I will construct representations of various interesting
algebras (such as rational Cherednik algebras and quantized Gieseker
varieties) using the geometry of parabolic Hilbert schemes of points on
plane curve singularities. A connection to Coulomb branch algebras of
Braverman, Finkelberg and Nakajima will be also outlined. The talk is
based on a joint work with Jose Simental and Monica Vazirani.