1. **Random surfaces and random permutations** ([Leonid Petrov](https://math.virginia.edu/people/lap5r/)): Imagine you have a 100x100x100 room, and you stack some number of 1x1x1 unit cubes in its corner. If you do this at random, what would be the shape of the pile? We will investigate the mathematical structure of such random 3D stepped surfaces, which leads to beautiful limit shapes. We will use basic combinatorics, coding, and we will potentially 3D print our results. We will also explore cutting edge research directions in this area, in particular, connections of random surfaces to random permutations. Most of the models we will explore are hands-on and computational, and we will be able to visualize and manipulate them.
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