I am currently an undergraduate at the University of Michigan majoring in Mathematics and Computer Engineering. I have quite broad interests in math and computer science/engineering, so if you have an interesting problem, I would love to hear it. I have done research in geometry, number theory, random matrix theory, and computer architecture. You can contact me via my email at the top of the page.
Notes, Thoughts and Projects
Now that I'm done applying to graduate school, I have some time to write about problems and projects I have been working on for fun. Stay tuned for updates to this section.
Here's a list of some problems and questions I have yet to come up with a satisfactory answer to. If you have thoughts on these, please let me know.
- Suppose C(m,n) is the minimum number of square tiles of integer side length needed to tile an m by n rectangle (e.g. C(2,3)=3). Is it true that C(m,n)=C(am,an) for any positive integers a,m,n? If not, what is a counterexample?
- Are all smooth involutions of the real numbers, R, conjugate to each other by smooth bijections from R to R? Note: if we relax smooth to continuously differentiable, this is true.
- Come up with a reasonable characterization of typical kinds of dynamic graph datasets (i.e. power law for dynamic graphs). Essentially, find a small collection of dynamic graphs made from real world data which capture the typical "kinds" of dynamic graphs, be able to explain their characteristics and differences, and be able to synthesize graphs with these characteristics. (Yes, this is for benchmarking.)
- Find a concise, elementary (not assuming background in coding theory) proof that the greedy solution to the n ropes problem is optimal: Suppose we have n ropes of various lengths. We can combine two at a time. For each combination, we add the length of the combined rope to a running cost function. Combine all of the ropes in a way that minimizes the total cost.