I earned my PhD at the University of Pennsylvania, working in combinatorics and probability. Within mathematics, I'm particularly interested in what large random structures look like. I think generating functions are awesome, which is probably pretty clearly reflected in the questions I answer.
Now I work as a data scientist, which is what they call statisticians when they want to pay them more and sound modern.
If you break a stick at two points chosen uniformly, the probability the three resulting sticks form a triangle is 1/4. Is there a nice proof of this?
What relationship, if any, is there between the diameter of the Cayley graph and the average distance between group elements?
Is there a simple way to compute the number of ways to write a positive integer as the sum of three squares?
What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$?
How can I generate random permutations of [n] with k cycles, where k is much larger than log n?