Research profile
Frederic Schuller
Author of work recommended on this site.
- 17
- on the reading lists
Why people read this work
On the reading lists
What this site's guides and courses recommend by Frederic Schuller, and why. Each opens its Library entry.
- A good place to startVideoStone’s theorem & construction of observables (L12)
One-parameter unitary groups and their self-adjoint generators.
Recommended in Guidebook 4A.13: Unbounded Operators and the Spectral Theorem · Guidebook 6B.13: Semigroups and Evolution Equations
- VideoConstruction of the tangent bundle (Lecture 10)
Gluing the tangent spaces into the tangent bundle.
Recommended in Guidebook 8A.3: Tangent Vectors and Bundles
- VideoDifferentiable structures: definition and classification (Lecture 7)
Smooth structures and how many a topological manifold can carry, dimension by dimension.
Recommended in Guidebook 8A.1: Smooth Structures
- VideoLecture 10: Metric Manifolds
Metrics on manifolds, and how a metric determines lengths, angles and a canonical connection.
Recommended in Guidebook 9A.1: Riemannian Metrics and Model Spaces
- VideoLecture 11: Symmetry
Flows of vector fields, push-forward and pull-back, and the Lie derivative.
Recommended in Guidebook 8A.6: Flows and the Lie Derivative
- VideoLecture 12: Integration on manifolds
Volume forms and integration on manifolds.
Recommended in Guidebook 8A.8: Differential Forms and Stokes’ Theorem
- VideoLecture 3: Multilinear Algebra
Tensors as multilinear maps, and the index notation that goes with them.
Recommended in Guidebook 8A.7: Tensors and Index Notation
- VideoLecture 4: Differentiable Manifolds
Charts, atlases and compatible smooth structures.
Recommended in Guidebook 8A.1: Smooth Structures
- VideoLecture 5: Tangent Spaces
Tangent vectors as derivations along curves, and the tangent space at a point.
Recommended in Guidebook 8A.3: Tangent Vectors and Bundles
- VideoLecture 7: Connections
Connections as the extra structure needed to differentiate vector fields.
Recommended in Guidebook 9A.2: Connections
- VideoLecture 8: Parallel Transport & Curvature
Parallel transport along curves, and curvature as the failure of transport around loops to return.
Recommended in Guidebook 9A.2: Connections
- VideoLecture 9: Newtonian spacetime is curved!
Even Newtonian gravity is the curvature of a connection: Schuller’s case that tides are curvature.
Recommended in Guidebook 9A.4: Curvature and What It Means
- VideoLie groups and their Lie algebras (Lecture 13)
Lie groups, their Lie algebras and the exponential map.
Recommended in Guidebook 8A.5: Lie Groups and Group Actions
- VideoSelf adjoint and essentially self-adjoint operators (Lec 07)
Unbounded operators, adjoints, and the difference between symmetric and self-adjoint.
Recommended in Guidebook 4A.13: Unbounded Operators and the Spectral Theorem
- VideoSpectra and perturbation theory (L08)
The spectrum of an unbounded operator, and perturbations of it.
Recommended in Guidebook 4A.13: Unbounded Operators and the Spectral Theorem
- VideoSpectral Theorem (L11)
The spectral theorem for self-adjoint operators and the functional calculus.
Recommended in Guidebook 4A.13: Unbounded Operators and the Spectral Theorem
- VideoTopological spaces: construction and purpose (Lecture 4)
Why topologies are defined the way they are, from someone who builds everything from scratch.
Recommended in Guidebook 7A.1: Topological Spaces and Quotients
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NP-RC-315874 is Frederic Schuller's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.
A window on one part of a person's work: papers here go back to 2021 and cover Ricci flow and its neighbouring flows, with the older work the site recommends, so this page is no measure of anyone's whole output. Being listed is not an endorsement by or of the person. If two people share this name, their work may appear together here. How it is put together.