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Matematiska kollokviet

Organiseras av Anders Björn, Milagros Izquierdo, Vladimir Kozlov och Hans Lundmark.

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Onsdag 26 september 2018, Johan Öinert, Blekinge tekniska högskola, Karlskrona

Talare: Johan Öinert, Blekinge tekniska högskola, Karlskrona

Titel: Epsilon-strongly group graded rings, Leavitt path algebras and crossed products by twisted partial actions

Tid och plats: Onsdag 26 september 2018,  Hopningspunkten, 13.15–14.15

Sammanfattning: Epsilon-strongly group graded rings constitute a class of rings which contains all strongly group graded rings and all crossed products associated with unital twisted partial group actions. A result of Năstăsescu, Van den Bergh and Van Oystaeyen (1989) gives a characterization of strongly group graded rings which are separable over their canonical 'degree zero' subrings. A more recent result of Bagio, Lazzarin and Paques (2010) gives a characterization of crossed products, associated with unital twisted partial group actions, which are separable over their coefficient subrings. We are able to simultaneously generalize both of these results by giving a characterization of separable epsilon-strongly group graded rings. We also provide examples of separable epsilon-strongly group graded rings (not strongly graded!) and thereby answer a question of Le Bruyn, Van den Bergh and Van Oystaeyen (1988).

Given an arbitrary group G, we will explain how to equip any Leavitt path algebra over a finite (directed) graph with an epsilon-strong G-gradation.

This talk is based on recent joint work with Patrik Nystedt (University West, Sweden) and Héctor Pinedo (Industrial University of Santander, Colombia).

Onsdag 3 oktober 2018, Håkan Lennerstad, Blekinge tekniska högskola, Karlskrona

Talare: Håkan Lennerstad, Blekinge tekniska högskola, Karlskrona

Titel: Distance-consistent graph labelings, the ampleness of a graph, and graph functionals

Tid och plats: Onsdag 3 oktober 2018,  Hopningspunkten, 13.15–14.15

Sammanfattning: A natural labeling of a simple connected graph $G=(V,E)$ is a labeling $c$ of the nodes with natural numbers $1,2,...,|V|$. Such a labeling induces a labeling distance $c(u,v)=|c(u)-c(v)|$ alongside the usual graph distance $d(u,v)$. A natural labeling that realizes the minimum $$l(G)=\min_{c}\sum_{u,v\in V}(c(u,v)-d(u,v))^2$$ is a distance-consistent labeling, and $l(G)$ is the ampleness of $G$. It trivial that $l(G)=0$ iff $G$ is a path graph, and I'll give the proof that $l(G)≤l(K_{n})$ for all $G$ with $n=|V$|. The normalized ampleness $L(G)=l(G)/(Kn), \, 0 \le L(G) \le1$ is studied for different graph classes such as the bipartite graph $K_{n,n}$, the star graph $S_{n}$, the cycle graph $C_{n}$ and a few other types, particularly for $n \to \infty$.
The quantity $$\min_{c}\sum_{u,v\in V}(c(u,v)-d(u,v))^2$$ is a graph functional; mapping graphs to non-negative integers. It can be thought of as the "inverse listness" of a graph - being zero for lists only (path graphs). The quantity $c(u,v)$ can be replaced by other quantities defining the "inverse cycleness" or "inverse starness" of any graph, in which case the corresponding functional is zero if an only if the graph is $C_{n}$ or $S_{n}$, respectively.

Onsdag 10 oktober 2018, Evgeniy Lokharu, Lunds universitet

Talare: Evgeniy Lokharu, Lunds universitet

Titel: TBA

Tid och plats: Onsdag 10 oktober 2018,  Hopningspunkten, 13.15–14.15

Sammanfattning: TBA

Fredag 12 oktober 2018, Alexandre Karassev, Nipissing University, Canada

Talare: Alexandre Karassev, Nipissing University, Canada

Titel: Dimension and decomposition complexity

Tid och plats: Fredag 12 oktober 2018,  Hopningspunkten, 10.15–11.15

Sammanfattning: In attempts to capture asymptotic properties of finitely generated groups, manifolds, and general metric spaces, various dimension- like properties have been introduced recently, including asymptotic dimension, asymptotic dimension growth, asymptotic property C and asymptotic property D. We prove that if X is a tree-graded space (as introduced by C. Drutu and M. Sapir) and the family of all pieces of X satisfies one of the dimension-like properties, then X satisfies the same property, with explicit control over the parameters used in the property. In particular, the free product of finitely generated groups G*H satisfies a dimension-like property if the property holds for each group G and H. This is a joint with Nikolay Brodskiy

Onsdag 17 oktober 2018, Sergey Vakulenko, St Petersburg, Ryssland

Talare: Sergey Vakulenko, St Petersburg, Ryssland

Titel: TBA

Tid och plats: Onsdag 17 oktober 2018,  Hopningspunkten, 13.15–14.15

Sammanfattning: TBA