**Quantization of fractional corner charge in C**

_{n}-symmetric higher-order topological crystalline insulatorsIn the presence of crystalline symmetries, certain topological insulators present a filling anomaly: a mismatch between the number of electrons in an energy band and the number of electrons required for charge neutrality. In this presentation, I will show how a filling anomaly can arise when corners are introduced in C

_{n}-symmetric crystalline insulators with vanishing polarization, having as a consequence the existence of corner-localized charges quantized in multiples of e/n. I will discuss the relationship between fractional charge and topological states and show how symmetry-protected, corner-localized topological states can exist even in the absence of an energy gap.Host: Jen