Hodge Atoms Learning Seminar
In a recent work, Katzarkov-Kontsevich-Pantev-Yue Yu introduce a new class of birational invariants called Hodge atoms to prove the irrationality of the very general cubic 4-fold. The theory of atoms lies at the intersection of several fields, combining ideas from Hodge theory, Gromov-Witten theory, Homological Mirror Symmetry, and non-Archimedean geometry. In this seminar, we will build up to the study of [KKPY25] and try to understand the basics of this new theory.
Schedule
Time: Fridays, 10:00–11:00 AM
Location: Towne 311
Starting: February 6, 2025
| Date | Topic | Speaker | References |
|---|---|---|---|
| Feb 6 | Introduction | Tony Pantev | Katzarkov et al. (2025) |
| Feb 13 | Non-commutative Hodge structures | Emerson Hemley | Katzarkov et al. (2008) |
| Feb 20 | Quantum cohomology | Frenly Espino | Fulton (1997), Givental (1999) |
| Feb 27 | Non-Archimedean geometry | Colton Griffin | |
| Mar 6 | F-bundles | Anson Law | Katzarkov et al. (2025), §3 |
| Mar 13 | Spring Break | ||
| Mar 20 | The A-Model F-bundle | Avik Chakravarty | Katzarkov et al. (2025), §3 |
| Mar 27 | Decomposition theorems | Andres Fernandez Herrero | Katzarkov et al. (2025), §4 |
| Apr 3 | Hodge Atoms | Emerson Hemley | Katzarkov et al. (2025), §5 |
| Apr 10 | G-Atoms | Tony Pantev | Katzarkov et al. (2025), §5 |
| Apr 17 | Motivic aspects | Daebeom Choi | Katzarkov et al. (2025), §5 |
| Apr 24 | Givental’s theorem | Lee, Y.-P., & Pandharipande, R. (2004) | |
| May 1 | Irrationality of cubic 4-folds | Ana Pavlaković | Katzarkov et al. (2025), §6 |
The primary means of communication will be through Discord. If interested, please contact me to join.
References
- Fulton, W. (1997). Notes on stable maps and quantum cohomology
- Givental, A. (1999). Tutorial on quantum cohomology
- Katzarkov, L., Kontsevich, M., Pantev (2008). Hodge theoretic aspects of mirror symmetry
- Katzarkov, L., Kontsevich, M., Pantev, T., & Yu, Y. (2025). Birational invariants and Hodge structures
- Lee, Y.-P., & Pandharipande, R. (2004). Frobenius manifolds, Gromov-Witten theory, and Virasoro constraints, Part I