#### Presentation Title

An Introduction to Quantum Networks

#### Presenter Status

Graduate Student, Mathematics

#### Presentation Type

Oral Presentation

#### Session

B

#### Location

Chan Shun 108

#### Start Date

18-5-2017 3:30 PM

#### End Date

18-5-2017 3:50 PM

#### Presentation Abstract

A network (or graph) is a set of nodes with connections between them. A quantum network describes the behavior of waves in a network of wires. One may study the spectrum of a quantum network, which is akin to determining the set of frequencies of waves on a network of guitar strings joined together. The usefulness of these quantum networks has been enhanced by the ability to study the spectrum by relying on closed paths of the network. In the last few decades, quantum networks have been a model of increasing interest in mathematical physics, chemistry, and engineering; some examples of application include nanotechnology, wave guides, and quantum chaos.

The talk will serve as an introduction to the topic of quantum graphs and their spectral properties. A family of graphs which are particularly amenable to demonstrate these network spectral connections are binary quantum graphs, the topic of my current research.

#### Biographical Sketch

Originally from Columbia, Maryland, Tori Hudgins graduated from Union College in May 2011 with a B.S. in Mathematics Education. She then taught high school mathematics at North Star High School in Lincoln, Nebraska. In pursuit of the ability to continue teaching mathematics at higher levels, she moved to Waco, Texas in 2014 and began graduate school at Baylor University. Having completed her coursework, she received her M.S. in Mathematics in May 2016, and is now currently working on dissertation research in quantum graphs and random matrix theory.

An Introduction to Quantum Networks

Chan Shun 108

A network (or graph) is a set of nodes with connections between them. A quantum network describes the behavior of waves in a network of wires. One may study the spectrum of a quantum network, which is akin to determining the set of frequencies of waves on a network of guitar strings joined together. The usefulness of these quantum networks has been enhanced by the ability to study the spectrum by relying on closed paths of the network. In the last few decades, quantum networks have been a model of increasing interest in mathematical physics, chemistry, and engineering; some examples of application include nanotechnology, wave guides, and quantum chaos.

The talk will serve as an introduction to the topic of quantum graphs and their spectral properties. A family of graphs which are particularly amenable to demonstrate these network spectral connections are binary quantum graphs, the topic of my current research.