As you prepare to embark on your senior thesis, ask yourself:
- What are you hoping to gain out of your senior thesis experience?
- Would you prefer to do an expository thesis or a research thesis?
- What would you like the role of computing to be in your thesis?
- What kinds of arguments in mathematics do you enjoy the most and why?
- What would you like to do after graduating from Reed?
- What ingredient would you be most sad to not have in your thesis?
While I’ve always liked projects that combine different areas of mathematics, over the years I’ve come to realize that the phenomena and questions I like the most come from the ergodic theory of dynamical systems and the methods and arguments I like the most are in analysis.
This year, I’m open to supporting theses in the following topics:
- Random Fourier series
- Filtering as estimation
- Decay of correlations in ergodic theory
- Stability of Hamiltonian equilibria
- Shift operators in spectral theory
- 1-loop approximations in quantum dynamics
I won’t state the possible expository goals or research problems precisely here, please just ask me if you’re interested. Some involve probability and some don’t, but all of them build on your foundation in MATH 321 Real Analysis. If you haven’t taken this required course yet, that is OK and you can work in parallel with that class in the Fall. If you have any questions, ideas of your own, or would like to discuss any of these topics in person, please send me an email to arrange a time to meet.
