2019 Thematic Program (I)

DG and A_infty enhancements with applications to internal Homs

[TMCSC]

March 08, 2019  16:00-17:00

W303  School of Mathematics, Sichuan University

[lecture ]20190308Paolo Stellari-01.png

SPEAKER

Paolo Stellari (Università degli Studi di Milano, Italy)

ABSTRACT

We provide a complete comparison between the localizations of the categories of dg categories, strictly unital A_infty categories, and cohomological unital A_infty categories by the corresponding classes of quasi-equivalences. A complete proof of this key result is missing in the literature. As an application, we can prove a claim of Kontsevich (and Drinfeld) that says that, over a field, the category of internal Homs between two dg categories is quasi-equivalent to the category of strictly unital A_infty functors between them. We also deduce some new results concerning the uniqueness of enhancements for 'geometric' triangulated categories. This is the result od joint works with A. Canonaco and M. Ornaghi and with A. Canonanco and V. Melani (in progress).

ORGANIZERD BY

An-Min Li (Chair) (Sichuan University)

Bohui Chen (Sichuan University)

Xiaojun Chen (Sichuan University)

Farkhod Eshmatov (Sichuan University)

Wenchuan Hu (Sichuan University)

Raphael Ponge (Sichuan University)

SUPPORTED BY

Natural Science Foundation of China

School of Mathematics, Sichuan University

Tianyuan Mathematical Center in Southwest China