Research

A broad description of my research interests and a list of my publications.

Research Interests

I am broadly interested in operator algebras – more specifically C\(^*\)-algebras. Most of my current projects are related to C\(^*\)-algebras arising from (partial) C\(^*\)-dynamical systems. In particular, I am studying 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.

I have also been working on projects related to quantum graphs. Quantum graphs arise as a noncommutative generalization of classical graphs in graph theory. 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.

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.