Organized by:
Leonardo Cavenaghi
Ludmil Katzarkov
Maxim Kontsevich
Tony Pantev
Birational geometry has recently acquired a new and unexpected source of invariants. Rather than being extracted from the geometry of a variety directly, they are read off from its quantum cohomology together with the Hodge-theoretic structures attached to it. The purpose of this event is to develop this circle of ideas systematically, to examine its foundations, and to strengthen its connections with birational geometry, with Hodge theory in both its classical and non-commutative forms, and with theoretical physics.
This is a continuation of the workshop Fundamentals for the Theory of Atoms and Related Topics, October 7–9, 2026
Tentative Schedule:
| Week 1 Foundations |
Genus-zero Gromov–Witten theory and quantum D-modules; F -bundles and ncHodge structures; Iritani’s blowup formula; integral and Hodge atoms; first applications. | T. Pantev, L. Cavenaghi, M. Kontsevich, T. Yu, J. Guéré |
| Week 2 Birational geometry and Hodge theory | Rationality and stable rationality; decomposition of the diagonal; Hodge loci and degenerations; mixed atoms and nc spectra; semiorthogonal decompositions; equivariant birational geometry, modular symbols and Chen–Ruan atoms. | M. Kontsevich, L. Katzarkov, D. Pomerleano, D. Auroux, C. Voisin, S. Schreieder, E. Shinder, Y. Tschinkel, I. Cheltsov, C. Birkar, A. Corti, C. Böhning, V. Benedetti, L. Manivel, A. Harder. |
| Week 3 Physics and advanced topics | tt∗ geometry and N = 2 theories; topolog- ical strings and the B-model; BPS spectra, wall-crossing and spectral networks; integrable systems and isomonodromy; homological mirror symmetry; open problems. | M. Kontsevich, L. Rastelli, S. Cecotti, L. Katzarkov, C. Vafa, D. Gaiotto, V. Pestun, R. Donagi. |