Victor Wu (Sydney): From directed graphs of groups to Kirchberg algebras. Oberseminar C*-Algebren.
Tuesday, 28.05.2024 16:15 im Raum SRZ 216/217
Directed graph algebras have long been studied as tractable examples of C*-algebras, but they are limited by their inability to have torsion in their K_1 group. Graphs of groups, which are famed in geometric group theory because of their intimate connection with group actions on trees, are a more recent addition to the C*-algebra scene. In this talk, I will introduce the child of these two concepts directed graphs of groups and describe how their algebras inherit the best properties of its parents, with a view to outlining how we can use these algebras to model a class of C*-algebras (stable UCT Kirchberg algebras) which is classified completely by K-theory.
Angelegt am Thursday, 04.04.2024 07:54 von Elke Enning
Geändert am Tuesday, 30.04.2024 07:17 von Elke Enning
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Eva Belmont (Case Western Reserve University): A deformation of Borel-complete equivariant homotopy theory
Wednesday, 29.05.2024 16:30 im Raum M4
Abstract: Synthetic homotopy theory is a general framework for constructing interesting contexts for doing homotopy theory: using the data of a spectral sequence in some category $\mathcal{C}$, one can construct another category which can be viewed as a deformation of $\mathcal{C}$. The motivating example is the fact, due to Gheorghe-Wang-Xu, that ($p$-complete, cellular) $\mathbb{C}$-motivic homotopy theory can be described as a deformation of the ordinary stable homotopy category, simply using the data of the Adams-Novikov spectral sequence. Burklund, Hahn, and Senger used this framework to study $\mathbb{R}$-motivic homotopy theory as a deformation of $C_2$-equivariant homotopy theory. In joint work with Gabe Angelini-Knoll, Mark Behrens, and Hana Jia Kong, we give (up to completion) a different synthetic description of this deformation, which generalizes to give a deformation of (Borel-complete) $G$-equivariant homotopy theory for other groups $G$.
Angelegt am Wednesday, 24.04.2024 07:50 von Claudia Rüdiger
Geändert am Wednesday, 24.04.2024 07:50 von Claudia Rüdiger
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Joan Claramunt (Madrid): A graph-theoretic characterization of a class of dynamical systems and its (C*)-algebras. Oberseminar C*-Algebren.
Tuesday, 11.06.2024 16:15 im Raum SRZ 216/217
We present a graph-theoretic model for dynamical systems given
by a homeomorphism f on the Cantor set X. This construction
gives a bijective correspondence between such dynamical systems
(X,f) and a subclass of two-colored Bratteli separated graphs.
We use this construction in order to write any dynamical system
of our interest as an inverse limit of a sequence of (what we
call) generalized finite shifts. This enables us to compute the
associated Steinberg algebra (resp. C*-algebra) of the dynamical
systems as colimits of the graph algebras (resp. graph
C*-algebras) associated with the different levels of the
corresponding separated graph.
In subsequent work we plan to apply this theory to relate the
type semigroup of the dynamical system with the graph monoid of
the corresponding separated graph, and with the non-stable
K-theory of the Steinberg algebra.
This is joint work with Pere Ara (Universitat Autònoma de
Barcelona).
Angelegt am Tuesday, 07.05.2024 07:48 von Elke Enning
Geändert am Tuesday, 07.05.2024 07:48 von Elke Enning
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Claudius Zibrowius (Ruhr-Universität Bochum): Khovanov homology and Conway mutatio
Wednesday, 12.06.2024 16:30 im Raum M4
Abstract: What has homological mirror symmetry ever done for you? I will give my personal answer to that question and discuss joint work in progress with Liam Watson and Artem Kotelskiy concerning the behaviour of Khovanov homology under Conway mutation.
Angelegt am Wednesday, 24.04.2024 07:17 von Claudia Rüdiger
Geändert am Wednesday, 24.04.2024 07:17 von Claudia Rüdiger
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Thor Wittich (HHU Düsseldorf): From Operations on Milnor-Witt K-theory to Motivic Knot Invariants
Wednesday, 19.06.2024 16:30 im Raum M4
Abstract:
Understanding (co-)homology operations has shown to be very useful in algebraic topology and algebraic geometry. In this talk we focus on operations of an invariant called Milnor-Witt K-theory, where the latter is an invariant of smooth algebraic varieties which arises naturally in motivic homotopy theory. The structure of the talk is as follows. We start with a short introduction to motivic homotopy theory and in particular to Milnor-Witt K-theory. Afterwards we explain results on additive, stable and non-additive operations on Milnor-Witt K-theory. Finally, we indicate how these operations lead to motivic knot invariants. The last part is ongoing joint work with Matthias Wendt based on unpublished ideas of Aravind Asok and Matthias Wendt.
Angelegt am Monday, 13.05.2024 07:03 von Claudia Rüdiger
Geändert am Monday, 13.05.2024 07:03 von Claudia Rüdiger
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