Tags: #resources/recommendations #projects/to-read #nograph #MOC
Recommendations
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From Dave:
- Rolfsen’s Knots and Links,
- Milnor’s Characteristic Classes,
- Milnor’s Morse Theory,
- Milnor’s Topology from a Differentiable Viewpoint,
- Gompf and Stipsicz’s 4-manifolds and Kirby Calculus.
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Lee, Smooth Manifolds #geomtop/manifolds #geomtop/differential-geometry
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Cannas da Silva, https://people.math.ethz.ch/~acannas/Papers/lsg.pdf #geomtop/symplectic-topology
- Skip chapters 4, 5, 25, 26, 30
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Folland, Analysis
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Kirillov, Lie Groups and Lie Algebras
- Daniel Litt #resources/recommendations
- See Lie group, Lie algebra
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Eliashberg, From Stein to Weinstein and Back #geomtop/symplectic-topology
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Milnor, Morse Theory
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Silverman, The Arithmetic of Elliptic Curves
- See elliptic curve
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Hartshorne, Algebraic Geometry
- See MOCs/Algebraic Geometry]]
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Weil, Basic Number Theory
- See Number theory
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Arnold, Methods in Classical Mechanics
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Pollack, Differential Topology
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Milnor, Lectures on h-Cobordism
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McDuff, Introduction to Symplectic Topology
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Peter J. Hilton Urs Stammbach, A Course in Homological Algebra (via Dan Nakano)
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Pramod Achar, Unreleased Text
- See geometric representation theory
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Eisenbud and Harris, https://www.maths.ed.ac.uk/~v1ranick/papers/eisenbudharris.pdf
- See schemes, MOCs/Algebraic Geometry|algebraic geometry]]
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Mumford, The Red Book of Varieties and Schemes
- See scheme
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Osvath and Szabo, https://web.math.princeton.edu/~petero/GridHomologyBook.pdf
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Frank Warner, Foundations of Differentiable Manifolds and Lie Groups
- See Lie groups
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Guillemin?, Stable Mappings and Their Singularities
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Nicolas Libedinsky, https://arxiv.org/abs/1702.00039
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Valenza, Fourier Analysis on Number Fields
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Taylor, Complex Analysis
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Simon, Complex Analysis
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Rick Miranda, Algebraic Curves and Riemann Surfaces
- See algebraic curve
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Voison, Complex Algebraic Geometry
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Carlson, https://www-fourier.ujf-grenoble.fr/~peters/Books/PeriodBook.f/SecondEdition/PerBook.pdf
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Seiberg Witten :
- The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds by Morgan.
- Some lecture notes: http://wwwf.imperial.ac.uk/~ssivek/papers/regensburg-notes.pdf
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Instanton Floer homology
- There are many references here: http://people.brandeis.edu/~ruberman/math221bs16/math121a06.html
- Example: http://people.brandeis.edu/~ruberman/math221bs16/mrowka_ClassNotes.pdf
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Fukaya category :
- Start from here: https://arxiv.org/pdf/1301.7056.pdf
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Casson invariants : Saveliev’s book: https://www.degruyter.com/view/title/121170/
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Goerss-Jardine, Simplicial Homotopy Theory.
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FGA Explained.
Light / Expository
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Littlewood’s Miscellany
- Contains Cambridge gossip!
Physics
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Supersymmetry for mathematicians
- See supersymmetry
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Geometry of Yang-Mills
- See Yang-Mills.
- Nat #resources/recommendations
- String theory for undergraduates
- Atiyah, The Geometry and Physics of Knots
- Thermodynamics: B. Diu et al, “Éléments de Physique Statistique”
- Applications of TFTs from Arun #resources/recommendations
- 2 volumes of Quantum Fields and Strings for Mathematicians (AMS)
- Some resources on mirror symmetry: https://www-math.umd.edu/research/seminars/rit-on-geometry-and-phsyics.html
- A ton of graduate physics courses: https://www.damtp.cam.ac.uk/user/tong/teaching.html
- More: https://twitter.com/dzackgarza/status/1390862843130548224 #resources/recommendations