Schedule
Please note that all times are in GMT+10.
Zoom details has been sent through email on 5th of June
(check your junk mail as well).
Please contact us if you have yet to receive it.
Please add the email cat.dynamics2021@gmail.com into your contact to prevent any emails from us going into your junk mailbox.
The discussion forum can be found here.
Week 1
Some useful references for this week:
https://www.maths.ed.ac.uk/~v1ranick/papers/keller.pdf (Amnon's suggestion)
https://hopf.math.purdue.edu/Neeman/triangulatedcats.pdf
https://www.math.purdue.edu/~arapura/preprints/perv2.pdf
https://www.maths.ed.ac.uk/~abayer/dc-lecture-notes.pdf
https://annals.math.princeton.edu/wp-content/uploads/annals-v166-n2-p01.pdf (Bridgeland's paper)
Monday (7th of June)
10am - 11am
Introduction to triangulated categories
Speaker: Amnon Neeman
derivedcat.pdfWednesday (9th of June)
10am - 11am
Introduction to t-structures
Speaker: Amnon Neeman
tstrint.pdfThursday (10th of June)
10am - 11am
Introduction to stability conditions
Speaker: Anand Deopurkar
2021-06-09-Note-14-27.pdfAnand_DiTS_examples_and_exercises.pdfFriday (11th of June)
10am - 11am
Workshop 1
Feel free to post your questions/comments here
DiTS Worksheet 1.pdfWeek 2
Thursday (17th of June)
10am - 11am
Mass growth and entropy
Speaker: Anthony Licata
Abstract: TBD
Wednesday (16th of June)
10am - 11am
Decorated marked surfaces (DMS) and Calabi-Yau-3 categories
Speaker: Yu Qiu
Abstract: We introduce DMS to study 3-Calabi-Yau categories associated to quivers with potential from triangulated surfaces. We show that the objects and morphisms can be realised as arcs and intersections. As applications, we prove the simply connectedness of the stability conditions on these 3-Calabi-Yau categories.
The references for the talk is the series of papers: 7, 9, 11, 13, 14, 15 on my homepage: https://ubw-q.github.io/
DMS2021.pdfFriday (18th of June)
10am - 11am
Workshop 2
Feel free to post your questions/comments here
DiTS worksheet 2.pdfFriday (18th of June)
5pm - 6pm
Serre dimension in triangulated categories
Speaker: Fabian Haiden
Abstract: Related references:
Link to Maxim's Kontsevich's talk recommended by Fabian Haiden
DiTS talk.pdfWeek 3
Monday (21st of June)
10am - 11am
Thurston's compactification of space of stability conditions
Speaker: Asilata Bapat
Abstract: We propose a natural compactification of the space of Bridgeland stability conditions of triangulated categories. The construction is analogous to the Thurston compactification of Teichmueller space. Under suitable conditions, we conjecture that the compactification is a real manifold with boundary. We will focus on 2-Calabi--Yau categories associated to quivers, which enjoy rich braid group actions. We will prove our conjectures in some small key examples and remark on work in progress about higher rank cases. The talk is based on joint work with Anand Deopurkar and Anthony Licata.
2021-06-21-dits-condensed.pdf[CANCELLED]
This talk has been cancelled due to personal illness
q-Deformation of stability conditions and quadratic differentials
Speaker: Yu Qiu
Abstract: We first review the works of Bridgeland-Smith and Haiden-Katzarkov-Kontsevich on stability conditions via quadratic differentials. Then we introduce the q-deformation of categories, stability conditions and quadratic differentials that link/unify the works of BS and HKK.
Friday (25th of June)
10am - 11am
Workshop 3
Feel free to post your questions/comments here
DiTS Worksheet 3.pdfWeek 4
Friday (2nd of July)
10am - 11am
Workshop 4
Read https://webusers.imj-prg.fr/~bernhard.keller/publ/KellerCYtriangCat.pdf
Feel free to post your questions/comments here