Lecture notes, books and articles

Differential geometry:

• Gauge theory for fiber bundles, Peter W. Michor
• Natural operations in differential geometry, Peter W. Michor
• The Convenient Setting of Global Analysis, Andreas Kriegl, Peter W. Michor
• Topics on Differential Geometry, Peter W. Michor
• Topology and Physics - a historical essay, Charles Nash
• Topological Interpetations of Lattice Gauge Field Theory, Doug Bullock, Charles Frohman, Joanna Kania-Bartoszynska
• What is supertopology, Ugo Bruzzo, Vladimir Pestov
• Preparation for Gauge Theory, George Svetlichny
• Supersolutions, Pierre Deligne, Daniel S. Freed
• Mathematical foundations of geometric quantization, Arturo Echeverría-Enríquez, Miguel C. Muñoz-Lecanda, Narciso Román-Roy, Carles Victoria-Monge
• Introduction to pseudo-differential operators, M. S. Joshi
• Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, Peter B. Gilkey
• Spinors, Spectral Geometry, and Riemannian Submersions, Peter B. Gilkey, John V. Leahy, Jeonghyeong Park
• Geometry of the Physical Phase Space in Quantum Gauge Systems, Sergei V. Shabanov
• On the Definition of Geometric Dirac Operators, Herbert Schröder

Physics:

• Dirac's formalism and mathematical suprises in quantum mechanics, François Gieres
• A Tensor Form of the Dirac Equation, N. G. Marchuk
• Extended Quantum Mechanics, Pavel Bóna
• Modern Mathematical Physics: what it should be, L. D. Faddeev
• Localization Regions of Local Observables, Bernd Kuckert
• The Concept of Particle Wieghts in Local Quantum Field Theory, Martin Porrmann
• Poisson-Lie Structures on Galilei Group, Y. Brihaye
• Further Representations of the Canonical Commutation Relations, Martin Florig, Stephen J. Summers
• Partial Dynamical Systems and the KMS Condition, Ruy Exel, Marcelo Laca
• Symmetric Hilbert-spaces Arising from Species of Structures, Madalin Guta, Hans Maassen
• A Tensor Form of the Dirac Equation, N. G. Marchuk
• Monstrous Moonshine and the Classification of CFT, Terry Gannon

Category theory:

• An Introduction to c-Categories, John C. Baez
• Limits in n-categories, Carlos Simpson
• Categorification, John C. Baez, James Dolan
• Higher-Dimensional Algebra IV.: 2-Tangles, John C. Baez, Laurel Langford
• Higher-Dimensional Algebra and Planck-Scale Physics, John C. Baez

Quantum groups:

• Introduction to Quantum Groups, P. Podles, E. Müller
• Universal C*-algebraic quantum groups arising from algerbaic quantum groups, J. Kustermans
• Projective Group Algebras, R. Casalbuoni
• On the Geometry of Inhomogeneous Quantum Groups, Paolo Aschieri
• Weight theory for C*-algebraic quantum groups, Johan Kustermans, Stefaan Vaes
• The Unitary Implementation of a Locally Compact Quantum Group Action, Stefaan Vaes
• Induced Corepresentations of Locally Compact Quantum Groups, Johan Kustermans
• Actions of compact groups, C*-index theorem, and families, E. V. Troitsky

Quantum logic:

• Quantum logic, A brief outline, K. Svozil
• Operational Quantum Logic: An Overview, Bob Coecke, David Moore, Alexander Wilce
• Classical and Quantum Probability, R. F. Streater

Noncommutative geometry:

• An Introduction to Noncommutative Geometry, Joseph C. Várilly
• Supersymmetric quantum theory and non-commutative geometry, J. Froehlich, O. Grandjean, A. Recknagel
• Lecture notes on C*-algebras, Hilbert C*-modules, and quantum mechanics, N. P. Landsman
• Projective Systems of Noncommutative Lattices as a Pregeometric Substratum, Giovanni Landi, Fedele Lizzi
• A short survey of noncommutative geometry, Alain Connes
• Notes for a Quantum Index Theorem , Roberto Longo
• A Survey Of Noncommutative Chern Characters, Do Ngoc Diep
• Remarks on Quantum Physics and Noncommutative Geometry, Lucian M. Ionescu
• A Survey of Noncommutative Dynamical Entropy, Erling Stormer
• Spectral Radii of Bounded Operators on Topological Vector Spaces, Vladimir G. Troitsky