The polynomial method for combinatorial problems - talk by John R. Schmitt
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John R. Schmitt, Professor of Mathematics at , Post-doc at Middlebury College, Vermont, USA, gave a talk at JKU during his research stay at our Institute of Algebra. Abstract: The polynomial method is a developing set of methods, mostly arising from linear algebra and algebraic geometry. Chief amongst these is Noga Alon?s Combinatorial Nullstellensatz (CN), which allows one to turn combinatorial problems into computational ones. We survey some of the applications of this particular theorem, including from the speaker?s own work in finite geometry and combinatorial design theory, and try to highlight some of the aspects of the computation the CN forces upon us. We then turn to a quantitative analogue of the CN due to Alon and Füredi and show its connections to classical number theory statements of Chevalley and Warning.