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                * Princeton Discrete Math Seminar *
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Speaker: Jonathan Tidor (Princeton)

Thursday 17th September, 3:00 in Fine Hall 224.

Title: Discrete geometry, semialgebraic graphs, and the polynomial method

Many problems in discrete geometry can be naturally encoded in a structure 
known as a semialgebraic graph. These include the Erdős unit distance
problem, questions about incidences of algebraic objects, and more. I will
discuss several new structural and extremal results about semialgebraic graphs.
These include a very strong regularity lemma with optimal bounds and
improvements to the Zarankiewicz problem and the Erdős–Hajnal problem for
semialgebraic graphs. These results are proved via a novel extension of the
polynomial method, building on the polynomial partitioning machinery of
Guth–Katz and Walsh. Based on joint work with Hung-Hsun Hans Yu.

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