Neil Hindman works on Ramsey theory and algebraic methods for finding structured monochromatic sets. With Vitaly Bergelson and Kendall Williams, he developed polynomial extensions of the Milliken–Taylor theorem, using ultrafilters and their algebra.[ref]
Polynomial Extensions of the Milliken-Taylor Theorem by Vitaly Bergelson and others. Original byline, abstract and Theorem 1.6
With Imre Leader and Dona Strauss, he also studied when different Milliken-Taylor systems can be monochromatic simultaneously. The coefficient patterns impose genuine compatibility conditions.[ref]
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