Schedule
Oct 17th Saturday:
9:00-9:30: Breakfast and Registration (Gregory Hall Room 213)
9:30-10:20: Vincent Bouchard Lecture 1
10:20-10:40: Break
10:40-11:30: Hsian-Hua Tseng Lecture 1
11:30-1:10: Lunch
1:10-2:00: Chiu-Chu Melissa Liu Lecture 1
2:00-2:30: Coffee Break
2:30-3:20: Alessandro Giacchetto Lecture 1
3:20-3:40: Break
3:40-4:40: Lightning Talks
4:40-5:00 Break
5:00-5:50: Vincent Bouchard Lecture 2
Oct 18st Sunday:
8:30-9:00: Breakfast
9:00-9:50: Hsian-Hua Tseng Lecture 2
9:50-10:10: Break
10:10-11:00: Alessandro Giacchetto Lecture 2
11:00-11:30: Coffee Break
11:30-12:20: Chiu-Chu Melissa Liu Lecture 2
Abstracts
Vincent Bouchard Lecture 1
Many of the other talks in this workshop mention the words "topological recursion": well, in this talk I will introduce the Eynard-Orantin topological recursion. I will do it from the point of view of Airy ideals, which I find pedagogically more intuitive. In this approach, topological recursion appears as the result of imposing a particular set of differential constraints on a partition function. I will explain the type of constraints we are interested in (the so-called "Airy ideals"), the Kontsevich-Soibelman existence and uniqueness theorem for the partition function, and how those constraints can be reformulated in terms of a topological recursion for multi-differentials living on a spectral curve.
Vincent Bouchard Lecture 2
I will explain how many examples of Airy ideals arise as particular representations of W-algebras. The resulting partition function is then expected to be the descendant potential of a CohFT, generating interesting enumerative invariants. The prototypical example is the Virasoro constraints for intersection numbers on the moduli space of curves. Other examples include Virasoro constraints for the descendant potential of the Norbury classes, W-constraints for r-spin intersection numbers, and more recently W-constraints for the descendant potential of the \Theta^{r,s} classes (the top degrees of the Chiodo classes), which is, by the way, a non-semisimple CohFT.
Chiu-Chu Melissa Liu Lecture 1
In this talk, I will present four versions of all-genus mirror symmetry relating Gromov-Witten (GW) invariants of semi-projective toric Calabi-Yau 3-orbifolds to the Chekhov-Eynard-Orantin Topological Recursion (TR) invariants of its mirror curve. The first two versions were conjectured by Bouchard-Klemm-Mariño-Pasquetti and proved in full generality in joint work with Fang and Zong. The last two versions were proved recently in joint work with Fang, Yu, and Zong.
Chiu-Chu Melissa Liu Lecture 2
I will explain how to apply the results in Lecture I to derive four versions of all-genus Crepant Transformation Conjecture (CTC) and Holomorphic Anomaly Equations (HAE), based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong.
Alessandro Giacchetto Lecture 1
We will explain how topological recursion à la Eynard–Orantin computes the correlators of semisimple cohomological field theories. We will discuss the correspondence between spectral curves and CohFTs, focusing on how the data of a spectral curve determine a TFT, an R-matrix, and a translation.
Alessandro Giacchetto Lecture 2
We will discuss the physical interpretation of the CohFT associated with a spectral curve in terms of B-twisted Landau–Ginzburg string theory, explaining the physical origin of the TFT, R-matrix, and translation. We will then show how this interpretation leads to a mathematically rigorous proof of gauge/string duality between matrix models and these string theories.
Hsian-Hua Tseng Lecture 1
We will introduce the structure of cohomological field theories, with Gromov-Witten theory as our main example. We will then focus on the Givental-Teleman reconstruction of the semi-simple theories, followed by some remarks on how Givental (might have) arrived at such results.
Hsian-Hua Tseng Lecture 2
We will discuss three applications of (semi-simple) CohFTs: Virasoro constraints, tautological relations, and algebraicity