Qile Chen (Boston College) |
Witten's r-spin class via logarithmic compactification
FJRW theory/Witten's top Chern classes were constructed by Fan-Jarvis-Ruan and Chang-Li-Li. The authors proved that the corresponding virtual cycles are represented by Chow cycles supported on proper loci inside non-proper moduli spaces parameterizing sections of certain line bundles. In this talk, I will focus on the example of r-spin curves to introduce a logarithmic approach using stable logarithmic maps of Abramovich-Chen-Gross-Siebert to construct a proper moduli space. This proper moduli space carries a reduced perfect obstruction theory whose associated virtual cycle is Witten’s r-spin class. Our logarithmic approach can be further applied to many interesting cases including FJRW theory, and more generally hybrid models. This is the first step toward a localization formula for higher genus invariants conjectured by Felix Janda. This is a joint work in progress with Felix Janda, Yongbin Ruan, Adrien Sauvaget, and Dimitri Zvonkine. |
10:30 - 11:00 | Coffee and Breakfast | Room: 2-449 |
11:00 - 12:00 | Interpolation problems for curves in projective space
Isabel Vogt (MIT) |
Room: 2-449 |
12:00 - 02:00 | Lunch | |
02:00 - 03:00 | The period-index problem for surfaces over a local field
Asher Auel (Yale) |
Room: 2-449 |
03:00 - 04:00 | Tea | Room: 2-449 |
04:00 - 05:00 | Plenary Talk: Witten's r-spin class via logarithmic compactification
Qile Chen (Boston College) |
Room: 2-449 |
Brown Organizers:
Dan Abramovich (Brown),
Kenny Ascher (MIT),
Dori Bejleri (Brown),
Melody Chan (Brown),
Nathan Pflueger (Amherst),
and
Dhruv Ranganathan (MIT).
Yale Organizers:
Asher Auel (Yale),
Max Kutler (Yale),
Kalina Mincheva (Yale),
Sam Payne (Yale),
Yuchen Liu (Yale).