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User:Aaron H. Potechin

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I am a mathematics graduate student at MIT. Before coming to MIT, I did my undergraduate study at Princeton and then attended Part III of the math tripos at the University of Cambridge on a Churchill scholarship. While I am interested in many different areas of mathematics, my research so far has been in combinatorics and computational complexity theory. My first successful research was related to the mathematics of the card game Set and resulted in the paper “Maximal Caps in AG(6,3)”. In the summer of 2008, I attended a combinatorics REU at the University of Minnesota in Minneapolis under Professor Victor Reiner and Professor Dennis Stanton which was very successful. My current research project is L (Logarithmic space) versus NL (Non-deterministic logarithmic space), a major open problem in computational complexity theory. This was my senior thesis project at Princeton and resulted in the paper “Bounds on monotone switching networks for directed connectivity.” I am continuing this work for my Ph.D. thesis and more results are forthcoming.