain mysterious. This workshop aims to foster exchange of knowledge, tools and problems among experts in commutative algebra-algebraic geometry and beyond in order to advance understanding of these generating functions. The workshop part will focus on various methods for computing these generating functions, results on algebraicity, and D-finiteness of formal power series in general. The remaining talks will report on recent refinements and applications of known prime characteristic invariants. Future directions and open problems will be discussed in the formal discussion sessions. Many of the talks should be accessible to non-experts.