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Update current_projects.md (#219)
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mathexlab/current_projects.md

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### Projects Spring 2026:
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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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2. **Straightedge and compass** ([Pedro Brunialti Lima de Andrade](https://pbrunialti.github.io/) and [Thomas Jaklitsch](https://math.virginia.edu/people/gvs3ka/)): TBA.
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2. **Straightedge and compass** ([Pedro Brunialti Lima de Andrade](https://pbrunialti.github.io/) and [Thomas Jaklitsch](https://math.virginia.edu/people/gvs3ka/)): Straightedge and compass constructions are incredibly old, dating back over 2000 years. They consist of the construction of lengths, angles, and other geometric figures using only an idealized unmarked straightedge and a compass.
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It is well known that one can construct regular hexagons, bisect angles, and construct square roots of lengths, among other figures. However, there are limitations to the kinds of operations that can be performed using only a straightedge and compass. In this project, we will learn the basic constructions and explore their limitations through a surprising connection with field theory, a branch of mathematics developed in the 18th and 19th centuries and therefore relatively very recent when compared to these ancient geometric methods.

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