**These problems are those I have encounted in my own research or suggested by mathematicians I know. The list
will be expanded …**

Classify multi-dimensional natural exponential families (NEF) by their variance mappings; reference paper. This problem was suggested by Prof. Gerard Letac, to whom I am grateful for his invaluable help.

Prove the conjecture on tail index and edge universality for sample covariance matrices; reference paper

Find the solution to a second-order partial differential equation (PDE) involving the Laplace transform of a finite measure; go to the discussion of this linked paper

Characterize the maximal zero-free domain of the Lapalce transform of a finite measure; link to the problem

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