4/09/2016

Day 1 of the conference. Lots of really good talks today, and an interesting diversity in material. Here are some thoughts on talks I got notes for.

Su Gao talked about non-archimedian Abelian Polish groups. Lots of really nice results and resolutions to some reduction problems.

Aristotelian Panagiotopolous talked about Menger compacta. There are some really interesting ideas here combining dimensional analysis with DST. More applications of Fraisse limits as well. I'm curious if these ideas can be extended into transfinite dimensions.

Kathryn Mann talked about automatic continuity for the homeomorphism group of a manifold. There were some tools presented here that I hadn't seen before. There is also a nice array of questions brought up by her results.

Richard Rast talked about tools for distinguishing isomorphism classes of countable models. There was some really creative uses of Scott sentences here, and the result feels like a breakthrough in this arena.

William Chan talked about an equivalence relation generated by admissible ordinals for reals. I wish he had more time. There was a lot of delicate set theory at play here. It was a very interesting synthesis of ideas.

Then there was lunch.

Joseph Zielinski talked about a proper he defined called locally Roelcke precompact. It is a natural generalization of a natural property with some interesting connections to locally compact spaces.

Martino Lupini talked about an object he has coined: the Lusky simplex. This one has a lot of functional analysis connections. Honestly this was significantly outside of my wheelhouse.

Konstantin Slutsky talked about different ways to categorize flows and how they interact with dimension. Allowing for the ignoring of very small sets, it turns out they are all essentially equivalent. I find this very unintuitive.

Konstantinos Beros explicitly defined some complete sets in the difference hierarchy. A really solid construction with tantalizing possibilities for generalization.

Aaron Hill closed the day out by applying the space of rank-1 transformations to reduce the complexity of problems in ergodic theory. It's been a trip watching him develop this theory over the years, and the tool he has created is kind of incredible. It will be interesting to see what else he has able to do in this direction.