Topology Seminar

Morten (an IST intern turned into PhD student) asked me to teach him the basics of topology.  I had forgotten that I agreed to this, until he reminded me when I returned to Austria earlier this month.  Filip also expressed interest in learning topology.  So, I set up a seminar so that I can teach him topology in about one month’s time.  When Novi caught wind of this, he signed up as well.  So now, I have 3 students in my topology seminar.

The goal of the seminar is to get them familiar with the fundamental tools that a Topologist uses. I will lecture a little bit, but will use most of the time to work on problems together.  Since Herbert is teaching a Geometry/Topology class in the Spring, I am alleviated from teaching Homology and Persistence.   I decided to start with the basics, in point set topology.  The minimal goal is to get to the fundamental group.  We’ve had two sessions so far and we’ve made it through the first chapter of Munkres’ topology.  At the end of the last seminar, I ended with the definition of a topology (and refused to tell them why the definition allows infinite unions but only finite intersections of open sets).

Tomorrow we’ll take a little bit of a detour from my plans to talk about Category Theory.  The topic came up at the end of the last lecture, so I thought it would be appropriate to introduce it in this class.  We’ll also look at some of the examples of topological spaces  (including the torus of course!)

Hopefully I don’t torture them too much with these seminars, but they asked for it, right?.  (A note to Novi who I know reads this: there will be a quiz tomorrow since I know you didn’t do your reading to catch up).

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