Here, I

__Definition__: * MY 2010 WINTER* begins on Sunday, December 27, 2009 (after I get back from Costa Rica) and ends on Saturday, May 1, 2010.

- December 29 (Tuesday)
- Updated my math-related webpages.

- December 30 (Wednesday)
- Meeting with Joel: some more motivations, updated questions and his recent work/draft on quivers.

- January 1 (Friday)
- Joel and Chandrika's paper,
"Modules with 1-dimensional socles and components of Lusztig quiver varieties in type A" : read Section 1 (p1)

- Joel and Chandrika's paper,
- January 4 (Monday)
- Joel and Chandrika's paper,
"Modules with 1-dimensional socles and components of Lusztig quiver varieties in type A" : read part of Section 2 (p2)

- Joel and Chandrika's paper,
- January 5 (Tuesday)
- Meeting with Joel: discussed about Joel and Chandrika's paper, as well as Kac-Moody Lie algebras.
- Joel and Chandrika's paper,
"Modules with 1-dimensional socles and components of Lusztig quiver varieties in type A" : read more of Section 2 (p2)

- January 6 (Wednesday)
- Humphreys: reread some of Section 10.1 and began Section 10.3 (p47-48, p51)
- Eisenbud: read the Introduction chapter.
We played bridge for the first time in the new year, coming 2nd overall (out of 8 pairs) and 1st in flight B (out of 3 pairs) in the open game.

- January 7 (Thursday)
- Joel and Chandrika's paper,
"Modules with 1-dimensional socles and components of Lusztig quiver varieties in type A" : went through the rest of Section 2 without a complete understanding, and read Section 3.1 in some detail (p2-3) - Sent in some revision suggestions for Joel and Chandrika's paper.

- Joel and Chandrika's paper,
- March 22 (Monday)
- Plan for the week: finish proofreading, think about surfaces and homologies

- Things I want to understand:
- Current Tasks:
- Math textbooks to read:
Fulton & Harris, "Representation Theory -- A First Course" (Fulton-Harris)- Humphreys, "Introduction to Lie Algebras and Representation Theory"

**Representation Theory**Bredon, "Topology and Geometry"

**Geometry**- Gelfand and Manin, "Methods of Homological Algebra" (Gelfand-Manin)
Mac Lane, "Categories for the Working Mathematician"

**Homological Algebra & Category Theory**- Eisenbud, "Commutative Algebra: with a View Toward Algebraic Geometry"
- Perrin, "Algebraic Geometry: An Introduction" [Course website]

**Algebraic Geometry**- Dror, "AKT-09" (online vide course on Algebraic Knot Theory, 2009 Fall)

**Algebraic Knot Theory**- Kassel, "Quantum Groups" (should finish)
- Turaev, "Quantum Invariants of knots and 3-Manifolds"
- Barkalov and Kirillov, "Tensor Categories and Modular Functors" (Barkalov-Kirillov)

**Quantum Groups & TQFTs** - Physics textbooks to read:
- Sakurai, "Modern Quantum Mechanics"
- Peskin & Schroeder, "An Introduction to Quantum Field Theory"
- Wen, "Quantum Field Theory of Many-body Systems"
- Perimeter Institute, PSI courses 2009-2010

**Quantum Field Theories** - Math papers to read: (not quite up to date)
- Brion's paper,
"Representations of quivers"

Lusztig's paper, "Canonical Bases Arising from Quantized Enveloping Algebras"

Crawley-Boevey and Schroeer's paper, "Irreducible components of varieties of modules"

Geiss, Leclerc and Schroer's paper,"Semicanonical bases and preprojective algebras"

Savage's paper,"Geometric and Combinatorial Realization of Crystal Graphs"

Savage's paper,"Finite-dimensional algebras and quivers"

Joel and Chandrika's paper,"Modules with 1-dimensional socles and components of Lusztig quiver varieties in type A" - Dror's paper,
"On Khovanov's categorification of the Jones polynomial"

Dror's paper,"Khovanov's homology for tangles and cobordisms" (Dror_2)

Lauda's paper,"A categorification of quantum sl(2)"

Khovanov's paper, "A categorification of the Jones polynomial" - Freedman, Nayak, Walker and Wang's paper,
"On picture (2+1)-TQFTs" - Dror's paper,
"The fundamental theorem of Vassiliev invariants" (Dror_3)

- Brion's paper,
- Physics papers to read: (not quite up to date)
- Levin and Wen's paper,
"String-net condensation: A physical mechanism for topological phases"

Kitaev's paper,"Fault-tolerant quantum computation by anyons"

Buerschaper and Aguado's paper,"Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models"

Lahtinen's expository paper,"Anyons, Quantum Double Symmetry and Topological Quantum Computation"

Hector's paper,"A Family of Non-Abelian Kitaev Models on a Lattice: Topological Condensation and Confinement" (Hector_2) - Hector's paper,
"Topological subsystem codes"

Poulin's paper,"Stabilizer Formalism for Operator Quantum Error Correction"

- Levin and Wen's paper,

Date | Rep Theory | Topology & Geometry | Homological Algebra & Category | TQFTs | Categorification | Quiver | Topological Phases | Topological QEC | Others | ||||||
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Apr.25 -May.1 |

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Last Update: 4 June 2010 |