Algebraseminariet

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 23 mars, Axel Hultman, Matematiska institutionen, Linköpings universitet

Titel: Coxeter groups

Sammanfattning: We shall get acquainted with Coxeter groups from a perspective heavily slanted toward combinatorics. Along the way, algebraic and geometric structures will show up. Objects like Schubert varieties, Hecke algebras, and Kazhdan-Lusztig polynomials may appear. We hope (sometimes perhaps too naïvely) that the combinatorics of Coxeter groups have interesting things to say about them. Some ideas in this direction will be presented.

Onsdag 19 april, Axel Hultman, Matematiska institutionen, Linköpings universitet

Titel: Coxeter groups

Sammanfattning: We shall get acquainted with Coxeter groups from a perspective heavily slanted toward combinatorics. Along the way, algebraic and geometric structures will show up. Objects like Schubert varieties, Hecke algebras, and Kazhdan-Lusztig polynomials may appear. We hope (sometimes perhaps too naïvely) that the combinatorics of Coxeter groups have interesting things to say about them. Some ideas in this direction will be presented.

Torsdag 25 maj, Axel Tiger Norkvist, Matematiska institutionen, Linköpings universitet

Titel: TBA
Sammanfattning: TBA

Torsdag 15 juni

Talare: TBA
Titel: TBA
Sammanfattning: TBA

Tidigare seminarier

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

Titel: Graded Ring Theory and Leavitt path algebras

Sammanfattning: In this talk I will discuss my research concerned with so-called epsilon-strongly group graded rings and Leavitt path algebras. Unlike in many common general reference works in algebra, we will NOT assume that our rings are equipped with a multiplicative identity element. I will begin my talk by presenting different ways to define local units for non-unital rings. Next, I will detail some background on Leavitt path algebras, which can be seen as algebraic analouge of certain graph C^*-algebras. This area of research has seen a lot of recent activity which prompted the inclusion of Leavitt path algebras in the 2020 Mathematics Subject Classification (MSC2020). I will also present some important work from the 1980s by Dade about strongly graded rings and how that relates to the recently introduce notion of epsilon-strongly graded rings. Finally, I will talk about some joint research with P. Lundström (previously known as P. Nystedt), J. Öinert and S. Wagner.

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 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.

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