BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Cihan Okay (Bilkent University) DTSTART:20201005T104000Z DTEND:20201005T113000Z DTSTAMP:20260422T135612Z UID:BilTop/1 DESCRIPTION:Title: C ommutative $d$-torsion $K$-theory and its applications\nby Cihan Okay (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held i n SB-Z11.\n\nAbstract\nCommutative $K$-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 talk we are intereste d in a $d$-torsion version of this construction: Let $G$ be a topological group. The aforementioned classifying space $B(\\mathbb{Z}/d\,G)$ is assem bled 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 sta ble unitary group\, following the ideas of Gritschacher-Hausmann. The corr esponding 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-theor etic problems that arise in quantum information theory. For this we introd uce another spectrum obtained from $k\\mu_d$ and show that a famous constr uction 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.\n\nFor a related talk see https://www.y outube.com/watch?v=XCTHaASjurg\n LOCATION:https://researchseminars.org/talk/BilTop/1/ END:VEVENT END:VCALENDAR