Abstract:  A multigraded ideal in a polynomial ring is called “Cartwright-Sturmfels” if it has a radical multigraded generic initial ideal. This notion originates from work of Cartwright and Sturmfels, and it has recently generated considerable interest due to some remarkable combinatorial and homological properties. In this talk, we will discuss the geometry of Hilbert schemes parametrizing Cartwright-Sturmfels ideals and exhibit a large class of smooth such Hilbert schemes. This is joint work with Ritvik Ramkumar.