12 March 2024
Thinking about new questions and the challenge of trying to contribute to these questions. This involves a wide variety of activities, from writing down new insights to solving a mathematical problem. Sometimes it means programming new algorithms and learning new areas of mathematics. Teaching is always an interesting addition to this mix for me.
That would have to be the research that will be the first chapter of my thesis. This project focuses on the numerical solution to optimal stopping problems in which the opportunities to stop arrive stochastically and dependently. Stopping problems are problems where we have to make a decision to stop, and then receive a payout. The goal here is to find the right moment to stop so you get a maximum payout. This is a very interesting question on which we recently published a preprint.
2 of my hobbies are board games and formalising mathematical proofs. I think I should explain the latter. Formalising is when mathematical proofs are presented to a computer in the form of program. This input is done in such a way the computer can verify if the proof is logically sound, and thus correct. This is something I do with the Mathlib library of mathematical definitions and postulations using Lean4. Lean is a popular programming language used for this purpose. For example, it was recently used to verify the proofs for the Liquid Tensor Experiment.