Yesterday I attended the Google I/O Extended event at Google NYC. I used to work there prior to graduate school, so it was great to be back there. I got to see some interesting tech talks, meet up with old friends from Google, and watch a live stream of the keynote.

When I got there, they had coffee and breakfast for everyone, so I happily helped myself to some while checking out the swag they gave us and snapping some pictures:

# Enayat Models – ASL 2016

I will be contributing a session at the ASL 2016 North American Annual Meeting, on Wednesday, May 25 at 4:45 PM.

Abstract: Simpson used arithmetic forcing to show that every countable model $\mathcal{M} \models \textsf{PA}$ has an expansion $(\mathcal{M}, X) \models \textsf{PA}^*$ that is pointwise definable. The natural question then is whether this method can be used to obtain expansions of (countable models) with the property that the definable elements of the expansion coincide with the definable elements of the original model. Enayat later showed that this is impossible. He proved that there are models with the property that every expansion upon adding a predicate for an undefinable class is pointwise definable. We call models with this property Enayat models. It is easy to iterate Enayat’s construction and obtain other models with this property. Elementary submodels of any Enayat model formed in this way are well-ordered by inclusion. I will present a construction of an Enayat model whose elementary substructures form an infinite descending chain.

# Pi5NY Math Competition

This past weekend, I had the opportunity to volunteer at the AMS Pi5NY Math Tournament. This tournament is held annually, open to middle schoolers in any of the 5 boroughs of NYC.

Students worked in teams of 5 on a set of 40 problems. I was a judge for two 8th grade teams. When one of the students finished a problem, they would come to me and I would check their answer, and then send them off to the scorers if their answers were correct.

It was a lot of fun and great to see so many young people enjoying math on a Saturday morning!

# Welcome to my site!

I will be using this site to announce upcoming talks, discuss interesting problems that I am working on, and for anything else that might be on my mind.