Research Interests
I am broadly interested in operator algebras — more specifically
C∗-algebras. My thesis concerns
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.
An aspect that has always fascinated me about the field of operator
algebras is its connection to the foundations of quantum theory.
Throughout my post-graduate studies, I have continued to explore this
connection through a pure mathematical lens. For example, I have also
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 non-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.
Preprints
- 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.
Published articles
- Foley, A.M., Kazdan, J., Kröll, L., Martínez
Alberga, S., Melnyk, O., and Tenenbaum, T. Spiders and their Kin: An
Investigation of Stanley’s Chromatic Symmetric Function for Spiders and
Related Graphs. Graphs and Combinatorics 37, 87–110 (2021).
DOI: https://doi.org/10.1007/s00373-020-02230-4
arXiv: https://arxiv.org/abs/1812.03476
Description: This publication covers the results
obtained during the Fields Undergraduate Summer Research Program 2018
(for more information on the program see here)
under the supervision of Angèle
Foley. As the title suggests, we are looking at the chromatic
symmetric function of simple graphs (a certain generalization of the
chromatic polynomial) for different graph classes. We give an infinite
family of graphs that extend an example given by Stanley and show that
the chromatic symmetric function uniquely determines graphs in this
class. We also examine the chromatic quasisymmetric function of natural
unit interval graphs.