[Csdmsemo] [math-ias] Special Mathematics Seminar: Speaker-Antoine Gloria, Wednesday, 5/23/2018

[Kristina Phillips]

INSTITUTE FOR ADVANCED STUDY

School of Mathematics

Princeton, NJ 08540

 

Mathematics Seminars

Week of May 21, 2018

 

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To view mathematics in titles and abstracts, please click on the talk's
link.

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Wednesday, May 23

 

Approximate spectral theory in heterogeneous media, asymptotic ballistic
transport, and beyond?

Speaker:              Antoine Gloria, Sorbonne University, Laboratoire
Jacques-Louis Lions

Time/Room:       3:30pm - 4:30pm/Dilworth Room

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=137597>
http://www.math.ias.edu/seminars/abstract?event=137597

 

In this talk I’ll consider the Schrödinger in heterogeneous media and shall
discuss long-time transport properties of localized initial conditions, and
more precisely the regime of asymptotic ballistic transport. To this aim
I’ll introduce an approximate spectral theory inspired by the Floquet theory
for periodic media that allows to diagonalize the Schrödinger operator up to
an error that we control by energy estimates combined with estimates on
"correctors". This yields asymptotic ballistic results for quasiperiodic
potentials up to stretched exponential times, as well as fine results in the
random setting. To conclude I'll discuss what direction could be taken to
tackle larger time scales.
 
This is joint work with Mitia Duerinckx and Christopher Shirley (Université
Libre de Bruxelles).

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