Department of

# Mathematics

Seminar Calendar
for events the day of Friday, September 18, 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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Friday, September 18, 2020

1:00 pm in Zoom,Friday, September 18, 2020

#### Positive Commutators, Propagation of Singularities, and trapping

###### Hadrian Quan   [email] (UIUC Math)

Abstract: In this talk I’ll describe the method of positive commutators, which is a flexible technique (=works on a manifold) for proving estimates about solutions of linear PDEs. Positive commutator estimates are useful for proving results about hyperbolic equations like the wave equation, or more generally any equations which involve a “flow”, by relating properties of solutions to the trajectories of an associated classical dynamical system. In particular they can give quantitative meaning to mysterious statements like “solutions of the wave equation propagate along light-cones.”

4:00 pm in Zoom,Friday, September 18, 2020