USask PIMS Geometry and Physics (GAP) Seminar: Puttipong Pongtanapaisan

Back in the old days, before the invention of Apple Wireless Airpods, people were more familiar with the tendency of the headphones in their pockets to become knotted. It seems natural to expect that the probability that a random curve is tangled increases with its length. In fact, Frisch, Wasserman, and Delbrück conjectured that sufficiently long ring polymers will be knotted with high probability. In this talk, I will discuss some models where the conjecture is known to be true, including a setting that I investigated with Jeremy Eng, Chris Soteros, and Rob Scharein. Topological techniques used in the proofs such as finite-type invariants will also be discussed.