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Abstracts for ONLINE Reading group: DT invariants, stability conditions and geometry

Alternatively have a look at the program.

ONLINE: Category theory for geometers

Posted in
Speaker: 
Reinier Kramer
Organiser(s): 
Gaetan Borot, Severin Charbonnier, Alessandro Giacchetto, Reinier Kramer and Campbell Wheeler
Date: 
Fri, 2020-04-10 10:00 - 11:30

I will give an informal introduction to categorical notions required for the seminar. This will make the talk somewhat disjointed, as I need to introduce several distinct objects. The main objects are derived categories. My main examples for these will be coherent sheaves on a scheme and quiver representations, and I will briefly recall these notions as well. Furthermore, I will briefly introduce A_\infty categories, giving the examples of path spaces and Fukaya categories.


Connection via the link:  
https://conf.dfn.de/webapp/conference/979130115

ONLINE: Introduction to Bridgeland stability

Posted in
Speaker: 
Campbell Wheeler
Organiser(s): 
Gaetan Borot, Severin Charbonnier, Alessandro Giacchetto, Reinier Kramer and Campbell Wheeler
Affiliation: 
MPIM
Date: 
Fri, 2020-04-17 16:00 - 17:30

Connection via the link: https://conf.dfn.de/webapp/conference/979130115/
or via the stream:  https://www.conf.dfn.de/stream/nr57d2v82ptdr

If you plan to join, please give Gaetan Borot (gborot[at]mpim-bonn.mpg.de) notice
in advance, so that we can make sure all people concerned are there before starting the talk.

Abstract:

Hall algebras techniques for DT theory

Posted in
Speaker: 
Severin Charbonnier
Organiser(s): 
Gaetan Borot, Severin Charbonnier, Alessandro Giacchetto, Reinier Kramer and Campbell Wheeler
Affiliation: 
MPIM
Date: 
Fri, 2020-04-24 16:00 - 17:30

Link: https://bbb.mpim-bonn.mpg.de/b/gae-nhq-dzk
Contact gborot@mpim-bonn.mpg.de to get the access code.

Abstract:

ONLINE: Stability conditions on quivers with potentials and triangulated surfaces

Posted in
Speaker: 
Alessandro Giacchetto
Organiser(s): 
Gaetan Borot, Severin Charbonnier, Alessandro Giacchetto, Reinier Kramer and Campbell Wheeler
Affiliation: 
MPIM
Date: 
Fri, 2020-05-01 16:00 - 17:30

Link: https://bbb.mpim-bonn.mpg.de/b/gae-nhq-dzk
Contact gborot@mpim-bonn.mpg.de to get the access code.

Abstract:

Stability conditions from quadratic differentials, Part II: global aspects and wall crossing

Posted in
Speaker: 
Campbell Wheeler
Affiliation: 
MPIM
Date: 
Fri, 2020-05-15 15:00 - 16:30

We will put everything we've done over the last two weeks together to prove the isomorphism between spaces of stability conditions associated to surfaces and spaces of quadratic differentials. We will go through wall crossing in some detail and use this to glue the previous local results together to get the isomorphism.

 

An introduction to refined Donaldson-Thomas theory

Posted in
Speaker: 
Matthew Young
Affiliation: 
MPIM
Date: 
Fri, 2020-05-22 16:00 - 17:30

The subject of this talk is the refined Donaldson-Thomas theory of Konstevich and Soibelman, as further developed by Davison, Efimov, Joyce, Meinhardt, Reineke and many others. The goal of this talk is to motivate the need for a refined (as opposed to numerical) Donaldson-Thomas theory, to state the main structural results of the theory in an accessible way and to illustrate these results in concrete examples. Time permitting, I will also discuss the relationship to the motivic approach to Donaldson-Thomas theory of Joyce and Song.

Riemann-Hilbert problems from DT theory

Posted in
Speaker: 
Gaetan Borot
Affiliation: 
MPIM
Date: 
Fri, 2020-05-29 18:00 - 19:30

I will start by recalling what are Riemann-Hilbert problems in the usual sense, basic notions attached to them and where they appear. Then, we will describe the notion of (variation of) BPS structure and carefully go through the definition of the corresponding Riemann-Hilbert problem (in a slightly generalized sense), and its explicit solution in the "uncoupled" case (far from being representative, but nevertheless instructive).

Riemann-Hilbert problems from refined DT

Posted in
Speaker: 
Anna Barbieri
Affiliation: 
Sheffield
Date: 
Fri, 2020-06-05 18:00 - 19:30

This talk is about an instance of a Riemann-Hilbert (RH) problem from refined  Donaldson-Thomas theory. First we will review the solution to the RH problem attached to an uncoupled BPS structure, then we will discuss the statement and a solution to an associated quantized RH problem, corresponding to refined DT theory. The foundation of the topic was presented in the previous talk by Gaetan.

Contact Gaetan Borot (gborot@mpim-bonn.mpg.de) to get 
access code.

 

DT and Joyce structures (after Bridgeland)

Posted in
Speaker: 
Severin Charbonnier
Affiliation: 
MPIM
Date: 
Fri, 2020-06-12 16:00 - 17:30

Link: https://bbb.mpim-bonn.mpg.de/b/gae-nhq-dzk

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