PCMI: Week One

The front entrance to the Hotel der Baer, featuring the titular accordion-playing bear, and Corey Manack (Franklin & Marshall).

The front entrance to the Hotel der Baer, featuring the titular accordion-playing bear and Corey Manack (Franklin & Marshall).

I have just finished (survived?) the first of my three weeks at the Park City Math Institute. The research topic this year is “Geometry of Moduli Spaces and Representation Theory.” ¬†For those of you not in the know, PCMI is an annual summer program sponsored by the Institute for Advanced Study, which brings together undergraduates, graduate students, secondary and post-secondary teachers, and researchers. It is a huge crowd and for me it has been very exciting to be around so many people who are interested in different facets of mathematics and mathematics education. I have mostly interacted with my group, the Undergraduate Faculty Program, but I have slowly been meeting people from all of the other groups. Our schedule has been jam-packed with exciting things, and in this post I will summarize some of them.

This year the IAS/PCMI changed locations from Park City proper to the Zermatt Resort near Midway, UT. I have heard from the organizers that there have been small hiccups, but from my point of view the transition is going smoothly. One of my fellow UFP members and second-time attendee described the new location as “better locally but not globally”, in the sense that the resort itself has many nice amenities, but it is harder to get to other places. I have certainly enjoyed the pool and the gym, but I did take several hours going to dinner in Midway and coming back, and missed a workshop I wanted to attend in the process. However, there are free shuttles and other ways of getting places, so it’s not too bad. And the view from my room is pretty great.

My group is being led by the very awesome (and fellow AMS blogger) Dagan Karp. We are learning some new math (algebraic stacks, oh my) and new pedagogy (critical education theory), which seems like a really great balance for a group of faculty at primarily undergraduate institutions. I am finding that the math and the pedagogy are both challenging and interesting, so I am really enjoying doing my homework (and I hear my teenage self say “NERD!”). I am still learning about both of these, so I think there is a better blog post that delves into these two topics at the end of this program. Stay tuned for that!

Tom explains moduli spaces.

My compatriot Tom Garrity (Williams College) explains moduli spaces.

There are also lots of cross-program activities, and we are invited to attend the research talks and the undergraduate lectures (although many of these conflict with our own schedule). I really enjoyed attending the first two lectures of Tom Garrity‘s undergraduate course on moduli spaces and representation theory. I love going to talks like these, because even if I know the material I love seeing how other people teach it. Tom is a particularly lively and entertaining lecturer, so it was a real treat. I stopped going mainly because I needed more time to do my increasingly more difficult homework. The students seemed to be really into the talks and material, and I really regret not pressuring any of my own students into coming (but I will certainly pressure them in the future!). And for some little-known Tom Garrity trivia: Tom, like myself, was born in Caracas, Venezuela!

Evelyn Lamb (University of Utah) tells us about mathematical writing.

Evelyn Lamb (University of Utah) tells us about mathematical writing.

The cross-program activities included a talk by Fields medalist Andrei Okounkov, which I did not really follow (mainly because I was sitting too far back and I really need to check the prescription of my glasses… which is a stupid excuse), an excellent talk about mathematics writing by my fellow AMS blogger Evelyn Lamb, and a very cool talk by Henry Segerman about making 3D models of 4D objects. I think by the end of each talk both Evelyn and Henry had several hundred new twitter followers.

In Evelyn’s talk, it was fun to see people pulling up her Scientific American blog while she was talking, and afterwards I heard several of the younger participants commenting on their brand new blogs. I think she did an excellent job explaining why writing mathematics for a general audience is important, and how one could go about doing it. Evelyn also had a Q&A session later in the evening, and people asked some really interesting questions about the writing process.

Henry Segerman (Oklahoma State University) shows us 3D models of 4D things. More fun than a barrel of monkeys!

Henry Segerman (Oklahoma State University) shows us 3D models of 4D things. More fun than a barrel of monkeys!

Henry brought lots of models for people to play with, and gave us some live demonstrations of his stereographic projection models. I still haven’t tried it, but his hypernom project, a collaboration with Vi Hart and Andrea Hawksley, looks like a real time suck (in a good way!). He recommended trying it on a tablet, since it reacts to motion (and then you can really feel like a hungry four-dimensional being). Henry did a 3D printing workshop last Friday and will be doing some more throughout next week, and I’m hoping to be able to go to one (so stay tuned for that as well).

The PCMI organizers are also good at organizing other activities. In particular, there were shuttles and buses to Park City all day Saturday so that participants could attend the Fourth of July festivities. I went for the parade with a few other people. This was my first 4th of July parade, so I have nothing to compare it too, but I thought it was pretty fun. My favorite floats were the triathlon training one (featuring actual people biking, running, and swimming!) and the PCMI party, which seemed more like a political rally for math, with whimsical signs like “Linear Independence Day”, “July 4th Dimension”, and my favorite, “Manifold Destiny”, and a giant Tangram of the US map.

It is hard to believe it’s only been a week! Anyway, I should get back to doing my homework for tomorrow. Like I mentioned above, stay tuned for two or more future PCMI posts. Happy linear independence day!

The PCMI float at the Park City 4th of July parade.

The PCMI float at the Park City 4th of July parade.

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