[Dottorcomp] Seminari di Algebra e Geometria - 24 febbraio 2023

[Lidia Stoppino]

Il giorno venerdì 24 febbraio 2023, alle ore 15,00

Fernando Muro (Universidad de Sevilla)

in aula seminari al piano C (e online) terrà il seguente seminario:

Title: The Donovan–Wemyss conjecture on compound Du Val singularities
Subtitle: An application of the triangulated Auslander–Iyama correspondence

Abstract: We will deal with compound Du Val singularities in the context of the Homological Minimal Model Program. Du Val singularities form an important class of isolated surface singularities. They are classified by ADE Dynkin diagrams, and correspond to conjugation classes of finite subgroups of SL(2,C). Compound Du Val singularities are hypersurface singularities in dimension 4 whose generic hyperplane section is a Du Val singularity. However, the latter, unlike the former, do not have a straightforward classification. In the isolated case with a smooth minimal model, Donovan and Wemyss conjectured in a 2013 preprint (published in 2016) that they could be classified by some finite-dimensional (non-commutative) algebras associated with the singularity. These algebras are called contraction algebras. Soon afterwards, some results appeared offering some evidence on the conjecture. Contraction algebras compute previously known invariants (length, width, Gopakuman–Vafa). They also distinguish between singularities whose previously known invariants coincide. 

We will show how this conjecture follows from the triangulated Auslander–Iyama correspondence. This is a classification result for algebraic triangulated categories with periodic cluster tilting objects. Similar results have been obtained in different algebraic and topological contexts by Lunts–Orlov, Canonaco–Stellari, Canonaco–Neeman–Stellari, Schwede, Schwede–Shipley, and Antieau (among others).

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Tutti gli interessati sono invitati a partecipare. Per chi viene in presenza da furori: la portineria è chiusa il venerdì pomeriggio, scrivete o suonate il citofono a me (ufficio C7) o ad Alberto Canonaco (ufficio C37). 

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Link per partecipare online:

https://us02web.zoom.us/j/84200312171
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Lidia Stoppino
Dipartimento di Matematica
Università di Pavia
Via Ferrata 5
27100 Pavia
Ufficio C.23 (primo piano)
Tel. +39 0382 985628
e-mail: lidia.stoppino a unipv.it 
pagina web: http://www.stoppino.it