I don't want to give away too much due to anonymity reasons, but the problems are generally in the following areas (in order from hardest to easiest):
- 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.
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I don't want to give away too much due to anonymity reasons, but the problems are generally in the following areas (in order from hardest to easiest):
- 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.