Theory of Atoms via Examples

The Theory of Atoms is a recent formalism introduced by Katzarkov, Kontsevich, Pantev, and Yu, which aims to integrate classical Hodge theory with symplectic geometry, seeking applications in birational geometry.

To properly understand it, we must gather concepts from many areas of knowledge, ranging from Gromov-Witten theory and enumerative algebraic geometry to classical and noncommutative Hodge theory. This series is designed to be an example-driven introduction, providing the essential background needed to understand this new theory.

Programme:

Place: Room 403 (IMI – BAS)

Lectures 1 & 2: Gromov–Witten Theory
Thursday, 18 September 2025
10:30–12:00 & 14:30–16:00

Lecture 3: Quantum Multiplication and Frobenius Algebras
Monday, 6 October 2025
15:30–17:00

Lecture 4: More on quantum multiplication
Wednesday, 8 October 2025
15:30–17:00

Lecture 5: Hodge Structures, Variation of Hodge Structures and Noncommutative Hodge Structures
Monday, 13 October 2025
14:00–15:30

Lecture 6: Variations of Noncommutative Hodge Structures
Monday, 13 October 2025
16:00–17:30

Lecture 7: F-bundles
Wednesday, 15 October 2025
15:30–17:00

Lecture 8: Atoms
Friday, 17 October 2025
14:00–15:00

Lecture 9: Examples
Friday, 17 October 2025
Time: 16:00–17:30

Bibliography:

[1] W. Fulton and R. Pandharipande, Notes on stable maps and quantum cohomology, 1997. Available at arXiv:alg-geom/9608011.

[2] L. Katzarkov, M. Kontsevich, and T. Pantev, Hodge theoretic aspects of mirror symmetry, in From Hodge theory to integrability and TQFT tt*-geometry, Proc. Sympos. Pure Math., vol. 78, Amer. Math. Soc., Providence, RI, 2008, pp. 87–117.

[3] L. Katzarkov, M. Kontsevich, T. Pantev, and T. Yue Yu, Birational invariants from Hodge structures and quantum multiplication, 2025. Available at arXiv:2508.05105.