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Home » HA Postdoc Seminar: Algebraic structure in harmonic analytic incidence problems (Colloquium Talk)

Seminar

HA Postdoc Seminar: Algebraic structure in harmonic analytic incidence problems (Colloquium Talk) March 24, 2017 (12:00 PM PDT - 12:50 PM PDT)
Parent Program: Harmonic Analysis
Location: MSRI: Simons Auditorium
Speaker(s) Marina Iliopoulou (University of California, Berkeley)
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Abstract/Media

Dvir's algebraic solution of the Kakeya problem in finite fields in 2008 triggered dramatic progress in incidence geometry. Extensive work since then has revealed that algebraic varieties play a crucial role in incidence geometric problems: in principle, point-line incidences are truly many when the lines cluster on low-degree varieties. Guth has recently exploited such ideas to improve on the restriction problem, a harmonic analytic problem with point-tube incidence flavour. In this talk, we will present the basic algebraic techniques used in such settings, and discuss their potential to yield results in other harmonic analytic problems.

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