Sofia Alexovičová – DIMACS REU 2026

Week 1

Following our arrival at Rutgers and the program orientation, I met online with my mentor, Filippo Calderoni, to discuss the direction of the project. I then began studying the Dr. Calderoni's lecture notes on orderable groups and worked on some of the exercises.

Week 2 (6/01-6/05)

On Monday, I met with my advisor to discuss my slides for Tuesday's introductory presentation about the project. On Thursday, I went over some of the exercises that I had been working on with Dr. Cecelia Higgins. I continued with reading the lecture notes.

Week 3 (6/08-6/12)

This week, I finally met with my mentor in person. We decided to begin by studying left-orders on the fundamental group of the Klein bottle and proving that there are only four of them, with the goal of later proving this for bi-orders on Baumslag–Solitar groups. However, after our second meeting of the week, I found a mistake in our proof, so I spent the rest of the week trying to fix it and make it work, but without much success.
On Saturday, I visited Princeton with Esmé and Sofia T to meet our mentor. I am very grateful to Dr. Calderoni for organizing this wonderful trip.

Week 4 (6/15-6/19)

I managed to fix the proof for the Klein bottle group and modified it to fit the Baumslag-Solitar group, but this time for bi-orders.

Week 5 (6/22-6/26)

This week was spent by polishing and typing up all of the proofs so far and reading more about Conradian orderings. On Friday's meeting with Dr. Calderoni, I was given papers by A.H. Clifford and V.V. Bludov about a construction of a nonabelian and nonsimple group, which is uniquely orderable. That is, it admits only two linear orders that are mutually inverse.

Week 6 (6/29-7/02)

Week 7 (7/6-7/10)

Week 8 (7/13-7/17)