Here, I list things that I'd like to learn.

- Math textbooks:
Kassel, "Quantum Groups" Barkalov & Kirillov, "Lectures on Tensor Categories and Modular Functors" Turaev, "Quantum Invariants of knots and 3-Manifolds" - Chari & Pressley, "A Guide to Quantum Groups"
(no hard copy, ~$45 used) - Schiffman & Etingof, "Lectures on Quantum Groups"
(no hard copy, ~$30)

**Quantum algebra & Quantum topology**Mac Lane, "Categories for the Working Mathematician" Gelfand & Manin, "Methods of Homological Algebra" - Jacob Lurie, "Higher Topos Theory"

**Category theory & Homotopy theory**Perrin, "Algebraic Geometry: An Introduction" - Connes, "Noncommutative Geometry"
(no hard copy, ~$130 used)

**Algebraic geometry & Noncommutative geometry**Bredon, "Topology and Geometry" - Dror's course on Algebraic Knot Theory "AKT-09" (Fall 2009, video recordings)

**Topology & Geometry**Fulton & Harris, "Representation Theory -- A First Course" Joel's notes on Representation theory of compact and reductive groups (Winter 2011)- Kleshchev, "Linear and projective representations of symmetric groups"
(no hard copy, ~$50 used) - Chriss & Ginzburg, "Representation Theory and Complex Geometry"
- Hong & Kang, "Introduction to Quantum Groups and Crystal Bases"
(no hard copy) - Humphreys, "Representations of Semisimple Lie Algebras in the BGG Category O"
(printed copy) - Ginzburg, "Perverse sheaves on a loop group and Langlands' duality"
(long paper)

**Representation theory** - Physics textbooks:
Nielsen & Chuang, "Quantum Computation and Quantum Information" Nakahara, "Geometry, Topology and Physics" - Heinonen, "Composite Fermions: A Unified View of the Quantum Hall Regime"

- Programming books:
- Oram & Wilson, "Beautiful Codes"
- Kernighan & Ritchie, "The C Programming Language"
- Skiena & Revilla, "Programming Challenges"

- Math textbooks:
- Jacob Lurie, "Higher Algebra"
(forthcoming)

**Category theory & Homotopy theory**- Eisenbud, "Commutative Algebra: with a View Toward Algebraic Geometry"
- Harris, "Algebraic Geometry -- A First Course"
- Hartshorne, "Algebraic Geometry"

**Algebraic geometry**- Hatcher, "Algebraic Topology"
- Bott & Tu, "Differential Forms in Algebraic Topology"
- Guillemin & Pollack, "Differential Topology"
(no hard copy)

**Topology**Humphreys, "Introduction to Lie Algebras and Representation Theory" - Knapp, "Lie Groups Beyond an Introduction"
- Bump, "Lie Groups"
(no hard copy)

**Representation theory**- Lee, "Introduction to Smooth Manifolds"
- Cannas da Silva, "Lectures on Symplectic Geometry"

**Geometry** - Jacob Lurie, "Higher Algebra"
- Physics textbooks:
- Sakurai, "Modern Quantum Mechanics"
- Peskin & Schroeder, "An Introduction to Quantum Field Theory"
- Wen, "Quantum Field Theory of Many-body Systems"
- Connes & Marcolli, "Noncommutative Geometry, Quantum Fields and Motives"
(forthcoming)

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Last Update: 21 May 2010 |