- #1
SuperUnison
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Hello, I’m looking for some feedback on my statement of purpose. I’m looking to get into a PhD program for high-energy theory. For a bit of background, I studied math during undergrad, then got into an accelerated quantum computing-focused physics masters’ program. I did alright (3.8 GPA) in undergraduate, but pretty poorly (3.3 GPA) in the masters’ program. This is because the program required me to take at least 50% grad-level classes, which I probably wasn’t prepared for with a math degree, and also because I had basically no outside help due to my own social awkwardness. I’m worried about seeming indecisive due to my academic history, especially because of the fact that my main reason for wanting to study high-energy physics is simply because I find it utterly fascinating. Also, I’m afraid I might be being a bit too pointed in the second paragraph.
The thing that attracted me to high-energy theory is its vastness and its diversity of ideas/structures/techniques. I’ve always been a bit intellectually restless, always following lines of flight between ideas and hunting for strange, new concepts. This has caused me to be a bit all-over-the-place when it comes to my interests. At least, until I found physics, and especially high-energy theory. This subject is big enough and wide enough that one could spend multiple lifetimes in understanding it. Once I truly understood this, all other options left my mind.
However, I feel that, with the proliferation of work on toy models and specific physical situations (such as black holes), there is a danger that the fundamental physics community may become entrenched in excessively specialized research and lose sight of its broader goals. In the absence of a fully-general theory of everything that we have full control of, what I’d like to do is take the methods developed in specific areas of fundamental physics research and attempt to generalize them or transplant them to other specific areas.
My path to fundamental physics was not a particularly straightforward one, but it was very instructive. I studied mathematics during my undergraduate at [undergrad school], taking in abstract algebra, number theory and real analysis. But the classes that turned out to be the most important were easily [Prof 1]’s Quantum Computing classes. This is where I was first exposed to quantum mechanics, although it was presented in a very “computer-science” way. The classes were quite interesting, combining physics, computer science and mathematics in an invigorating way. However, some questions lingered in my mind, and there were many things that seemed arbitrary or unmotivated.
At [masters’ school], I learned quantum computing in a much more “physical” way. This answered a lot of questions I had from my classes at [undergrad school], and this is likely the point I chose physics over mathematics. However, I realized quite quickly that my interests laid not in quantum computing, but in fundamental physics. I decided to use the opportunity I had been given as a springboard toward a physics PhD program, tailoring my curriculum towards this end. While transitioning from an undergraduate mathematics program to a graduate-level physics program was quite challenging, it made abundantly clear to me the difference between solving problems in mathematics and solving problems in physics. It also taught me the importance of seeking help when I needed it.
The [masters’ program] program also gave me my first taste of research. Both of the required Quantum Computing classes in the program included some research component. For my Intro to Quantum Computing class, the final consisted of a poster session and presentation. I was intrigued by a continuous-variable version of the quantum teleportation algorithm, and made my poster about this topic. For the Advanced Quantum Computing course, I chose to write a summary of Blais et. al.’s “Quantum-information processing with circuit quantum electrodynamics,” an important paper in the development of the transmon qubit.
Despite the fact that the [masters’ program] program was focused on quantum computing, I managed to slip my own interests in at a few points. During the Summer of 2023, I conducted an independent research project supervised by professor [Prof 2] on the applications of quantum information theory to black holes. This is when I was first truly exposed to the methods and techniques of high-energy theory, and it confirmed for me that this is what I what I wanted to do.
After graduation in the Fall of 2023, I wasn’t satisfied. I wanted to know more, badly. I revisited the books I had only skimmed through for my research project, reading and working through them far more deeply. Using Zee’s Quantum Field Theory in a Nutshell and Lancaster and Blundell’s Quantum Field Theory for the Gifted Amateur as my main guides, I understood the formalisms and concepts of physics that I had previously struggled with, giving me the confidence to move on to more advanced topics, such as string theory. I was completely taken with the theory’s multiplicity of objects, its connections to basically all fields of mathematics and the way in which it seemed to subsume the existing structures of theoretical physics within itself.
I would like to pursue a Ph.D. in order to pursue a career in high-energy physics research, either in academia or a national laboratory. One of my main research goals is the advancement of our understanding of string theory by the exploration of its behavior in exotic/unusual scenarios. This leads me to an interest in non-geometric backgrounds, exotic branes, and non-supersymmetric theories. I’m also interested in exploring the structural aspects of the theory. Developments such as double/exceptional field theory and the various string matrix models have convinced me that there’s still a great deal of structure in string theory that has not yet been understood. I’m also interested in the relationship between matrix models and noncommutative geometry.
