Tags: #recommendation #reading_projects #nograph #MOC

Recommendations

• Lee, Smooth Manifolds #manifolds #differential_geometry

• Cannas da Silva, https://people.math.ethz.ch/~acannas/Papers/lsg.pdf #symplectic

  • Skip chapters 4, 5, 25, 26, 30

• Folland, Analysis #qual_analysis

• Kirillov, Lie Groups and Lie Algebras

  • Daniel Litt #recommendation
  • See Lie group, Lie algebra

• Eliashberg, From Stein to Weinstein and Back #symplectic

• Milnor, Morse Theory

• Silverman, The Arithmetic of Elliptic Curves

  • See elliptic curve

• Hartshorne, Algebraic Geometry

  • See MOCs/Algebraic Geometry]]

• Weil, Basic Number Theory

  • See Number theory

• Arnold, Methods in Classical Mechanics

• Pollack, Differential Topology

• Milnor, Lectures on h-Cobordism

• McDuff, Introduction to Symplectic Topology

• Peter J. Hilton Urs Stammbach, A Course in Homological Algebra (via Dan Nakano)

• Pramod Achar, Unreleased Text

  • See geometric representation theory

• Eisenbud and Harris, https://www.maths.ed.ac.uk/~v1ranick/papers/eisenbudharris.pdf

  • See [[scheme|schemes]], MOCs/Algebraic Geometry|algebraic geometry]]

• Mumford, The Red Book of Varieties and Schemes

  • See scheme

• Osvath and Szabo, https://web.math.princeton.edu/~petero/GridHomologyBook.pdf

• Frank Warner, Foundations of Differentiable Manifolds and Lie Groups

  • See [[Lie group|Lie groups]]

• Guillemin?, Stable Mappings and Their Singularities

• Nicolas Libedinsky, https://arxiv.org/abs/1702.00039

• Valenza, Fourier Analysis on Number Fields

• Taylor, Complex Analysis

• Simon, Complex Analysis

• Rick Miranda, Algebraic Curves and Riemann Surfaces

  • See algebraic curve

• Voison, Complex Algebraic Geometry

• Carlson, https://www-fourier.ujf-grenoble.fr/~peters/Books/PeriodBook.f/SecondEdition/PerBook.pdf

• 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

• 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

• Fukaya category :

  • Start from here: https://arxiv.org/pdf/1301.7056.pdf

• Casson invariants : Saveliev’s book: https://www.degruyter.com/view/title/121170/

• Goerss-Jardine, Simplicial Homotopy Theory.

• FGA Explained.

Light / Expository

• Littlewood’s Miscellany
  • Contains Cambridge gossip!

Physics

• [[attachments/Supersymmetry for mathematicians.pdf|Supersymmetry for mathematicians]]❗
  • See supersymmetry
• [[attachments/Atiyah-Geometry-of-Yang-Mills-Field.pdf|Atiyah, Geometry of Yang Mills]]❗
  • See Yang-Mills.
  • Nat #recommendation
• String theory for undergraduates
  • Leo #recommendation
• Atiyah, The Geometry and Physics of Knots
• Thermodynamics: B. Diu et al, “Éléments de Physique Statistique”
• Applications of TFTs from Arun #recommendation
  • https://arxiv.org/abs/1604.06527
  • https://arxiv.org/abs/1908.09916
• 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 #recommendation

Journals

To Review/2021-04-26_Journals attachments/Journals.pdf❗