A Generalization of the Multilinear Kakeya Theorem

Abstract: The Multilinear Kakeya Inequality is a geometric estimate on the overlap of tubes in Euclidean space useful to the understanding of high order interactions between wave packets in harmonic analysis. We will discuss the evolution of the problem of achieving this estimate from the linear Kakeya problem and the combinatorial heuristics of the joints problem. Finally, we will discuss a slight modification that replaces the tubes with neighborhoods of Lipschitz graphs.

commutative algebraalgebraic geometrygeneral mathematicsnumber theoryrings and algebras

Audience: undergraduates

( video )

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PRiME: Pomona Research in Mathematics Experience

Series comments: PRiME is hosting a series of talks which will take place on Fridays in July. All are welcome to join us either in person at Pomona College or virtually over Zoom. There will be two types of series.

PROFESSIONAL DEVELOPMENT WORKSHOPS

We will have a series of 2-hour workshops geared for undergraduate students, graduate students, and faculty. The Morning Sessions will take place from 10:00 AM - 12:00 PM Pacific, while the Afternoon Sessions will take place from 2:00 PM - 4:00 PM Pacific. The Student Professional Development Series (geared for undergraduates) will meet at Pomona College in Estella 1051 (Argue Auditorium); while the Faculty Professional Development Series (geared for graduate students and junior faculty) will meet in Estella 1021 (Noether Auditorium).

COLLOQUIUM SERIES

We will have outside speakers to visit with us on Fridays from 4:30 PM - 6:00 PM Pacific. We will meet in person at Pomona College in Estella 1051 (Argue Auditorium).

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