Events can be found on calendar page, with code HA.
A study group on Hodge atoms.
Organizer: Will Donovan, Marco Rampazzo
Recent developments have brought significant progress to the long-standing problem of irrationality of very general cubic fourfolds. A breakthrough was achieved by Katzarkov, Kontsevich, Pantev and Yu through the introduction of new birational invariants, called Hodge atoms, which combine classical Hodge theory with Gromov–Witten invariants. These invariants arise from the structure of quantum cohomology and exhibit interesting properties under birational transformations such as blowups.
Building on these ideas, Benedetti, Manivel, and Perrin have recently announced a proof of irrationality of very general Gushel–Mukai fourfolds, based on this novel atom formalism.
It would be very interesting to explore further applications of Hodge atoms to rationality questions for Fano fourfolds of K3 type, and to see whether one can extract more general principles from this approach.
With this in mind, we plan to organize a study group aimed at covering the foundational material in arXiv:2508.05105 in a reasonably self-contained way, with particular emphasis on the irrationality of very general cubic fourfolds. We also aim to understand the recent proof of irrationality for very general Gushel–Mukai fourfolds presented in arXiv:2603.17487, and to discuss possible further developments and applications of these ideas.