Irena Swanson, Purdue University

**Date**: Thursday, February 23, 10:30 am.

**Abstract**

Primary decompositions are a basic tool in commutative algebra, but they also arise in other contexts. In this talk I will discuss some connections with algebraic geometry, partial differential equations, algebraic statistics, and computational complexity. Determinants of n x n matrices can be computed in polynomial time, whereas the computation of permanents is #P-complete. On the algebra side, in polynomial rings the ideals generated by determinants have a simpler and nicer structure than those generated by permanents, and in particular, the determinantal ideals are prime ideals whereas the permanental ideals have many primary components. This is one instance in which primary decompositions capture a computational difficulty. Other instances have to do with the Castelnuovo–Mumford regularity and numbers of associated prime of powers of ideals. I will touch on the 2016 work of Jason McCullough and Irena Peeva producing a family of counterexamples to the Eisenbud–Goto conjecture and simultaneously to the Stillman question and a Bayer–Huneke–Stillman question. I will finish the talk with my work with Jesse Kim on the complexity of primary decompositions of second powers of prime ideals and more recent work with Rosie Rissner on fluctuations of numbers of associated primes of powers of ideals.

**Place**: Celis multipurpose room- C-116

**Research interest**

Commutative algebra. She is also a creator of mathematical quilts, and is the inventor of a quilting technique, “tube piecing”, for making quilts more efficiently. She has published over 60 articles and written three books.

**Note**: speaker will be available to the entire community for questions and to socialize on

- Wednesday 22, 3:30 – 5:00 pm at Celis 202
- Thursday 23, 9:00 – 10:30 am at Celis 119
- Friday 24 9:30 – 11:00 am at Celis 206