Teaching

I worked as a grader and\or instructor in the following classes: Linear Algebra I & II, Analysis I & II, Discrete Mathematics, Set Theory I, and Analysis for Physicists. 

I have also served as a teaching assistant in Mathematical Logic I, and in Set Theory I.

Open problem

Sierpinski's conjecture: in 1914, Mazurkiewcz deployed the well-ordering theorem in order to construct a subset of the plane which intersects every straight line exactly twice. Sierpinski (who was his PhD advisor) then asked whether there exists a Borel subset of the plane with this property (which would hopefully mean a more hands-on approach in the construction). 

There have been many attempts to get insight as to the possible existence or inexistence of these so-called two-point sets, of which I note a few. Larman proves that a two-point set cannot be Fσ (a countable union of closed sets), the strongest result directly towards the conjecture (as far as I am aware).  Miller proves that assuming the constructibility axiom, there is a coanalytic  two-point set (that is, the complement of a coordinate projection of some Borel set in 3-space). He (and independently Chad, Knight and Suabedissen) show that there is a model of ZF set theory in which one cannot well-order the reals but which contains a two-point set (proving that the strength of the full well-ordering theorem is unnecessary). Chad, Knight and Suabedissen also prove in that paper that assuming the continuum hypothesis, there exists a countable set of concentric circles in the plane which contains a two-point set (from which it follows that it must be Lebesgue-measurable), and a result of Schmerl says that any sequence of concentric circles with radii approaching infinity contains a two-point set (unconditionally).

We note that a slight modification of the original proof yields a Lebesgue two-point set.

Chess

The following is my favorite chess game, which I think everyone who is interested in the game should review. It was played between Alireza Firouzja and Hikaru Nakamura on Chess.com in 3+0 blitz.

1. e4 e5 2. Nc3 Nc6 3. Bc4 Bc5 4. Qg4 Qf6 5. Nd5 Qxf2+ 6. Kd1 Kf8 7. Nh3 Qd4 8. d3 d6 9. Qf3 h5 10. Ne3 Nf6 11. Ng5 Bg4 12. Nxg4 hxg4 13. Qe2 g3 14. Nxf7 Rxh2 15. Rf1 Qf2 16. Rxf2 gxf2 17. Qf1 Nh5 0-1

A video review is also available.