Categorical Enumerative Invariants and Large N Matrix Models
유필상
27동 325호
0
50
12.14 17:42
| 구분 | Geometry Physics and Symmetry |
|---|---|
| 일정 | 2026-01-14(수) 10:00~12:00 |
| 세미나실 | 27동 325호 |
| 강연자 | Jakob Ulmer (Université Paris 13) |
| 담당교수 | 유필상 |
| 기타 |
This series of talks explores a categorical approach to enumerative geometry and its connections to large N matrix models from mathematical physics.
We begin by explaining the motivation for Categorical Enumerative Invariants (CEI), which arises naturally from ideas in homological mirror symmetry. After outlining their construction, we discuss known comparisons with classical enumerative theories such as Gromov-Witten invariants, and explain how CEI fit into the framework of Kodaira-Spencer gravity (also known as BCOV theory).
In the second talk, we shift perspective to large N matrix models, presenting a homological-algebraic viewpoint inspired by the Batalin--Vilkovisky formalism. From this approach, familiar structures such as the Gaussian Unitary Ensemble and Chern-Simons theory re-emerge naturally. We then highlight structural parallels with the CEI framework introduced earlier, indicating the relevance of large N matrix models to open enumerative theories.
In the final talk, we combine these two viewpoints, following ideas from open–closed BCOV theory. This unified framework leads to natural quantization statements and motivates a conjectural explanation of well-known dualities between enumerative invariants and large N matrix models, like Kontsevich’s matrix model for intersection theory and the Gopakumar--Vafa duality. The perspective is inspired by recent developments in twisted holography.
