Ava Ostrem's REU 2025 Web Page

About Me

Name: Ava Ostrem
Email: ava.ostrem (at) rutgers.edu
Office: CoRE 448
Home Institution: Rutgers University - New Brunswick
Project: Compactness in the Mathematical Universe
Mentor: Prof. Filippo Calderoni

About My Project

Large cardinals axioms postulate the existence of combinatorial properties of infinity. These axioms are far beyond the usual axioms of mathematics and expand the burden of the mathematical universe. A well-studied consequence of large cardinal axioms is compactness. Compactness denotes the extent to which mathematical structures are determined by their local behavior. We will examine some famous compactness properties for algebraic structures and investigate new ones.

Research Log

Week 0: May 27-May 30

I'm going to start counting the weeks at zero to keep in the set theory theme. We moved in to the dorms on Tuesday and had orientation on Wednesday. I started reading Chapter II of Ekler and Metlof's Almost Free Modules for some set theory background. I also set up my website on Friday and felt very accomplished for 'shelling into the server'.

References & Links

Here are the papers and books I have read for my project:
  1. Almost Free Modules, Ekler and Metlof