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Seminar

Analytic Number Theory Seminar: Incidences and the polynomial method March 23, 2017 (02:00 PM PDT - 03:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Miguel Walsh (University of Oxford)
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In recent years, the polynomial method has proven a powerful tool in different areas of mathematics, including number theory, harmonic analysis, computer science and combinatorics. We will discuss some improvements of this method over Euclidean space, including a sharp polynomial partitioning theorem over arbitrary varieties and new estimates on the behaviour of the connected components of real algebraic sets. As an application of these results, we provide a general degree-sensitive incidence bound for families of algebraic varieties of arbitrary degree and dimension.

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