I will give two talks that should be about 30 minutes each. The first is to help prepare for the Octoberfest in Ottawa next weekend, while the second is the talk I gave at the AMS meeting in Baltimore in Jan., 2014. This is all joint work with John Kennison and Bob Raphael. Titles and abstracts of each follow:

1. Limit closures of some full subcategories

The three subcategories are:

1. Metric spaces inside the category of separated uniform spaces.

2. Integrally closed domains inside the category of commutative rings.

3. Integral domains inside the category of commutative rings.

2. Completions of subcategories of domains

The subcategories of domains include the 2nd and 3rd above, as well as many others. The central hypothesis is that every domain lies inside a field belonging to the subcategory in question.