Proposal F18 Student Vinal

Sponsored Research Newsletter Fall 2018

Student Spotlight - Greg Vinal '19, Mathematics, Mosiac Knots

WHAT IS YOUR PROJECT?My project is finding all the prime knot mosaics that fit on a 6x6 grid. Now, that’s a loaded description, but in simpler terms we’re trying to find all the drawings of knotted up loops that can fit onto a grid of a given size. Once we’ve found all the knots for a 6x6 grid, which is the main crux of this research, we hope that we can generalize our program to find all knots on a 7x7 grid and so on. This way, if we were given enough time and computational power, we could find all the knots that could fit on any size grid.
HOW IS YOUR PROJECT FUNDED? My project is funded by the Geneseo Foundation Undergraduate Full-time Summer Fellowship.
WHAT DID YOU HOPE TO GAIN FROM WORKING ON THIS PROJECT? I hoped to get a deeper understanding of knot theory and sharpen up my code writing, which I think I have accomplished.
IS THERE ANYTHING THAT HAS SURPRISED YOU?
The one thing that surprised me was how many possibilities there were for knots on a grid. Most computing that I’ve done can be run in a matter of seconds, but the amount of possibilities and computations needed really helped me to appreciate how many possibilities there were and how necessary it was for computers to check the possibilities.
HOW HAS WORKING ON THIS PROJECT IMPACTED YOUR LONG TERM PLANS? My aim is towards graduate school at this point, and I think that this project has helped me to attain that goal as well as give me deeper insights into what math research looks like. This was both substantive and accessible for an undergraduate student.
WHAT HAVE YOU ENJOYED THE MOST? I really enjoyed working with Dr. Heap and doing actual research, which was really gratifying and I enjoyed making math rather than learning about it, so to speak.
WHAT ADVICE DO YOU HAVE FOR OTHER STUDENTS WHO MAY BE INTERESTED IN WORKING ON A RESEARCH PROJECT? I would say that students should talk to their professors and get to know them. They’ve been doing research for a long time and they can help guide you through the difficult aspects of the research.