Symplectic Geometry and Fourier Analysis
E893439
"Symplectic Geometry and Fourier Analysis" is a mathematical work by Nolan Wallach that explores the interplay between symplectic geometry, representation theory, and Fourier-analytic methods.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Symplectic Geometry and Fourier Analysis canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10931405 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Symplectic Geometry and Fourier Analysis Context triple: [Nolan Wallach, hasWrittenWork, Symplectic Geometry and Fourier Analysis]
-
A.
Introduction to Symplectic Topology
Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
-
B.
Fourier restriction theory
Fourier restriction theory is a branch of harmonic analysis that studies when and how the Fourier transform of a function can be meaningfully restricted to lower-dimensional subsets such as curves or surfaces.
-
C.
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
-
D.
McDuff–Salamon theory of J-holomorphic curves
The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
-
E.
Kähler geometry
Kähler geometry is a branch of differential geometry studying complex manifolds equipped with a compatible symplectic form and Riemannian metric, leading to rich interactions between complex, symplectic, and Riemannian geometry.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Symplectic Geometry and Fourier Analysis Target entity description: "Symplectic Geometry and Fourier Analysis" is a mathematical work by Nolan Wallach that explores the interplay between symplectic geometry, representation theory, and Fourier-analytic methods.
-
A.
Introduction to Symplectic Topology
Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
-
B.
Fourier restriction theory
Fourier restriction theory is a branch of harmonic analysis that studies when and how the Fourier transform of a function can be meaningfully restricted to lower-dimensional subsets such as curves or surfaces.
-
C.
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
-
D.
McDuff–Salamon theory of J-holomorphic curves
The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
-
E.
Kähler geometry
Kähler geometry is a branch of differential geometry studying complex manifolds equipped with a compatible symplectic form and Riemannian metric, leading to rich interactions between complex, symplectic, and Riemannian geometry.
- F. None of above. chosen
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ scholarly work ⓘ |
| academicDiscipline | pure mathematics ⓘ |
| author |
Nolan R. Wallach
NERFINISHED
ⓘ
Nolan Wallach NERFINISHED ⓘ |
| field |
Fourier analysis
ⓘ
mathematics ⓘ representation theory ⓘ symplectic geometry ⓘ |
| genre | research monograph ⓘ |
| hasAuthor | Nolan R. Wallach NERFINISHED ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
researchers in harmonic analysis ⓘ researchers in representation theory ⓘ researchers in symplectic geometry ⓘ |
| language | English ⓘ |
| relatedTo |
Fourier transform
ⓘ
Hamiltonian mechanics NERFINISHED ⓘ Lie algebras NERFINISHED ⓘ Lie groups NERFINISHED ⓘ geometric quantization ⓘ representation theory of semisimple Lie groups ⓘ |
| topic |
Fourier-analytic methods in representation theory
ⓘ
Hamiltonian group actions ⓘ applications of symplectic geometry to representation theory ⓘ geometric methods in representation theory ⓘ harmonic analysis on Lie groups ⓘ interplay between symplectic geometry and Fourier analysis ⓘ moment maps ⓘ unitary representations of Lie groups ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Symplectic Geometry and Fourier Analysis Description of subject: "Symplectic Geometry and Fourier Analysis" is a mathematical work by Nolan Wallach that explores the interplay between symplectic geometry, representation theory, and Fourier-analytic methods.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.