** Title: **
Smooth affine varieties, cotangent bundles and the growth rate of
wrapped Floer cohomology

**Abstract:**
Any smooth affine variety has a symplectic structure obtained from its embedding in complex affine space.
We show that many cotangent bundles are not symplectomorphic to smooth affine varieties. For instance this is true for cotangent bundles of simply connected n dimensional manifolds whose Betti numbers are greater than that of the n-torus. Other examples include manifolds whose fundamental group growth rate is faster than any polynomial of degree n. To prove this we use a tool called the growth rate of wrapped Floer homology which assigns a number to any pair of well behaved Lagrangians.