Research School
Topological Fukaya categories of surfaces with stops via gentle algebras
Organizer: Sibylle Schroll (University of Cologne)
This research school will consist of a series of 6 lectures and 3 research talks from 2-5:20pm (UTC+2) from 25-27 August 2021.
The school will take place on Zoom. To participate, please apply by emailing your name, affiliation and status (eg PhD student, postdoc etc) to rsgentlealgebras@gmail.com before 20 August 2021.
Research School: Topological Fukaya categories of surfaces with stops via gentle algebras
25th to 27th of August 2021
Gentle algebras are classical objects in the representation theory of associative algebra. Remarkably, they connect to many other areas of mathematics. In particular, in the context of homological mirror symmetry, the work in [Haiden-Katzarkov-Kontsevich 2017] and [Leikili-Polishchuk 2020] shows that the partially wrapped Fukaya category of a graded marked surface is triangle equivalent to the derived category of a homologically smooth graded gentle algebra with zero differential. In these lectures, we will give an overview of this result.
There will be six lectures over three days from 2-3pm (German time/UTC+2) and 3:15-4:15pm (German/UTC+2), followed by one research talk 4:30-5:20pm (German time/UTC+2) each day
25.08.21 - 2pm - Lecture 1: Basics on gentle algebras (Liqian Bai - Northwestern Polytechnical University); [notes][video]
25.08.21 - 3:15pm - Lecture 2: Dg-gentle algebras and graded marked surfaces (Wen Chang - Shaanxi Normal University); [notes][video]
25.08.21 - 4:30pm - Research talk: Categorical action of the braid group of the cylinder (Agnès Gadbled - Université Paris-Saclay, Orsay); [notes][video]
26.08.21 - 2pm - Lecture 3: A-infinity structures I. Definitions (Haibo Jin- University of Cologne); [notes][video]
26.08.21 - 3:15pm - Lecture 4: A-infinity structures II. Twisted objects (Haibo Jin- University of Cologne); [notes][video]
26.08.21 - 4:30pm - Research talk: Fukaya categories of symmetric products of disks (Gustavo Jasso - University of Bonn) ;[notes][video]
27.08.21 - 2pm - Lecture 5: A-infinity categories from graded marked surfaces (Liqian Bai - Northwestern Polytechnical University); [notes][video]
27.08.21 - 3:15pm - Lecture 6: Topological Fukaya categories from graded marked surfaces (Wen Chang - Shaanxi Normal University); [notes][video]
27.08.21 - 4:30pm - Research talk: A geometric model of the derived category of skew-gentle algebras (Yadira Valdivieso - University of Leicester); [notes][video]
[Haiden-Katzarkov-Kontsevich 2017] Flat surfaces and stability structures. Publ. Math. Inst. Hautes Études Sci. 126 (2017), 247–318.
[Leikili-Polishchuk 2020] Derived equivalences of gentle algebras via Fukaya categories. Math. Ann. 376 (2020), no. 1-2, 187–225.
For other relevant references click here
For more details, please contact the organizer at rsgentlealgebras@gmail.com.