Let $S\subset {\rm Sh}_K(G,X)$ be a connected component of a shimura variety, and let $V\subset S$ be a subvariety. As an analogue of the toric and abelian setting, a subvariety $W\subset V$ is called anomalous if there exists a weakly special subvariety $A\subset S$ containing $W$ such that
$$\dim W > \max\{0, \dim A+\dim V-\dim S\}.$$
Let $V^{\rm oa}$ be the complement in $V$ of the union of all anomalous subvarieties of $V$. In this talk, we will explain how to prove the openness of $V^{\rm oa}$ by using o-minimality theory.

This is joint work with Christopher Daw.