While string theory is my main interest, it is not my only one. I’m also interested in applying the recently-developed framework of generalized symmetries to deepen our understanding of string theory and other theories of physics, and possibly construct new ones. I’d also like to use some of the insights recently developed in the theory of scattering amplitudes as inspiration for further understanding.
The thing that attracted me to high-energy theory is its vastness and its diversity of ideas/structures/techniques. I’ve always been a bit intellectually restless, always following lines of flight between ideas and hunting for strange, new concepts. This has caused me to be a bit all-over-the-place when it comes to my interests. At least, until I found physics, and especially high-energy theory. This subject is big enough and wide enough that one could spend multiple lifetimes in understanding it. Once I truly understood this, all other options left my mind.
However, I feel that, with the proliferation of work on toy models and specific physical situations (such as black holes), there is a danger that the fundamental physics community may become entrenched in excessively specialized research and lose sight of its broader goals. In the absence of a fully-general theory of everything that we have full control of, what I’d like to do is take the methods developed in specific areas of fundamental physics research and attempt to generalize them or transplant them to other specific areas.
My path to fundamental physics was not a particularly straightforward one, but it was very instructive. I studied mathematics during my undergraduate at [undergrad school], taking in abstract algebra, number theory and real analysis. But the classes that turned out to be the most important were easily [Prof 1]’s Quantum Computing classes. This is where I was first exposed to quantum mechanics, although it was presented in a very “computer-science” way. The classes were quite interesting, combining physics, computer science and mathematics in an invigorating way. However, some questions lingered in my mind, and there were many things that seemed arbitrary or unmotivated.
At [masters’ school], I learned quantum computing in a much more “physical” way. This answered a lot of questions I had from my classes at [undergrad school], and this is likely the point I chose physics over mathematics. However, I realized quite quickly that my interests laid not in quantum computing, but in fundamental physics. I decided to use the opportunity I had been given as a springboard toward a physics PhD program, tailoring my curriculum towards this end. While transitioning from an undergraduate mathematics program to a graduate-level physics program was quite challenging, it made abundantly clear to me the difference between solving problems in mathematics and solving problems in physics. It also taught me the importance of seeking help when I needed it.
The [masters’ program] program also gave me my first taste of research. Both of the required Quantum Computing classes in the program included some research component. For my Intro to Quantum Computing class, the final consisted of a poster session and presentation. I was intrigued by a continuous-variable version of the quantum teleportation algorithm, and made my poster about this topic. For the Advanced Quantum Computing course, I chose to write a summary of Blais et. al.’s “Quantum-information processing with circuit quantum electrodynamics,” an important paper in the development of the transmon qubit.
Despite the fact that the [masters’ program] program was focused on quantum computing, I managed to slip my own interests in at a few points. During the Summer of 2023, I conducted an independent research project supervised by professor [Prof 2] on the applications of quantum information theory to black holes. This is when I was first truly exposed to the methods and techniques of high-energy theory, and it confirmed for me that this is what I what I wanted to do.
After graduation in the Fall of 2023, I wasn’t satisfied. I wanted to know more, badly. I revisited the books I had only skimmed through for my research project, reading and working through them far more deeply. Using Zee’s Quantum Field Theory in a Nutshell and Lancaster and Blundell’s Quantum Field Theory for the Gifted Amateur as my main guides, I understood the formalisms and concepts of physics that I had previously struggled with, giving me the confidence to move on to more advanced topics, such as string theory. I was completely taken with the theory’s multiplicity of objects, its connections to basically all fields of mathematics and the way in which it seemed to subsume the existing structures of theoretical physics within itself.
I would like to pursue a Ph.D. in order to pursue a career in high-energy physics research, either in academia or a national laboratory. One of my main research goals is the advancement of our understanding of string theory by the exploration of its behavior in exotic/unusual scenarios. This leads me to an interest in non-geometric backgrounds, exotic branes, and non-supersymmetric theories. I’m also interested in exploring the structural aspects of the theory. Developments such as double/exceptional field theory and the various string matrix models have convinced me that there’s still a great deal of structure in string theory that has not yet been understood. I’m also interested in the relationship between matrix models and noncommutative geometry.
While string theory is my main interest, it is not my only one. I’m also interested in applying the recently-developed framework of generalized symmetries to deepen our understanding of string theory and other theories of physics, and possibly construct new ones. I’d also like to use some of the insights recently developed in the theory of scattering amplitudes as inspiration for further understanding.
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