Bi-annual Algebraic and Tropical Meetings of
Brown and YaLE

Spring 2018 @ MIT
May 1, 2018

The BATMOBYLE is a vehicle for bringing together the algebraic and tropical geometry groups of Brown and Yale (and surrounding universities!) for a biannual day of talks.

Qile Chen

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 BreakfastRoom: 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).

Previous BATMOBYLEs: Fall 2014, Spring 2015, Fall 2015, Spring 2016, Fall 2016, Spring 2017, Fall 2017.