Talk - Model Theory and You
09 Oct 2020 -
Today I gave my first talk at my new department. I was pretty nervous going into it for a few reasons. Obviously giving your first talk at a new institution is going to be stressful. This was going to be my introduction to a lot of the older grad students, and I really wanted to make a good first impression. This was also my first zoom talk, and my first proper talk using pre-made slides. I typically take a more improvisatory approach to my talks, and I plan out 4-5 different (similar) talks, and change what I’m presenting based on audience interest and time constraints. Since I almost always give blackboard talks, it’s easy to introduce or omit an example on the fly without my audience catching on. This is not unlike many magic tricks I perform where the ending depends on the spectator’s choices. Since the audience hasn’t seen the trick before (or the talk, in this case) you can totally change the ending without anyone knowing. Of course, this goes out the window when you’re writing slides in advance. If you skip an example, your audience sees you skip past a few slides. I’m glad I’m getting experience with this more structured setup, but it’s still out of my comfort zone. It forces you to, basically, set the talk in stone, and I’m worried that what I set will not live up to my expectations. Thankfully, in this instance, the talk was extremely well received. I’m trying to convince my department to care more about logic, and it seems this was a good first impression for both me and the subject I’m evangelizing. If anyone is interested in seeing the slides, I’ve attached them to this post.
Model Theory and You: Infinite Proofs for Free
Model Theory is the branch of mathematical logic that deals with “truth” in axiomatic structures. Perhaps surprisingly, Model Theory is extremely insensitive to the notion of cardinality, and we can leverage this insensitivity to prove infinite theorems by considering only finite objects. In this talk we will discuss the fundamentals of Model Theory, as well as the Logical Compactness theorem, which we will use to prove theorems in combinatorics and algebra. Time permitting, we will state the Lowenheim-Skolem Theorem, and outline some potential applications.
You can see the GSS page here, and the talk slides here. I’ve since noticed some simple typos, and I think I can probably do a better job explaining the Tarski-Vaught Theorem. But I’m leaving these in for posterity (and laziness).