Math grad student and his mentees research the Bergman Kernel

Isaac Cinzori, a 2nd-year mathematics Ph.D. student, co-mentored undergrad students in a research project on complex variables alongside CMU Professor Debraj Chakrabarti. The researchers were selected to give a presentation at the Young Mathematicians Conference and published in the Journal of Mathematical Analysis and Applications.  

The research took ideas from calculus and used complex numbers (numbers containing a non-real number) instead of real numbers. They were looking for a formula for the function called the Bergman kernel. Prior to the research of this group, another graduate student Rasha Almughrabi did important work in this space and created a baseline for Cinzori and his group.  

A major part of this project was allowing undergraduate students to do real math research, write findings, and attend conferences. Cinzori and his group submitted an abstract to the Young Mathematicians Conference at Ohio State University. The research was accepted and Cinzori and the undergraduate students traveled to Ohio to give a 20-minute presentation on their work. 

The paper was also published in the Journal of Mathematical Analysis and Applications. This journal was their first choice. The paper summarized the group’s research and recaptured work other researchers were doing that laid the foundation for their research. 

Cinzori hopes this research exposed undergraduate students to how real research works, so they can keep pushing the field of mathematics forward. After he finishes his Ph.D., Cinzori would like to become a professor and keep helping students dig deeper into mathematics research.