\noindent suppose we view the three-dimensional sphere as: $s^3 = \{(z,w) \subset \mathbb{c}^2|\ |z|^2 + |w|^2 = 1\}. $ if we are given a complex curve $v_f = \{(z,w)|0 = f(z,w) \in \mathbb{c} [z,w]\},$ we can then examine the intersection $k = v_f \cap s^3.$ in the transverse case, this intersection $k$ will be a link i.e. an embedded one-manifold in the three-sphere. this talk will be interested in the question: question: which links can arise from complex curves in the above manner? i will discuss the history of this problem, focusing first on the case where $f(z,w)$ has an isolated singularity at the origin where the question is completely answered. i’ll then discuss how a powerful set of knot invariants defined by ozsvath and szabo and independently by rasmussen using the theory of pseudo-holomorphic curves can provide information on the above question. more precisely, ozsvath and szabo and rasmussen defined a numerical invariant of knots, denoted $\tau(k)$, which we show provides an obstruction to knots arising in the above manner. more surprisingly, suppose we focus on knots whose exteriors, $s^3 - k$, admit the structure of a fiber bundle over the circle, the so-called $fibered$ knots. in this case we show that $\tau(k)$ detects exactly when a fibered knot arises as the intersection of the three-sphere with a complex curve satisfying a certain genus constraint. our proof relies on connections between ozsvath-szabo theory and certain geometric structures on three-manifolds called contact structures.