- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- The Maslov index and the spectrum of differential operators
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
The Maslov index and the spectrum of differential operators Latushkin, Yuri
Description
This is a joint work with M. Beck, G. Cox, C. Jones, R. Marangell, K. McQuighan, A. Sukhtayev, and S. Sukhtaiev. In this talk we discuss some recent results on connections between the Maslov and the Morse indices for differential operators. The Morse index is a spectral quantity defined as the number of negative eigenvalues counting multiplicities while the Maslov index is a geometric characteristic defined as the signed number of intersections of a path in the space of Lagrangian planes with the train of a given plane. The problem of relating these two quantities is rooted in Sturm's Theory and has a long history going back to the classical work by Arnold, Bott, Duistermaat, Smale, and has attracted recent attention of several groups of mathematicians. We will briefly mention how the relation between the two indices helps to prove the conjecture that a pulse in a gradient system of reaction diffusion equations is unstable. We will also discuss a fairly general theorem relating the indices for a broad class of multidimensional elliptic self-adjoint operators.
Item Metadata
Title |
The Maslov index and the spectrum of differential operators
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2017-06-21T10:02
|
Description |
This is a joint work with M. Beck, G. Cox, C. Jones, R. Marangell, K. McQuighan, A. Sukhtayev, and S. Sukhtaiev.
In this talk we discuss some recent results on connections between the Maslov and the Morse indices for differential operators. The Morse index is a spectral quantity defined as the number of negative eigenvalues counting multiplicities while the Maslov index is a geometric characteristic defined as the signed number of intersections of a path in the space of Lagrangian planes with the train of a given plane. The problem of relating these two quantities is rooted in Sturm's Theory and has a long history going back to the classical work by Arnold, Bott, Duistermaat, Smale, and has attracted recent attention of several groups of mathematicians.
We will briefly mention how the relation between the two indices helps to prove the conjecture that a pulse in a gradient system of reaction diffusion equations is unstable. We will also discuss a fairly general theorem relating the indices for a broad class of multidimensional elliptic self-adjoint operators.
|
Extent |
30 minutes
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: University of Missouri
|
Series | |
Date Available |
2017-12-19
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0362118
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Faculty
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International