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DTSTAMP:20260313T102957
DTSTART;TZID=America/Detroit:20260316T160000
DTEND;TZID=America/Detroit:20260316T170000
SUMMARY:Workshop / Seminar:Extreme Superposition: Rogue Waves of Infinite Order\, Universality\, and Anomalous Temporal Decay
DESCRIPTION:Focusing nonlinear Schrödinger equation serves as a universal model for the amplitude of a wave packet in a general one-dimensional weakly-nonlinear and strongly-dispersive setting that includes water waves and nonlinear optics as special cases. Rogue waves of infinite order are a novel family of solutions of the focusing nonlinear Schrödinger equation that emerge universally in a particular asymptotic regime involving a large-amplitude and near-field limit of a broad class of solutions of the same equation. In this talk\, we will present several recent results on the emergence of these special solutions along with their interesting asymptotic and exact properties. Notably\, these solutions exhibit anomalously slow temporal decay and are connected to the third Painlevé equation. Finally\, we will extend the emergence of rogue waves of infinite order to the first several flows of the AKNS hierarchy—allowing for arbitrarily many simultaneous flows—and report on recent work regarding their space-time asymptotic behavior under a general flow from the hierarchy.
UID:143125-21892183@events.umich.edu
URL:https://events.umich.edu/event/143125
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics,Seminar
LOCATION:East Hall - EH 1866
CONTACT:
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DTSTAMP:20260307T202415
DTSTART;TZID=America/Detroit:20260316T160000
DTEND;TZID=America/Detroit:20260316T170000
SUMMARY:Workshop / Seminar:GLNT: Igusa stacks and the cohomology of Shimura varieties
DESCRIPTION:Abstract: Igusa stacks are $p$-adic geometric objects\, recently introduced by Mingjia Zhang\, that roughly parametrize ways to $p$-adically uniformize (global) Shimura varieties by local Shimura varieties. In joint work with Patrick Daniels\, Pol van Hoften\, and Mingjia Zhang\, we construct Igusa stacks for all abelian type Shimura data and apply them to the study of $\ell$-adic cohomology of Shimura varieties. I will discuss the geometric ingredients that go into the construction as well as how it naturally fits into Fargues--Scholze's framework of categorical local Langlands
UID:143321-21892900@events.umich.edu
URL:https://events.umich.edu/event/143321
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4096
CONTACT:
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