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Research Blog:

I post on my current research, topics of interests, ideas for future projects, and solutions of textbooks I am currently working through. You can subscribe to the right for updates!

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  • Writer's pictureAlex Cassem

Wow, my last post on my blog was a little over 6 months ago, and well, a lot has happened since. First, I moved to Medford, MA (north of Boston) to attend Tuts University for graduate school in cosmology and theoretical physics. (I am a doctoral/PhD student). I am taking the normal courses you would think one would take as a first year, quantum theory 1, electromagnetism 1, and classical mechanics, but I am also taking a fourth class, quantum field theory 1 (or advanced quantum mechanics as it is called in Tufts' course catalog). This has been rather challenging, and I am hanging on by a thread (grade wise with respect to getting at least an A-). This has been eating up a lot of my time. However, I have found time for some of my other hobbies.

I have been working on solutions for Nakahara's textbook, but have only had time to complete two chapter worth, chapter 3 and 4 but I wanted to be thorough since it is completely new mathematics that I have never been exposed to. That is linked below this paragraph. It has started to become quite a large file due to all the images I had to create for chapter 4 (you will see what I mean).

geometry and topology solutions
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Download PDF • 16.12MB

I have also been taking advantage of the area I am living in, namely Harvard is right next door (20 minute bike ride max) over in Cambridge, and MIT is about another 10 minutes over south of Harvard (or a 30 minute travel all together). There is also the subway which connects both of them quite quickly, and, if the (for the love of god) Green line construction finally finishes near Tufts, then you can ride the Green line from Tufts (Medford) to Park street (Boston Commons), then back up the Red line to Kendall/MIT then Harvard. (I am explaining this in detail since, well, coming from a town of ~9k people, this is pretty cool).

I also went to visit Salem, since it is practically next door, and the witch trials, in a pure curosity sense, is pretty neat and cool. But then I got distracted and went to visit a pirate museum as well for most of my time there.

Finally, with respect to research, I have not had much time at all, namely because any of the topics I would like to get into require a large learning curve. So, I have been tackling that, and trying to find a good problem that is still within string and/or string-cosmology, that I can attempt now. I think I have found possibly two, but we shall see over winter break. And speaking of winter break, I already have my work cut out for me so that I can take a "special class" during the spring, but for now I will keep that under the wraps. Otherwise, I hope everyone had a great summer, and is surviving this fall semester or fall in general for those not in academia.

  • Writer's pictureAlex Cassem

Good (morning/afternoon/evening), it has been quite some time since I last posted or even updated my blog. But, now that summer is finally here, I (might) have the time to do the activities that I enjoy: reading, learning more physics, maybe make a research outline for my first year of graduate school (and start it)...

So, if you can't tell, I have goals for this summer. One of them is to complete one or two textbook solutions, primarily, the ''Geometry, Topology, and Physics 2nd edition'' textbook by M. Nakahara since. So far, out of the 14 chapters that are in the book I have completed (drum roll) 2.... The end of the semester was quite hectic due to finals, wrapping up research projects to a good point, and finalizing my travel plans to Boston to visit Tufts (and determine a place to live). I also gave a presentation there (in where I will update this post later to have the link), I will attach slides at the end of this post, as well as a few photos of my trip.

Finally, I will also post the two chapters I have finished of Nakahara's textbook at the end of this post. Cheers to a good summer and a good time in the month of June!

tufts-mit presentation 5-10-2022
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Download PDF • 3.77MB

geometry and topology solutions
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Download PDF • 500KB




  • Writer's pictureAlex Cassem

Updated: Apr 8, 2022

The end of my last undergraduate semester is coming up quick, and I am really trying to end on a high note (all A's to start with). However, to stay somewhat sane after doing all these discrete mathematics these past months (discrete sets, abstract algebra with discrete groups and rings, proofs after proofs after proofs... (boring ones, some are fun)), I have been keeping up with my usual physics of interest: strings and geometrical physics (although not much albeit).

I did one of the larger problems in chapter 6 of "Strings in a Nutshell," namely the derivation for the T-duality of the non-linear sigma model. That is attached here:

strings nutshell ch 1-6
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Download PDF • 410KB

However, when I am trying to go past the bosonic string, and the more complicated calculations such as tadpoles, 1-loop corrections, and higher-order supercurrent conformal algebra, I have decided to also go through Nakahara's textbook on geometry, topology, and physics.... by of course producing solutions to the textbook (what else am I suppose to do when learning a subject on my own...)

For example, before I go this text, I had to do a lot of googling, and guessing on what the Mobius transformation was for the exercise in chapter 5. However, it is quite clear after reading Nakahara's textbook what it is now. So, expect chapter one and possibly two also from that text being posted on my (this) website soon.

OH, also the other big news.... I am going to Tufts University for graduate school to obtain my PhD! I was waiting for a long time to hear back from the University of Texas at Austin with respect to my application, so I decided to just go for it. Mainly because after being put on the official waitlist, seeing people on forums be both accepted and rejected (recently more rejections went out), I went with Tufts. Tufts also has been giving the impression (I say this since you never know) that they truly want me there at Tufts University. And really, the feeling of being wanted will sell any undergraduate to go to that specific school; because it means they care about your future (and this case, its not because they want my money.... like some, they really care).

So hopefully, in either 4 to 6 years (my goal is 4, yes I know, that's a big goal, but I plan to really go for it, get classes out of the way, and focus on research right away, in other words, no "dilly-dallying around,") I will have my PhD in theoretical cosmology!

Have a great week, the school year is almost over, make sure to end on a high note!

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