# Undergraduate Math Research

# at

# St. Norbert College

## Poss-Wroble Fellowship

The Summer Undergraduate Research Program in Mathematics at SNC consists of eight weeks of full time work open to St. Norbert College students with a declared mathematics major or minor. On the application form, students provide a list of their mathematics and other relevant course work, their research interests, and how a research experience would contribute to their professional goals. Students do not need to propose a project. Faculty members may already have projects in mind. The Mathematics Discipline reviews all applications and chooses which applicants will be awarded the summer positions. The research students (Poss-Wroble Fellows) are required to present their work at a national conference, which includes either MathFest in August or the Joint Mathematics Meetings in January, and at the Pi Mu Epsilon Regional Undergraduate Math Conference on the SNC campus in November. Interested students are encouraged to speak with a member of the Mathematics Discipline, either before or after completing an application. Faculty members can offer insight into past projects along with the research projects proposed for the upcoming summer program.

# CURRENT PROJECTS

### SUMMER 2023

# Present Bias in Group Work

#### Sarah Kulas with mentor Seth Meyer

In this project, we discuss how procrastination is affected in a group setting. We begin by reviewing why a single individual procrastinates using findings by Kleinberg and Oren. The general idea is that a person inflates the cost of having to do a task in the present because doing work right now feels much harder than putting off that same work until tomorrow. Yet, when we get to tomorrow, this idea still applies and we end up putting off the task until the last minute when we are forced to do it for a much larger cost. We investigated this procrastination problem by using a fan graph with a source vertex, sink vertex, and weighted edge costs. To find the optimal path for doing a task requires finding the cheapest path from the source to the sink. In this project, our goal is to find the most expensive path that a group could take.

# Classifying Character Degree Graphs with Seven Vertices

#### Dylan schuster with mentor Jacob Laubacher

In this project, we discuss graphs with seven vertices in an effort to classify which of them appear as the prime character degree graphs of finite solvable groups. This classification is complete for the disconnected graphs. Of the 853 non-isomorphic connected graphs, we were able to demonstrate that twenty-two occur as prime character degree graphs. Forty-four graphs remain unclassified.