*Joel Foisy (SUNY Potsdam) - Intrinsic linking and knotting in directed graphs*

*January 23rd, 4:00 PM, Innovation E105*

**Abstract:** *Hugh Howards asked if any directed graphs are intrinsically linked, meaning that for every spatial embedding, there exists a non-split pair of linked cycles that are both consistently oriented. In 2015, J.F., Hugh Howards, and Natalie Rich showed that the double of K6 is an intrinsically linked directed graph. One can further ask if there are intrinsically knotted directed graphs (contain a consistently oriented cycle that is knotted in every spatial embedding). Fleming and J.F. showed that such a graph does exist. Fleming and J.F. have also made some progress in determining which tournaments (oriented complete graphs) are intrinsically linked (knotted).*