## Complexity of elliptic functions and the maximal compact subgroup of certain anti-affine groups.

#### Harry Schmidt (Oxford)

For any lattice in $$\mathbb{C}$$ Weierstrass constructed a meromorphic function $$\wp$$ that is periodic with respect to that lattice. This function satisfies the infamous differential equation $\dot{\wp}^2 = 4\wp^3 -g_2\wp - g_3.$
Macintyre discovered that the real and imaginary parts of the inverse of $$\wp$$ can be locally defined by a Pfaffian chain of differential equations. In this talk we will discuss how to express the graph of the real and imaginary parts of $$\wp$$ as zero-sets of a fixed explicit number of functions that are part of a Pfaffian chain of fixed complexity.