[Turkmath:4598] Fwd: Topology Seminar - Oct 5

[Cihan Okay]

Dear all,

Bilkent topology seminars will start next week.

Here is the first talk:

Time: Oct 5, 2020 @ 13:40 UTC+3
Speaker: Cihan Okay
Affiliation: Bilkent University

Title:  Commutative $d$-torsion $K$-theory and its applications

Abstract: Commutative $K$-theory is introduced by Adem-Gomez-Lind-Tillmann.
as a generalized cohomology theory obtained from topological $K$-theory.
The construction uses classifying spaces for commutativity, first
introduced by Adem-Cohen-Torres Giese. In this paper we are interested in a
$d$-torsion version of this construction: Let $G$ be a topological group.
The aforementioned classifying space $B(\mathbb{Z}/d,G)$ is assembled from
tuples of pairwise commuting elements in $G$ whose order divides $d$. We
will describe the homotopy type of this space when $G$ is the stable
unitary group, following the ideas of Gritschacher-Hausmann. The
corresponding generalized cohomology theory will be called the commutative
$d$-torsion $K$-theory, and will be denoted by $k\mu_d$. Our motivation for
studying this cohomology theory comes from applications to
operator-theoretic problems that arise in quantum information theory. For
this we introduce another spectrum obtained from $k\mu_d$ and show that a
famous construction from the study of quantum contextuality, known as
Mermin's square, corresponds to a non-trivial class in this generalized
cohomology theory. This refines the topological approach to quantum
contextuality developed earlier jointly with Raussendorf.


To see the upcoming talks visit: https://researchseminars.org/seminar/BilTop

If you are interested you can contact me for the Zoom link.

Best,
Cihan
http://cihan.okay.bilkent.edu.tr/
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