Copenhagen
Groups and Operator Algebras Seminar

We meet on Wednesdays from 15:15 to 16:15. If you have any questions about the seminar or want to be added to the email list, please contact one of the organizers:

James Hyde: jth@math.ku.dk
Pieter Spaas: pisp@math.ku.dk

Upcoming seminars:

10/04/2024, Aud 9.

Lyudmyla Turowska (Chalmers University of Technology, Gothenburg)

Title: No-signaling quantum bicorrelations and quantum graph isomorphisms

Abstract:   I will discuss quantum no-signaling correlations introduced by Duan and Winter and its different subclasses (quantum commuting, quantum and local). They will appear as strategies of non-local games with quantum inputs and quantum outputs. I will then introduce an analogue of bisynchronous correlations and characterise them by tracial states on the universal C*-algebra of the projective free unitary group, showing that in the quantum input/output setup, quantum permutations of finite sets must be replaced by quantum automorphisms of matrix algebras. As an application, I will discuss quantum graph isomorphisms by giving their non-local game interpretation, and compare our approach with the existing algebraic notions of quantum graph isomorphisms. In the case of classical graphs our operational notion of quantum isomorphism leads to new quantum symmetries.

This is a joint work with Michael Brannan, Sam Harris and Ivan Todorov.

17/04/2024, TBA.

Note: This is the Department Special Analysis Lecture.

Per Enflo 

Title: On the invariant subspace problem in Hilbert spaces

Abstract:  I will present a method to construct invariant subspaces - non-cyclic vectors - for a general operator on Hilbert space. It represents a new direction of a method of "extremal vectors", first presented in Ansari-Enflo [1]. One looks for an analytic function l(T) of T, of minimal norm, which moves a vector y near to a given vector x. The construction produces for most operators T a non-cyclic vector, by gradual approximation by almost non-cyclic vectors. But for certain weighted shifts, almost non-cyclic vectors will not always converge to a non-cyclic vector. The construction recognizes this, and when the construction does not work, it will show, that T has some shift-like properties. And for those T, one uses the information obtained to produce non-cyclic vectors.

22/04/2024, TBA.

This is the Department Harald Bohr Lecture, and it takes place on Monday.

László Lovász (Eötvös Loránd University and Alfréd Rényi Institute of Mathematics)

Title: Discrete or continuous?

Abstract:  From Zeno's paradoxes to quantum physics, the question of the continuous nature of our world has been prominent and remains unanswered. Does space-time really exist, or is it just a good model for an enormous, but finite number of elementary particles?

Discrete structures behave quite differently from continuous ones. The great success story of mathematics in the 18-th and 19-th centuries was the development of analysis, with extremely powerful tools such as differential equations or Fourier series, and with by now very standard methods like the famous (infamous?) epsilon-delta technique. Discrete mathematics had a later start, but for importance of its applications it is catching up. Its proof techniques are different, such as enumeration or induction. In the continuous world, algorithms are mostly computations, with numerical analysis at the center. In the discrete world, algorithmic ideas are more diverse, including searching, recurrence, and (yes!) pulling in methods from continuous mathematics.

I will argue that these worlds are not as far apart as they seem. The use of computers forces us to approximate continuous structures by finite ones; but perhaps more surprisingly, very large finite structures can be very well approximated by continuous structures, and this approximation gets rid of inconvenient and unnecessary details. Many fundamental questions of mathematics, probability, or physics can be asked in both settings, and their approaches cross-fertilize each other.

01/05/2024, TBA.

Hannes Thiel (Chalmers University of Technology, Gothenburg)

Title: Semiprime ideals in C*-algebras

Abstract:  Nonclosed ideals of bounded operators play a prominent role in the theory of singular traces as developed by Dixmier, Connes and many others, and the Calkin correspondence is a powerful tool that can be used to answer many questions about nonclosed ideals in this context. For general C*-algebras, a systematic study of nonclosed ideals was initiated by Pedersen in the late 1960s, but much less is known in this broader setting. 

We show that a not necessarily closed ideal in a C*-algebra is semiprime (that is, an intersection of prime ideals) if and only if it is closed under roots of positive elements. Quite unexpectedly, it follows that prime and semiprime ideals in C*-algebras are automatically self-adjoint. This can be viewed as a generalization of the well-known result that closed ideals in C*-algebras are semiprime and self-adjoint. 

This is joint work with Eusebio Gardella and Kan Kitamura.

08/05/2024, TBA.

TBA

Title: TBA

Abstract:  TBA

15/05/2024.

No Seminar (Department day)

22/05/2024, TBA.

TBA

Title: TBA

Abstract:  TBA

29/05/2024, TBA.

TBA

Title: TBA

Abstract:  TBA

03/06/2024, TBA.

This is the department Harald Bohr Lecture, and it takes place on Monday.

Jean Francois Le Gall (Université Paris-Saclay)

Title: TBA

Abstract:  TBA

12/06/2024, TBA.

Amine Marrakchi (ENS Lyon)

Title: TBA

Abstract:  TBA