- One problem on using quantum mechanics and C*-algebra techniques for non-Markovian stochastic processes. The interchange between the physics and probability languages often trips the models up, so pretty much everything tends to fail here.
- Three problems in random matrix theory and free probability; these require strong combinatorial skills and a good understanding of novel definitions, requiring multiple papers for context.
- One problem in saddle-point approximation; I've just recently put together a manuscript for this one with a masters student, so it isn't trivial either, but does not require as much insight.
- One problem pertaining to bounds on integral probability metrics for time-series modelling.
I'd be very curious to know how any LLMs fare. I completely understand if you don't want to continue the discussion because of anonymity reasons.
Happy to try to answer more specific questions if anyone has any, but yes, these are among my active research projects so there's only so much I can say.