Benjamin Adenbaum
Classification of Irreducible Reflection Groups
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After introducing the definition of a real reflection group, we will sketch a proof of the classification of irreducible reflection groups following the treatment of Humphreys.
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Brian Mintz
Latin squares and beyond, what's wrong with six? How an incorrect proof of a 200-year-old conjecture was fixed after over fifty years.
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A Latin square is an n by n array of cells filled with the number in S = {1, 2, ..., n} such that every row and column contains each of these numbers exactly once. An Euler square is a pair of "orthogonal" Latin squares, which are superimposed to yield every pair of S^2 exactly once. It was long conjectured that Euler squares couldn't exist when n = 4k+2 for some natural number k, and there was even a proof of this after a few centuries. However, in 1959, mathematicians discovered not only a flaw in this proof, but that there are actually Euler squares for ALL n of this form, except 2 and 6! If you want to learn about the stained glass artwork in the middle of the first floor in Kemeny Hall, or just a neat way to make magic squares of any size, you're sure to enjoy this talk!
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Matthew Ellison
L-Systems DIY
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L-systems are an easy-to-learn language to describe and visualize recursive structures, introduced by theoretical botanist Aristid Lindenmayer in the 60s. We'll begin with a rapid overview of how L-systems work using the typical turtle-graphics setup. Then you'll have the opportunity to get creative with some modeling challenges. Please bring a laptop which is ready to run Python3 programs!
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Jonathan Lindbloom
A brief introduction to matrix-free and randomized matrix computations
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Many problems in both the pure and applied sciences rely on computations with matrices of an increasingly large size as the ambient problem is scaled up. These computations may involve inverse-matrix-vector products, traces, diagonals, and log-determinants. At some point, traditional methods for these calculations become computationally infeasible. In this talk, we survey some algorithms for "matrix-free" and randomized matrix computations that are suitable for very large problems.
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Matthew Ellison
Expander graphs and compressed sensing
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Expander graphs are graphs which are sparse but still well-connected. Compressed sensing is about recovering sparse signals through the efficient use of linear measurements. After introducing each, we will look at the 2007 breakthrough work of Xu and Hassibi on applying expander graphs to compressed sensing.
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