A broad description of my research interests and a list of my publications and preprints.
An aspect about the field of operator algebras that has always fascinated me is its connection to the foundations of quantum theory and specifically quantum information. Now, I am particularly interested in applying my mathematical foundation to current challenges in quantum computing.
Throughout my graduate studies, I have explored this connection to quantum information through a pure mathematical lens. For example, I have been working on projects related to quantum graphs. Quantum graphs arise as a noncommutative generalization of classical graphs in graph theory. They have first been introduced as a generalization of confusability graphs in error correction. There are two main approaches to this noncommutative generalization, which have been shown to be equivalent in the past. The first approach involves a quantization of the edge relation and the second is given by a quantiziation of the adjacency matrix. I am mainly interested in finding appropriate generalizations of concepts in graph theory to the theory of quantum graphs. Additionally, I have recently started to explore aspects of complexity theory in connection to non-local games.
On the operator algebraic side, my thesis concerned C\(^*\)-algebras arising from partial C\(^*\)-dynamical systems. In particular, I studied the ideal structure of crossed product C\(^*\)-algebras using injective envelope techniques. The rich structure of injective envelopes allows for powerful tools to connect properties of the reduced crossed product such as the intersection property to dynamical properties of the action. You can find my thesis here.
Fanizza, M., Kroell, L., Mehta, A., Paddock, C.,
Rochette, D., Slofstra, W., and Zhao, Y. The NPA hierarchy does not
always attain the commuting operator value (2025).
arXiv: https://arxiv.org/abs/2510.04943
Description: In this preprint, we show that there
exists a non-local game for which the Navascués-Pironio-Acín (NPA)
hierarchy does not attain the commuting operator value at any finite
level. This is a consequence of our main result that proves that
determining whether the commuting operator value of a non-local game is
strictly greater than \(\frac{1}{2}\)
is undecidable. Our contribution involves establishing a computable
mapping from Turing machines to boolean constraint systems non-local
games in which the halting property of the machine is encoded as a
decision problem for the commuting operator value of the game.
Kennedy, M., Kroell, L., and Sehnem, C.
Primality and the ideal intersection property for reduced crossed
products (2025).
arXiv: https://arxiv.org/abs/2504.14454
Description: This preprint concerns the ideal structure
of ordinary C\(^*\)-dynamical systems.
By using injective envelope techniques we obtain a full dynamical
description of when the reduced crossed product of a C\(^*\)-dynamical system is prime, i.e., when
the intersection of any two non-zero ideals is non-zero. Furthermore, we
obtain a full dynamical description of the ideal intersection property
for C\(^*\)-dynamical systems by
FC-hypercentral groups.