Symbolic powers of ideals, Part 1

The symbolic powers of an ideal is an algebraic construction that encodes important information about its underlying algebraic variety. Symbolic powers are related to several important theorems and theories from different areas of mathematics, ranging from Krull’s principal ideal theorem in algebraic geometry, to the theory of evolutions in relation with Fermat’s last theorem.

In the first talk, I will introduce the notion of symbolic powers and discuss some of its basic properties. In the second talk I will present some results originating from my research. In particular, I will show connections with algebraic geometry, combinatorics, and linear optimization.