My name is Ahmed, but a lot of my friends know me by 'kal'. (It's from my last name, Khalil, in case you were curious.)
I am currently a student at Rutgers University double majoring in Mathematics and Chemical Engineering.
So what else should you know about me?
Well, I love math... a lot. It's kind of nerdy, I know, but I genuinely find it beautiful and awe-inspiring. In fact, I love it so much that I am spending my summer studying mathematical logic under Dr. Grigor Sargsyan.
When I'm not doing math (it happens haha) I love to spend time with my family, exercise, travel, watch movies, and...(add other classic responses here haha)
I'm a fairly nice person, so if you want to reach out for whatever reason (such as asking me a question about logic), feel free to make use of the contacts section below :)
|Week One||My advisor, Dr. Grigor Sargsyan, and I had our first meeting in Brooklyn, NY, where we discussed my REU summer research project for the first time: “A Proof Of Hilbert’s Nustellensatz using Model Theoretic Techniques”. Since I had to give a presentation of the project to the REU coordinators, Grigor gave me a high level overview of what I should aim to have accomplished by the end of the REU. For the next several days I worked diligently on my presentation. I gave the presentation on Friday, June 5th.|
|Week Two||I met with my advisor once again. Between the two meetings that we had this week we were able to discuss the texts that I had begun reading on “Model Theory.” Grigor made sure that my foundation in logic was sound and that I had a comprehensive understanding of the definitions of first order languages, L-structures, theories, and so on. He then told me what I should be reading for our next meeting.|
|Week Three||After reading the relevant material, I met with my advisor again. We discussed Vaught’s Test and the notion of ‘Back and Forth,’ the colloquial phrase used to describe the technique for proving that the theory of dense linear orders (DLOs) is omega categorical. We then began to discuss quantifier elimination, which is a fundamental concept used in the proof of Hilbert’s Nustellensatz. I then began reading about proving that the theory of DLOs admits quantifier elimination.|
|Week Four||This week I discussed my reading on quantifier elimination in the theory of DLOs with Grigor. After helping me understand some of the concepts that were giving me trouble, we discussed the idea of complete theories. Grigor then suggested that I read about proving that the theory of divisible abelian groups (DAG) admits quantifier elimination. We also discussed the fact that many books on model theory were written with the primary audience intended to be graduate students or the like. Grigor suggested that if I had time I should attempt to make a series of lecture notes that would be comprehensive for the undergraduate reader.|
If you'd like to reach me just shoot me an email and I will get back to you as soon as possible.