Rational curves on Calabi-Yau threefolds have received enormous attention since the eighties. A driving force has been the Clemens conjectures, which concern the finiteness of curves with fixed degree on the generic quintic threefold, their $(-1, -1)$-normal bundle, and their smoothness. These conjectures have inspired many developments in enumerative geometry, deformation theory, Hodge theory, and differential geometry.

This one-week conference and school aim to bring together researchers and students working in Hodge theory, singularities, enumerative geometry and differential geometry. We will discuss the recent introduction, solution, and consequences of the log Clemens conjectures as in (arXiv:2601.11813). The event will serve as a starting point for future progress in the relative Clemens program, exploring the wider settings where these conjectures are valid and expanding the applications of their solutions.