Department of

# Mathematics

Seminar Calendar
for Harmonic Analysis and Differential Equations events the year of Tuesday, October 20, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, February 4, 2020

1:00 pm in 347 Altgeld Hall,Tuesday, February 4, 2020

#### Local smoothing estimates for Fourier Integral Operators

###### David Beltran (U. Wisconsin, Madison)

Abstract: The sharp fixed-time Sobolev estimates for Fourier Integral Operators (and therefore solutions to wave equations in Euclidean space or compact manifolds) were established by Seeger, Sogge and Stein in the early 90s. Shortly after, Sogge observed that a local average in time leads to a regularity improvement with respect to the sharp fixed-time estimates. Establishing variable-coefficient counterparts of the Bourgain—Demeter decoupling inequalities, we improve the previous best known local smoothing estimates for FIOs. Moreover, we show that our results are sharp in both the Lebesgue and regularity exponent (up to the endpoint) in odd dimensions. This is joint work with Jonathan Hickman and Christopher D. Sogge.