# Unifying 4-Dimensional Knot Theory (19w5118)

Arriving in Banff, Alberta Sunday, November 3 and departing Friday November 8, 2019

## Organizers

(Indiana University)

(University of South Alabama)

This workshop proposes to develop a better understanding of knotting in dimension four. In this realm, loops can never be knotted -- there is simply too much room" in which to perform a smooth deformation. Instead, the interesting knotted objects are surfaces. One way to view a knotted surface is to imagine a knotted loop that evolves over time, although there are many ways to visualize these objects. We propose to bring together a variety of different perspectives in the theory of knotted surfaces; notably, we will connect classical decompositions with several brand new breakthroughs in order to formulate a more unified theory of knotted surfaces and spur a renaissance in this field of study.