For "homework" read chapters 1 and 2 of Topology: A Categorical Approach and attempt the following:
We'll start to follow along with the Albin lectures (found here). For the 10th, aim for listening to the first two lectures + whatever supplemental reading you think might be relevant / helpful from Hatcher (link).
Instead of assigning problems, look at Albin's homework #1 (link) and choose one you think might be tractable to work on. As usual we can discuss on slack or via ad-hoc meetings in the upcoming weeks.
Cheng hasn't assigned any homework.
In preperation for Dr. Jean-Eric Pin's lecture on the Generalized Star Height Problem, we will discuss the following concepts:
No need to prep for this one. Max will use the Collatz Conjecture (which he surely will not resolve) as a motivating example for a tutorial on Ivy, and more generally, on formal methods and inductive invariants.
Read chapter 2 through section 2.6 (Nets) of Infinite Dimensional Analysis: A Hitchhiker's Guide. We will discuss the covered topics.
Read through section 2.8 (Compactness) of Infinite Dimensional Analysis: A Hitchhiker's Guide. We will discuss the covered topics.