Mathematics

see also Differential Geometry

reviews

Introduction to Sporadic Groups
by Luis J. Boya (1101.3055 [hep-th], 18 pages)

Differential K-theory. A survey
by Ulrich Bunke (Universität Regensburg), Thomas Schick (Georg-August-Universität Göttingen) (1011.6663 [hep-th], 50 pages)

Gauge Theory and Langlands Duality
by Edward Frenkel (0906.2747 [hep-th], 32 pages)

Three lectures on classical integrable systems and gauge field theories
by M.Olshanetsky (0802.3857 [hep-th], 36 pages)

Surface Operators and Knot Homologies
by S. Gukov (hep-th/0706.2369, 37 pages)

Sasakian Geometry, Holonomy, and Supersymmetry
by C.P. Boyer, K. Galicki (math.DG/0703231, 39 pages)

Lectures on Hopf Algebras, Quantum Groups and Twists
by P. Aschieri (hep-th/0703013, 20 pages)

Lectures on Complex Geometry, Calabi-Yau Manifolds and Toric Geometry
by V. Bouchard (hep-th/0702063, 63 pages)

Introduction to the Gopakumar-Vafa Large N Duality
by D. Auckly, S. Koshkin (math.GT/0701568, 260 pages)

Toric Geometry and Calabi-Yau Compactifications
by M. Kreuzer (hep-th/0612307, 12 pages)

The Unitary Representations of the Poincare Group in Any Spacetime Dimension
by X. Bekaert, N. Boulanger (hep-th/0611263, 50 pages)

Topology of Fibre bundles and Global Aspects of Gauge Theories
by A. Collinucci, A. Wijns (hep-th/0611201, 42 pages)

What Does(n't) K-theory Classify?
by J. Evslin (hep-th/0610328, 91 pages)

Affine quantum groups
by G. W. Delius, N. J. MacKay (math/0607228, 15 pages)
concise review for Encyclopedia of Mathematical Physics (Elsevier, 2006)

Physics and Mathematics of Calogero Particles
by A.P. Polychronakos (hep-th/0607033, 65 pages)

Lectures on Generalized Complex Geometry and Supersymmetry
by M. Zabzine (hep-th/0605148, 34 pages)

A Brief Review of Supersymmetric Non-linear Sigma Models and Generalized Complex Geometry
by U. Lindström (hep-th/0603240, 16 pages)

Lectures on Twistors
by I. Bars (hep-th/0601091, 39 pages)

Complex Geometry and Supergeometry
by E. D'Hoker, D.H. Phong (hep-th/0512197, 42 pages)

Lectures on the Langlands Program and Conformal Field Theory
by E. Frenkel (hep-th/0512172, 128 pages)

Hopf Algebra Approach to Feynman Diagram Calculations
by K. Ebrahimi-Fard, D. Kreimer (hep-th/0510202, 30 pages)

Clifford Algebras in Physics
by M. Rausch de Traubenberg (hep-th/0506011, 38 pages)

Particle Physics as Representations of the Poincare Algebra
by L. Brink (hep-th/0503035, 25 pages)

Geometric Transitions
by M. Rossi (math.AG/0412514, 44 pages)

Lectures on Elliptic Functions and Modular Forms in Conformal Field Theory
by N.M. Nikolov, I.T. Todorov (math-ph/0412039, 87 pages)

Fourier Mukai Transforms and Applications to String Theory
by B. Andreas, D.H. Ruiperez (math.AG/0412328, 52 pages)

Introduction to Nonequilibrium Quantum Field Theory
by J. Berges (hep-ph/0409233, 131 pages)

Introduction to Yangian Symmetry in Integrable Field Theory
by N. MacKay (hep-th/0409183, 36 pages)

2D Quantum Gravity, Matrix Models and Graph Combinatorics
by P. Di Francesco (math-ph/0406013, 60 pages)

Conformal Field Theory and Torsion Elements of the Bloch Group
by W. Nahm (hep-th/0404120, 63 pages)

Monstrous Moonshine: The First Twenty-five Years
by T. Gannon (math.QA/0402345, 32 pages)

Lectures on Integrable Hierarchies and Vertex Operators
by A.A. Vladimirov (hep-th/0402097, 28 pages)

Les Houches Lectures on Strings and Arithmetic
by Gregory W. Moore (hep-th/0401049, 61 pages, 3 figures)

Automorphic forms: a physicist's survey
by B. Pioline, A. Waldron (hep-th/0312068, 22 pages)

Lectures on Instanton Counting
by H. Nakajima, K. Yoshioka (math.AG/0311058, 60 pages)

Lectures on Mirror Symmetry, Derived Categories, and D-branes
by A. Kapustin, D. Orlov (math.AG/0308173, 30 pages)

Lectures on D-branes and Sheaves
by E. Sharpe (hep-th/0307245, 87 pages)

