## Department Colloquium

### Friday, April 16th, 2021

**Time:** 2:30 p.m. **Place:** Online (via Zoom)

**Speaker:** Michael Perlman (Queen's University)

**Title:** Measuring hypersurface singularities via differential operators and Hodge theory.

**Abstract: ** Given a polynomial with complex coefficients, its set of zeros is a geometric object known as an algebraic hypersurface. We will discuss two invariants defined via differential operators that can detect and measure singularities of these hypersurfaces: the Bernstein-Sato polynomial and the Hodge ideals. Via the example of the hypersurface defined by the n x n determinant, we will illustrate that these invariants are two sides of the same coin: the mixed Hodge structure.

**Michael Perlman** is Coleman Postdoctoral Fellow in the Department of Mathematics and Statistics at Queen's University. He obtained his Ph.D. in Mathematics in May 2020 from the University of Notre Dame. His research is in Algebraic Geometry, Commutative Algebra, and their interactions with Representation Theory.