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For an under-determined system of linear equations, there exists infinitely many solutions. However, with more information, for example, if we know the the optimal solution is sparse, we can recover the desired solution.
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I have been attending an awesome summer school at ICTS on Advances in Applied Probability at ICTS. Find the link here! There are many interesting things I have learnt here. Things that were related to my interests were the: optimal transport course by Dr Jose Blanchet, non-parametric matrix estimation by Dr Devarat Shah, and a talk on Gaussian mean estimation by Dr Praneeth Netrapalli. Find the videos for these talks on YouTube.