4/10/2016

Day 2 of the Conference:

Solecki began the morning with an exposition on the Pseudoarc and projective Fraisse limits. In particular he realizes the Pseudoarc as a quotient of a portion of a projective Fraisee limit and uses the structure there to provide a proof of its homogeneity, I feel like I want to start a seminar on just Fraisse theory.

Next Martin Sabok talked about the topological conjugacy relation for Toeplitz subshifts. Lots of twists and turns with the results in this talk. Its also nice to see some of the more recent techniques of Jackon and Gao (and Seward and Khrone) being used by other people.

Bruno Braga talked about coarse and uniform embeddings. Banach spaces everywhere. The most exciting part of this talk for me was a clever retooling of the fact that you can extend maps continuously from closed sets to the whole space in the metric space setting. Its nice to see classics get respun.

Clinton Conley talked about one-ended subforests and treeability of groups. This and the previous were both chalk talks. There are the seeds of some very powerful techniques here.

I started running out paper here.

Steve Jackson then discussed the Borel combinatorics of Abelian group actions. This was a summary of recent work Jackson, Gao, and Khrone have put into this field. They have developed some pretty impressive/extendable  tools for studying the combinatorics of these actions. There are a surprising number of complications even at the hyperfinite level.

Samuel Coskey finished the morning off with a proof of a continuous logic version of the Lopez Escobar theorem. Continuous logic is super cool, and I'm pretty sure I am going to try and give an expositroy talk on just it for the GLG.

We then had lunch, and I started getting nervous in anticipation of my talk.

Robin Tucker Drob opened up the afternoon section talking about weak containment versus strong containment for group actions in the measure setting. There was a nice generalization of some older work here, along with what appears a good multipurpose lemma.

Next up was Simon Thomas, who attempted to embarrass us all with an exposition of some basic questions that we seem  to be unable to solve. I always enjoy it when Martin measures show up, and I think he did a good job of explaining why these problems are actually a bit hairy. Still, it is embarrassing to have simply statable, obvious-looking problems floating around without solutions.

I am now officially out of paper.

Peter Burton talked about Furstenburg entropy and its behavior under weak containment. There are some intriguing open problems here about what kinds of entropy a group can generate under different actions.

Andrew Marks defined a jump operation for Borel graphs in analogy with the jump operation for equivalence relations (not the Friedman-Stanley one). Cool result with some big hammers at play in the proof.

Cheng Chang showed that the problem of classifying continua is a universal orbit equivalence relation. The construction here, reducing the problem of classifying closed to classifying continua is quite clever.

Cody Dance then talked about the external ultrapower of HOD in L(R) via the club filter on omega_1. He is able to use this analysis to give a nice answer to a seemingly sticky combinatorial problem in L(R). Another nice interweaving of inner model theory and determinacy,

I ended the day with talk about my research. It seemed to go okay.

Then I got stuck at my layover...