Pinched Veronese rings are an example of affine semigroup rings that are formed by removing a generator of a Veronese subring of a polynomial ring. One of the first examples of a non Cohen-Macaulay ring comes from this family, and so natural questions abound about the local cohomology modules of such rings. In joint work with Vaibhav Pandey, we study homological properties of these rings, including the Cohen-Macaulay, Gorenstein, and complete intersection properties. If the underlying field is of prime characteristic, we also find that nearly all pinched Veronese rings are F-nilpotent, a new singularity type of recent interest. https://arxiv.org/abs/2111.05810 Speaker(s): Kyle Maddox (University of Kansas)