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* Princeton Discrete Math Seminar *
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Speaker: Jonathan Tidor (MIT)
Thursday 11th November, 3:00 in Fine Hall 224.
Title: Induced arithmetic removal and arithmetic property testing
The triangle removal lemma of Ruzsa and Szemerédi is a fundamental application
of Szemerédi's graph regularity lemma. Later generalized to the graph removal
lemma and the induced graph removal lemma, these results and techniques are also
a key step in Alon and Shapira's classification of testable graph properties.
Analogously, one can also prove arithmetic removal lemmas from an appropriate
arithmetic regularity lemma. Intriguingly, it is known that the techniques of
arithmetic regularity are not capable of proving an induced arithmetic removal
lemma (specifically over F_p^n for p>2). We develop a novel Ramsey-inspired
technique called "patching" that allows us to overcome this difficulty and prove
an induced arithmetic removal lemma. As an application of this result, we
resolve a central problem in arithmetic property testing by classifying the
testable linear-invariant properties.
Based on joint work with Jacob Fox and Yufei Zhao.
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Next week: Oliver Janzer.
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