Department of Mathematics Calendar

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The Department of Mathematics is a bustling place full of new ideas. We host several events that occur throughout the year, including seminars, colloquium, conferences, and social events. Our seminars and colloquium are open to the public: all students, faculty, or alumni who are interested are welcome to join us for exciting talks on the leading edge of mathematics research!

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Harmonic Analysis and Differential Equations Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
141 Altgeld Hall
Date
Nov 15, 2022   1:00 pm  
Speaker
Tal Malinovitch (Yale)
Contact
Burak Erdogan
E-Mail
berdogan@illinois.edu
Views
37

Scattering for Schrodinger operators with conical decay

Abstract: In this talk, I will discuss the scattering properties of Schrodinger operators with potentials that have short-range decay along a collection of rays in . This generalizes the classical setting of short-range scattering in which the potential is assumed to decay along all rays. For these operators, we show that any state decomposes into an asymptotically free piece and a piece that may interact with the potential for a long time. We give a microlocal characterization of the scattering states in terms of the dynamics and a corresponding description of their complement. We also show that in certain cases these characterizations can be purely spatial.

I will state our results, sketch some of the main ideas in the proof, and briefly discuss some examples of these interacting states for different systems. This is joint work with Adam Black.

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