Mathematics Colloquia and Seminars

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Description

One unifying theme of low-dimensional topology is the use of diagrammatic descriptions and decompositions to translate questions in smooth topology into combinatorial data. Knotted 2-dimensional spheres in 4-dimensional space have been known to exist for more than a century (see Artin's work from 1925). During this era, numerous techniques have been used to describe these knotted embeddings, such as movies of knots, broken surface diagrams, braid charts, and (more recently) triplane diagrams. The goal of this talk is to provide insights into the different types of diagrams and explain how to move between them. I will show how ideas in dimension three can be lifted to concepts in knot theory in dimensions four and FIVE dimensions. The background for this talk will be minimal as I will introduce all the necessary concepts and show lots of pictures.