Boston Computation Club - Math Café

Café #1 - January 20

For "homework" read chapters 1 and 2 of Topology: A Categorical Approach and attempt the following:

• 1.1 draw examples
• 1.3 check Zariski Topology property
• 1.10 prove quotient topology characterized by given universal prop
• 2.2 prove or disprove a local consistency property
• 2.9 proof about locally compact Hausdorff spaces
• 2.15 prove or disprove a compactness property
• Optionally, exercises: 1.11, 2.21

Café #2 - February 10th at 1:30-2:30pm EST

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.

Café #3 - Selected Topics in Kleene Algebra

Cheng hasn't assigned any homework.

Café #4 - Prep for Jean-Eric Pin's Lecture

In preperation for Dr. Jean-Eric Pin's lecture on the Generalized Star Height Problem, we will discuss the following concepts:

1. first order logic
2. words and languages
3. finite deterministic automata
4. regular expressions
5. monoids
• free monoids
• monoid morphism
6. metric spaces
   • completion of a metric

Dr. Pin has provided us with some hand-written nodes which we can use as a resource.

Café #5 - The Collatz Conjecture, in Ivy

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.

Café #6 - Infinite Analysis & Nets

Read chapter 2 through section 2.6 (Nets) of Infinite Dimensional Analysis: A Hitchhiker's Guide. We will discuss the covered topics.

Café #7 & #8 - More Infinite Analysis

Read through section 2.8 (Compactness) of Infinite Dimensional Analysis: A Hitchhiker's Guide. We will discuss the covered topics.