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27/06/2017, 15:00 — 16:00 — Room P3.10, Mathematics Building

Louis H. Kauffman, *University of Illinois at Chicago*

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Knotoids and Virtual Knot Theory

Knotoids are open-ended knot diagrams whose endpoints can be in different regions of the diagram. Two knotoids are said to be isotopic if there is a sequence of Reidemeister moves that connects one diagram to the other without moving arcs across endpoints. The definition is due to Turaev. We will discuss three dimensional interpretations of knotoids in terms of projections of open-ended embeddings of intervals into three dimensional space, and we shall discuss a number of invariants of knotoids based on concepts from virtual knot theory. Knotoids are a new branch of classical knot theory and they promise to provide a way to measure the “knottiness” of open interval embeddings in three space. This talk is joint work with Neslihan Gugumcu.