Presenter: Sanskriti Timseena, College of Arts and Sciences/ Honors College, Mathematics
Authors: Sanskriti Timseena
Faculty Advisor: Kenan Ince, College of Arts and Sciences, Mathematics
Institution: Westminster College
Knot Theory has countless real-world applications: physics, biology, cryptography are just a few examples of fields that use the tools and language of knots. Mathematical knots are closed, non-self-intersecting curves that live in 3-dimensional space. A generalized crossing change on a knot involves taking an even number of strands, cutting them open, twisting the cut up strands and glueing them back together. A simple crossing change is when only two strands are used and twisted round once. The enzyme Topoisomerase II is known to perform a sequence of crossing changes in knotted DNAs to simplify them. Our research project focused on strategies to untie and classify knots. We also collaborated to develop software able to graphically manipulate knots. From previous research, we are able to find the untwisting number of any knot by using its Goeritz matrix. Using this algorithm, we attempted to classify and untwist the 9_35 knot. We collaborated with professor Frank Swenton of Middlebury College to explore the possibility of using software to untwist the 9_35 knot.