KYLE MICHAEL KEANE
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Quantitative Analysis
For more information, please read about my other professional skills

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Differential equations are one of the most important mathematical tools in theoretical physics. In my research, I used differential equations to understand the time evolution of a qubit state. The normal evolution of qubits involves a simple solution to the Schrodinger Equation. When there is a driving force that is resonate with the energy spacing of the two states of a qubit, then the solution of the Shrodinger Equation is a bit more complex, but still uses the standard techniques of calculus. The measurement of solid-state qubits involves forces coming from stochastic noise that requires the techniques of Ito calculus. Each stage of evolution must be analyzed separately using the appropriate techniques.

Bayesian Analysis

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Bayes' Theorem is a very famous and fundamental theorem in probability theory. Simply put, it describes quantitatively how to adjust one's beliefs when new evidence is considered. For instance, it is more likely that a person with long hair is a woman because it is more likely that women have long hair in our culture. In simple logic, if A implies B, then one cannot assume that B implies A. It is important to remember that conditional probabilities are statistical correlations, which are expressed in similar terms to logic; however, these cannot be interchanged when making logical arguments. Implying, correlating, and causing are extremely different verbs; remember, correlation does not imply causation.

Combinatorics

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Combinatorics is an especially elegant system for counting possibilities. I used combinatorics as a tool to calculate the frustrated magnetic ground state of electrons on a Kagome lattice. Very simply, a complete basis for the state space of N electrons can be found by counting all pairwise connections of N points spread evenly around a circle (shown to the left).
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About Me
I am currently a Lecturer at Massachusetts Institute of Technology (MIT) in the Department of Materials Science and Engineering. I teach computational materials science, human-centered design, and engineering technology that helps people with disabilities. I am not very active on social media, but you can find some digital breadcrumbs on the following sites:
  > LinkedIn
  > GitHub

  • About
  • Teaching
  • Research
  • Advocacy
  • Speaking
  • Advising
  • Creative
  • Publications
  • Work