## Title: #

How Many Different Unknots Are There?

## Abstract: #

A knot is defined mathematically as a closed non-self-intersecting curve in three-dimensional space, and as mathematicians we would like to know how many different knots exist. That is a hard question. So instead, we can ask the question, how many different knots exist that have no crossings? In classical knot theory the answer to this question is not interesting since there is only one. However, when we restrict ourselves to specific knots called Legendrian knots, the answer becomes that there are infinitely many which was proven by Yakov Eliashberg and Maia Fraser in 1995. In this talk, we will explore this question and see why there are infinitely many Legendrian unknots. The talk is designed for any undergraduate student who is interested in math.