Polish-German seminar on quantum groups, graphs and symmetries via representation theory

Talks

  • Date: Friday, 9 September 2022, 11:00
    Speaker: Daniel Gromada, Czech Technical University Prague (CVUT)
    Title: Constructing simple and non-simple quantum graphs
    Abstract: In this talk, we summarize different ways of constructing quantum graphs. We explain the recently obtained classification of simple quantum graphs over 2x2 matrices. We also introduce more general concepts such as weighted quantum graphs.

    Das ganze tschechische Volk ist eine Simulantenbande. -- military doctor Bautze (from Hašek's novel Švejk)
    (Freely translated by Moritz: The Czech people are a bunch of simulants/malingerers (Bande=Gang))

  • Date: Wednesday, 22 June 2022, 9:00 (!) Polish-German time / 16:00 Korean time
    Speaker: Hun Hee Lee (Seoul National University, Republic of Korea)
    Title: Quantum channels with quantum group symmetry
    Abstract: In this talk we will focus on the quantum channels satisfying compact quantum group symmetry, i.e. covariant channels. We first examine the known cases using irreducible representations of compact groups for the possible symmetry. Our main contribution is that we could provide a rather complete description of covariant channels when the symmetry satisfies the "multiplicity-free" condition. It turns out that this scenario is closely related to the "measure-and-prepare" programmability of quantum channels due to a recent result by Winter, et al.
    Secondly, we will demonstrate that any compact quantum groups can also be used as the symmetry for quantum channels. Through the case of SU_q(2) we will explain the necessity of the Heisenberg picture for non-Kac type quantum groups.
    Finally, we will visit a few examples including the case of Weyl covariant channels using projective representations and the cases of the symmetric group of order 4 and its quantum version.
     
  • Date: Wednesday, 27 April 2022, 14:00
    Speaker: Alexander Wendel (Saarland U)
    Title: Quantum Channels and Entangled States associated to Easy Quantum Groups
    Abstract: In 2017 Brannan and Collins constructed highly-entangled spaces and states from the representation theory of the orthogonal quantum groups. A key role in their construction is played by the famous Jones-Wenzl projections. These projections are usually defined via a certain commutation property and are projections onto irreducible representations of the orthogonal quantum group.

    Shortly before (2014/2016) Freslon and Weber gave a combinatorial characterisation of the irreducible representations and fusion rules of easy quantum groups.
    We are going to combine these two papers to investigate howfar one can carry over the results of Brannan and Collins to other easy quantum groups. Especially we are going to show that the projections onto irreducibles satisfy a similar characterisation as the Jones-Wenzl projections and are going to characterise by this the image of these projections. We are then going to transfer some results on entangled spaces to the symmetric quantum group and indicate how to carry out these constructions for other easy quantum groups.

  • Date: Wednesday, 30 March 2022, 14:00
    Speaker: Adam Skalski (IMPAN)
    Title: Quantum channels related to representations of compact quantum groups.
    Abstract: I will introduce basic definitions and certain qualitative notions related to quantum channels, explaining how via the Stinespring theorem one can relate them to properties of isometries between finite-dimensional Hilbert spaces. Then I will describe how such objects arise from representations of compact quantum groups, and how the quantum group structure gives tools to study resulting channels. The talk will be mainly based on the articles of Mike Brannan, Benoit Collins, Hun Hee Lee and Sang Gyoun Youn.

    These are the days of miracle and wonder
    (...)
    Staccato signals of constant information

     
  • Date: Wednesday, 16 February 2022, 14:00
    Speaker: Mateusz Wasilewski (IMPAN)
    Title: Introduction to quantum graphs
    Abstract: I will present three different perspectives on quantum graphs. I will then try to convince you that each of these three approaches has its merits, by discussing random models of quantum graphs, quantum Cuntz-Krieger algebras and quantum automorphisms. Along the way I will mention several future research directions.

    I’m trying to learn something new. I’m trying to surround myself with people that inspire me, or at least inquire similar desires.
    (Kendrick Lamar)
     
  • Date: Wednesday, 26 January 2022, 12:00
    Speaker: Moritz Weber (Saarland University)
    Title: Partitions, „easy" quantum groups and representation theory
    Abstract: In this first talk of our new seminar, I will outline the general frame and aims of our joint project. I will then briefly review aspects of the representation theory of compact matrix quantum groups, before discussing some diagrammatical calculus, partitions of sets and so called „easy" quantum groups. Some open questions we are interested in will be mentioned.

    It is easy to leave the home of reality and get lost in the woods of mathematics, but only a few know how to return.
    (Hugo Steinhaus)

Postal address

Saarland University
Department of Mathematics
Postfach 15 11 50
66041 Saarbrücken
Germany

Physical address

Saarland University
Campus building E 2 4
66123 Saarbrücken
Germany