Luis Núñez-Betancourt: D-modules, Bernstein–Sato polynomials and numerical invariants over direct summands

Direct summands of regular rings play an important role in the interactions between commutative algebra, algebraic geometry, algebraic combinatorics, and representation theory. For instance, rings associated to toric, determinantal, Grassmannian, Veronese, and Segre varieties are direct summands of polynomial rings. In addition, invariant rings under certain group actions also belong to this class of rings. In this talk we will discuss structural properties of certain D-modules over direct summands in characteristic zero and prime. We will also see consequences for the Bernstein–Sato polynomial. Time permitting, we will discuss properties of log-canonical thresholds and the F-jumping numbers for this family of rings. This is joint work with Josep Àlvarez-Montaner and Craig Huneke.