Math Students Join Professor to Complete Summer Research

Dr. David Lyons with student researchers

The opportunity for connection with faculty played a decisive part in Ashley Swogger’s ’23 decision to attend LVC. She capitalized on that opportunity, joining Dr. David Lyons’ renowned Mathematical Physics Research Group.

“I knew LVC was the right choice when I came for LVC Live. I received a private tour of parts of campus and talked with some of the math professors—one had even emailed me after I submitted my application,” said Swogger, a mathematics and secondary education major. “These connections would never have happened at my other top choice for college.”

Through his fifth National Science Foundation grant, Lyons recruited Swogger and Jesse Arnold ’23 to join his research group when they took his Linear Algebra class.

“I was very happy to recruit Ashley and Jesse for this summer’s research,” said Lyons. “I had both of them as first-year students in an introductory class for majors. It has been great to see their inventiveness at work and watch their engagement and maturity grow over the past two years. We had a great time this past summer. It was one of the finest teamwork summers I have ever had with any group of students.”

Lyons and the students researched permutations and stabilizers, making conjectures from patterns observed in their research and trying to prove them into accepted theorems. To prepare, Swogger and Arnold spent two weeks tackling a crash course on quantum information and computation, Dr. Lyons’s area of expertise.

Arnold, also a mathematics and secondary education major, is enamored with the interesting discoveries that are waiting to be made through arithmetic and calculation.

“When I took Calculus in high school, I knew that I enjoyed mathematics and the interesting discoveries that were just waiting to be made. That knowledge partially fueled my decision to do summer research,” said Arnold, a section leader of his high school drumline who chose LVC because of the Pride of The Valley Marching Band in addition to the academic reputation.

To facilitate their research, the scholars spent the summer on campus. While initially worried that the campus may be lonely, they found a tight-knit community of students staying for the summer.

“Overall, being on campus for the summer was a lot of fun,” Swogger said. “I met new people and made many unforgettable memories. I would recommend that every student spends a summer on campus if they can.”

Once the summer was over, and their research was complete, the team used their last week to create a poster for LVC Inquiry and other conferences.

“I learned a lot this summer about quantum information and computation, and I also learned LaTeX, a mathematical typing software that will be useful to know how to use for future college classes and beyond,” said Swogger.

The group’s research, titled “Local unitary classes of states invariant under permutation subgroups,” can be found here.


Kayleigh Johnson, Marketing & Communications Intern

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