Alzheimer's Disease - My Researches In The Medical Sphere
As a child, I was always curious about the world. Since we had an extensive library at home, I was constantly reading, both from our library and from the internet. By the third grade, I was reading about things like nuclear fission and cloning on Wikipedia. Of course, my mother is a biologist and my father is a businessman, so there weren’t any physics books in our house; nevertheless, I always enjoyed watching the Science Channel, and it was shows like Through the Wormhole and Sci Fi Science: Physics of the Impossible that most interested me; the ideas of relativity, quantum physics, and string theory were simultaneously bizarre and fascinating. As I grew older, I became more and more intrigued not only by the phenomenology but also by the beautiful mathematical construction of physics.
In 2015, I came to Vanderbilt to study physics and mathematics. In May, I will graduate with a triple major in Physics, Math, and Engineering Science with a minor in Computer Science. I have taken courses beyond those required for the physics major, and I have specifically prepared myself for the study of particle physics by taking Mathematical Methods for Physicists, two semesters of Quantum Mechanics, and Intro to Particle Physics. I am also working on attaining honors in Physics, and my senior thesis will be on my research on maximal subalgebras of simple Lie algebras. Indeed, Physics involves a lot of Mathematics, which is why I have also taken a Math major.
In preparation specifically for studying Particle Physics, which relies heavily on group theory and algebra, I have taken not only the basic Abstract Algebra course but also the higher-level Modern Algebra course. Moreover, I feel that my courses in engineering have helped to complement my learning in physics. For example, Fluid Mechanics, one of the three main subdivisions of Classical Mechanics, is not offered in the Physics department, but I am currently taking that course in the Mechanical Engineering department. Additionally, much of modern physics research, including my own, involves coding, so a background in Computer Science is invaluable to any physics student.
Further preparation includes regularly attending colloquia hosted by the Vanderbilt Physics and Astronomy department, each of which is a chance to learn about a wide range of topics in modern Physics. I also regularly attend talks given by professors in the Department of Mathematics, which broaden my knowledge and understanding of Mathematics. Additionally, over this past summer, I attended a conference at the University of California Santa Barbara on Quantum Thermodynamics, which was which was not only a valuable learning opportunity, but also a chance to get a window into how professional academia functions.
Previously, from December 2016 until August 2017, I worked in Laura Dugan’s lab at the Vanderbilt University Medical Center doing research on aging in mice. I quantified and analyzed lysosomes in neurons using Image J and Excel and linked the administration of an anti-inflammatory compound in mice to decreases in murine neurological aging.
Additionally, I performed hundreds of non-survival mouse surgeries, performed immunofluorescence on mouse brain tissue samples, and assessed Western blots of protein lysates. This research focused on how to reduce and prevent symptoms of aging in the brain. While it is not Physics research, I feel like I learned a lot about data analysis and the scientific process, as well as learning general laboratory techniques and procedure.
Alzheimer’s disease is an irreversible, progressive brain disorder that slowly destroys memory and thinking skills, and eventually the ability to carry out simple tasks. Alzheimer's disease is one of the leading causes of death in the United States, especially among the elderly, surpassed only by heart disease and cancer. Moreover, caring for a person with Alzheimer’s disease can have high physical, emotional, and financial costs, which makes Alzheimer’s disease one of the costliest diseases.
The problem is that the cause of Alzheimer's disease is poorly understood, and effective treatments are lacking. The research I did at the Vanderbilt University Medical Center was research on such drugs; of the drugs I worked with, a certain anti-inflammatory compound shows great promise in reducing the symptoms of aging in the brains of mice, and one day may be used in humans. These drugs may very well be effective treatments for Alzheimer’s disease in the future.
Since August 2017, I have been doing independent research with Thomas Kephart in the Vanderbilt Physics and Astronomy department, continuing the work of his former post-doc, Robert Feger, with LieART (Lie Algebras and Representation Theory). LieART is a software approach to doing calculations with Lie algebras. LieART is a Mathematica package that can calculate products of representations for Lie algebras as well as subalgebra representation decompositions. However, LieART previously could only find certain maximal subalgebras of simple Lie algebras. In fact, LieART could find most of the regular subalgebras but only find a handful of special subalgebras.
My research has largely dealt with modifying the LieART Mathematica package to find the branching rules of maximal subalgebras of simple Lie algebras. I have successfully implemented this modification and tested it for Lie algebras up to rank 15, and I am currently writing a paper on the matter. My research focus is now shifting to extending LieART to also handle Lie superalgebras in addition to Lie algebras. Specifically, the goal is to replicate the functionality of Lie algebras for Lie superalgebras, including representation, subsuperalgebras, branching rules, tensor products, and much more. Superalgebras have important uses in the study of supersymmetry, higher dimensional theories of gravity, string theory, and M-theory.
Grand Unified Theories (GUTs) were first developed in the 1970s, wherein the symmetry group of the Standard Model of Particle Physics is embedded in a higher symmetry and, at high energy, the three symmetry interactions of the Standard Model which define the electromagnetic, weak, and strong interactions are merged into one single force. At very high energies, the higher symmetry governs the physics; however, as the energy becomes lower, the higher symmetry breaks down to the Standard Model symmetry group. Thus, we are interested in how the irreducible representations of Lie algebras decompose into representations of a given maximal subalgebra during such a symmetry breaking. Expansive tables already exist for such branching rules; however, it is sometimes necessary to go beyond what is already computed. That is where my extension of the LieART program comes in.
LieART can now handle the calculation of all these branching rules which are necessary for such Grand Unified Theories; these Grand Unified Theories make important steps towards unifying three of the fundamental forces into one theoretical framework and gets us one step closer to understanding the nature of the universe. Lie algebras are also applied in the study of gravitation [2], condensed matter physics, quantum chemistry, and engineering [3], all of which can benefit from my extension of LieART. Even more ambitions than Grand Unified Theories, string theory and M-theory have the common goal of constructing a single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe. That is, string theory and M-theory attempt to unify all four fundamental forces. These two theories have a critically important property: supersymmetry. Supersymmetry is a principle that proposes a relationship between two basic classes of elementary particles: bosons, which (roughly speaking) carry forces, and fermions, which (roughly speaking) constitute matter.
The way supersymmetry is formulated is using a certain mathematical structure called Lie superalgebras, and these Lie superalgebras are precisely what I do research on. Specifically, I work on constructing a Mathematica program that will do superalgebra calculations for theoretical physicists studying supersymmetry, string theory, and M-theory. This work has the potential to help make significant progress towards an ultimate understanding of the universe.
Future goals
I will pursue a Ph.D. in theoretical particle physics, and afterwards a research position, for a simple reason: I tremendously enjoy researching physics. While at Vanderbilt University, I experienced the vast increase in productivity that comes with spending significant time on research; the National Science Foundation Graduate Research Fellowship Program would provide me this time during my early years of graduate school. Moreover, graduate school is one of the most important learning opportunities in my life and having this fellowship will give me the flexibility to pursue top graduate programs and engage in research with world-class physicists. My dream is to push forward our understanding of the most fundamental building blocks of the universe, and this grant would certainly put me many steps closer to that dream.
