I have a broad range of interests in mathematics, physics, computer science, and the Earth sciences. Much of what I post will cover one of my hobbies, the evaluation of integrals and series, but more serious topics will usually fall into one of the following categories:
- Number theory:
- Algebraic number theory
- Elliptic curves and modular forms
- Physics:
- General relativity and astrophysics
- Quantum mechanics
- Computer science:
- Microprocessors and microcode computer systems
- Scientific computing and data science
- Earth science:
- Geology
The image in the sidebar is an icosahedral tessellation of a sphere as shown in Continued Fractions and Modular Functions by W. Duke. The symmetries of this tiling correspond to Möbius transformations that are intimately related to the functional equations satisfied by Ramanujan’s continued fraction.