Seiberg-Witten Theory, Symplectic Forms, and Hamiltonian Theory of Solitons
by E. D'Hoker, I.M. Krichever, D.H. Phong (hep-th/0212313, 47 pages)

Enumerative geometry and knot invariants
by Marcos Marino (hep-th/0210145, 69 pages, 13 figures)

Large N Dualities and Transitions in Geometry
by A. Grassi, M. Rossi (math.AG/0209044, 76 pages)

What Do Topologists Want from Seiberg-Witten Theory?
by K. Iga (hep-th/0207271, 51 pages)

K-Theory in Quantum Field Theory
by D.S. Freed (math-ph/0206031, 56 pages)

An Introduction to Symmetric Spaces
by U. Magnea (cond-mat/0205288, 65 pages)

Noether's Variational Theorem II and the BV Formalism
by R. Fulp, T. Lada, J. Stasheff (math.QA/0204079, 15 pages)

Ten Lectures on Jet Manifolds in Classical and Quantum Field Theory
by G. Sardanashvily (math-ph/0203040, 77 pages)

Structures in Feynman Graphs - Hopf Algebras and Symmetries
by D. Kreimer (hep-th/0202110, 41 pages)

Bits and Pieces in Logarithmic Conformal Field Theory
by M. Flohr (hep-th/0111228, 90 pages)

Lectures on Calabi-Yau and special Lagrangian geometry
by Dominic Joyce (math.DG/0108088, 56 pages)

Math and Physics
by Jose M. F. Labastida (hep-th/0107079, 20 pages)

Heat Kernel Approach in Quantum Field Theory
by I. Avramidi (math-ph/0107018, 66 pages)

The Octonions
by J. Baez (math.RA/0105155, 56 pages)

Algebraic Quantum Field Theory and Operator Algebras
by B. Schroer (math-ph/0102018, 69 pages)

Overview Of K-Theory Applied To Strings
by Edward Witten (hep-th/0007175, 20 pages)

An Elementary Introduction to Groups and Representations
by B.C. Hall (math-ph/0005032, 128 pages)

An Introduction to Quantum Algebras and Their Applications
by R. Jaganathan (math-ph/0003018, 15 pages)

A Short Survey of Noncommutative Geometry
by Alain Connes (hep-th/0003006, 45 pages)

Fields, Strings, Matrices and Symmetric Products
by R. Dijkgraaf (hep-th/9912104, 52 pages)

An Introduction to Conformal Field Theory
by M.R. Gaberdiel (hep-th/9910156, 69 pages)

q-Deformed Heisenberg Algebras
by J. Wess (math-ph/9910013, 63 pages)

Dirac's Formalism and Mathematical Surprises in Quantum Mechanics
by F. Gieres (quant-ph/9907069, 39 pages)

Monstrous Moonshine and the Classification of CFT
by T. Gannon (math.QA/9906167, 65 pages)

Chern-Simons Gauge Theory: Ten Years After
by J.M.F. Labastida (hep-th/9905057, 62 pages)

3-Sasakian Manifolds
by C.P. Boyer, K. Galicki (hep-th/9810250, 59 pages)

Deformation Quantization: Twenty Years After
by D. Sternheimer (math.QA/9809056, 39 pages)

About Symmetries in Physics
by F. Gieres (hep-th/9712154, 42 pages)

Lectures in Topological Quantum Field Theory
by J.M.F. Labastida, C. Lozano (hep-th/9709192, 62 pages)

Quantum Groups, Roots of Unity and Particles on quantized Anti-de Sitter Space
by Harold Steinacker (hep-th/9705211, 115 pages, 8 figures)

An Introduction to n-Categories
by J. Baez (q-alg/9705009, 34 pages)

Equivariant Localization of Path Integrals
by R.J. Szabo (hep-th/9608068, 250 pages)

Dictionary on Lie Superalgebras
by L. Frappat, A. Sciarrino, P. Sorba (hep-th/9607161, 145 pages)

Dirac's Canonical Quantization Programme
by H.-J. Matschull (quant-ph/9606031, 40 pages)

New Results in Topological Field Theory and Abelian Gauge Theory
by G. Thompson (hep-th/9511038, 57 pages)

Dirac Operator and Eigenvalues in Riemannian Geometry
by G. Esposito (gr-qc/9507046, 105 pages)

Links, Quantum Groups, and TQFT's
by S. Sawin (q-alg/9506002, 36 pages)

Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
by S. Cordes, G. Moore, S. Ramgoolam (hep-th/9411210, 247 pages)

2D Gravity and Random Matrices
by P. Di Francesco, P. Ginsparg, J. Zinn-Justin (hep-th/9306153, 190 pages)

An Anyon Primer
by S. Rao (hep-th/9209066, 88 pages)

The Mathai-Quillen Formalism and Topological Field Theory
by M. Blau (hep-th/9203026, 34 pages)

Intersection Theory, Integrable Hierarchies and Topological Field Theory
by R. Dijkgraaf (hep-th/9201003, 73 pages)

links

Geometric Langlands Program