UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

April 10, 2018

939 Evans Hall


3:45PM: Random monomial ideals and their homological properties

Lily Silverstein

Randomness is an important tool in algebra, especially from an algorithmic perspective. I will discuss our recent work looking at the random behavior of monomial ideals. We describe several random models, inspired by earlier models for random graphs and random simplicial complexes, and give results on properties such as Hilbert function and Krull dimension. We also prove "threshold behavior" in the model parameters. In this talk I'll focus on properties related to the minimal free resolutions of random monomial ideals, in particular projective dimension, Cohen-Macaulayness, and genericity/the Scarf complex. I'll also discuss some open problems and ongoing work.

3:45PM: Random monomial ideals and their homological properties

Lily Silverstein

Randomness is an important tool in algebra, especially from an algorithmic perspective. I will discuss our recent work looking at the random behavior of monomial ideals. We describe several random models, inspired by earlier models for random graphs and random simplicial complexes, and give results on properties such as Hilbert function and Krull dimension. We also prove "threshold behavior" in the model parameters. In this talk I'll focus on properties related to the minimal free resolutions of random monomial ideals, in particular projective dimension, Cohen-Macaulayness, and genericity/the Scarf complex. I'll also discuss some open problems and ongoing work.

5:00PM: Liaison among curves in P3

Ritvik Ramkumar

In this talk we will study the equivalence relation generated by linked curves in P3. In particular, we will define the Rao module and show that (up to shifts and duals) it completely determines an equivalence class. Time permitting we will study curves that are cut out by three surfaces.

Return to Seminar Listing