Algebraseminariet vid Linköpings universitet

Detta är en seminarieserie vid Matematiska institutionen. Serien organiseras av Erik Darpö (ALGD). 

Tid och lokal

Seminarietiden är vanligtvis torsdagar kl  10:15-12:00 i Hopningspunkten som ligger i B-huset, ingång 23, plan 2, Campus Valla i Linköping.

Kommande seminarier

Torsdag 26 januari, Joakim Arnlind, Matematiska institutionen, Linköpings universitet, del 1

Titel: Noncommutative Levi-Civita connections

Sammanfattning:  Over the last 40 years, it has become apparent that it is fruitful to extend geometric notions to the setting of noncommutative algebras; both from a mathematical point of view, when studying geometric spaces with few (or no) interesting functions, and from a physical point of view, where noncommutative geometry lies at the heart of constructing theories of quantum gravity.

While the topological aspects of noncommutative geometry are by now fairly well studied, the Riemannian aspects are far less understood, although a lot of progress has been made during the last decade. In particular, the role of the Levi-Civita connection, which is an important object in Riemannian geometry, as well as a fundamental one in general relativity, is not completely understood.

In this series of lectures, I will present an algebraic view on Riemannian geometry, illustrating how one can make sense of e.g. differential forms, vector bundles, metrics and connections in a noncommutative setting. Moreover, I will present material related to the work I've done on the existence and uniqueness of Levi-Civita connections for noncommutative vector bundles.

Torsdag 16 februari, Joakim Arnlind, Matematiska institutionen, Linköpings universitet, del 2

Titel: Noncommutative Levi-Civita connections

Sammanfattning:  Over the last 40 years, it has become apparent that it is fruitful to extend geometric notions to the setting of noncommutative algebras; both from a mathematical point of view, when studying geometric spaces with few (or no) interesting functions, and from a physical point of view, where noncommutative geometry lies at the heart of constructing theories of quantum gravity.

While the topological aspects of noncommutative geometry are by now fairly well studied, the Riemannian aspects are far less understood, although a lot of progress has been made during the last decade. In particular, the role of the Levi-Civita connection, which is an important object in Riemannian geometry, as well as a fundamental one in general relativity, is not completely understood.

In this series of lectures, I will present an algebraic view on Riemannian geometry, illustrating how one can make sense of e.g. differential forms, vector bundles, metrics and connections in a noncommutative setting. Moreover, I will present material related to the work I've done on the existence and uniqueness of Levi-Civita connections for noncommutative vector bundles.

Torsdag 9 mars, Daniel Lännström, Matematiska institutionen, Linköpings universitet

Titel: TBA
Sammanfattning: TBA

Torsdag 30 mars

Talare: TBA
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Sammanfattning: TBA

Onsdag 19 april

Talare: TBA
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Sammanfattning: TBA

Torsdag 25 maj

Talare: TBA
Titel: TBA
Sammanfattning: TBA

Torsdag 15 juni

Talare: TBA
Titel: TBA
Sammanfattning: TBA

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Organisation