Saturday, August 1, 2009


Introductory Remarks

(In case anyone is wondering, I made this at 4:45 PM on 11 August, but I wanted it to be the second entry, so I modified the entry date and time. The entire raison d'etre of this post is to keep track of all the wonderful resources on and off the internet that I use, or will use.)

It is hard to pick between the Library of Congress classification for mathematics or the Mathematics Subject Classification (MSC) scheme. But I think I will try to stick to the latter.

A more comprehensive description of the mathematical classification scheme is also useful.

We should be aware of the Mathematics Subject Classification (MSC) scheme and the attempted format for bibliography entries.

One last caveat: Although I try to separate items into the LOC classification, I will also duplicate entries if they are useful in many fields (e.g. Neretin's Categories of Symmetries and Infinite-Dimensional Groups can be used in Lie groups, Lie Algebras, for some examples of semigroups, or for some examples in category theory — thus it will appear several times!).

Mathematical–Physics Bibliography

00 General Mathematics

00A: General and Miscellaneous Topics

  1. David S. Dummit, Richard M. Foote, Abstract Algebra.
    Third edition. John Wiley & Sons, Inc., Hoboken, NJ, 2004. xii+932 pages.
  2. Gerald B. Folland, Real analysis. Modern techniques and their applications.
    Second edition. Pure and Applied Mathematics (New York). A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1999. xvi+386 pages.
    Shields Library QA300 .F67 1999.
  3. Serge Lang, Algebra.
    Graduate Texts in Mathematics 211, Springer-Verlag, Third Edition (2000) xvi+914 pages.
  4. Elliot H. Lieb, Michael Loss, Analysis.
    Second edition. Graduate Studies in Mathematics 14. American Mathematical Society, Providence, RI (2001). xxii+346 pages.
  5. Erich Schechter, Handbook of Analysis and its Foundations.
    Academic Press (1997) xxii+883 pages.

02 Logic and foundations

02-01: Elementary exposition (collegiate level)

  1. Yu. I. Manin, A course in mathematical logic.
    Translated from the Russian by Neal Koblitz. Graduate Texts in Mathematics, Vol. 53. Springer-Verlag, New York-Berlin, 1977. xiii+286 pages.
    DOI: 10.1007/978-1-4419-0615-1.

03 Mathematical Logic and Foundations

03B: General logic

  1. Carlos Simpson, "Computer theorem proving in math."
    Eprint: arXiv:math/0311260v2 [math.HO], 29 pages.
    Lett. Math. Phys. 69 (2004), 287–315

03C: Model theory

  1. John Goodrick, Byunghan Kim, Alexei Kolesnikov, "Amalgamation functors and homology groups in model theory."
    Eprint: arXiv:1105.2921v1 [math.LO], 64 pages. Submitted on 15 May 2011.
  2. David Marker, Model Theory: An Introduction.
    Graduate Texts in Mathematics, 217. Springer-Verlag, New York, 2002. viii+342 pages.
    DOI: 10.1007/b98860.

03E: Set theory

  1. F. William Lawvere, Robert Rosebrug, Sets for Mathematics.
    Cambridge University Press, Cambridge, 2003. xiv+261 pages.
  2. Michael A. Shulman, "Set theory for category theory."
    Eprint: arXiv:0810.1279v2 [math.CT], 39 pages.
  3. Carlos Simpson, "Set-theoretical mathematics in Coq."
    Eprint: arXiv:math/0402336v1 [math.LO], 16 pages.

03G: Algebraic logic

  1. Joseph A. Goguen, "Types as Theories."
    Eprint: CiteseerX, 29 pages.
    In Topology and category theory in computer science (Oxford, 1989), pages 357–390, Oxford Sci. Publ., Oxford Univ. Press, New York, 1991.
  2. Jacob Lurie, "On Infinity Topoi."
    Eprint: arXiv:math/0306109v2 [math.CT], 60 pages.

05 Combinatorics

05-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Anders Björner, Francesco Brenti, Combinatorics of Coxeter groups.
    Graduate Texts in Mathematics, 231. Springer, New York, 2005. xiv+363 pages.
    DOI: 10.1007/3-540-27596-7.
  2. J. A. Bondy, U. S. R. Murty, Graph Theory.
    Graduate Texts in Mathematics, 244. Springer, New York, 2008. xii+651 pages.
    DOI: 10.1007/978-1-84628-970-5.

05A: Enumerative combinatorics

  1. Christian Krattenthaler, "Advanced Determinant Calculus."
    Eprint: arXiv:math/9902004v3 [math.CO], 67 pages. Revised 31 May 1999.
    Séminaire Lotharingien Combin. 42 (1999) (The Andrews Festschrift), paper B42q, 67 pp.

06 Order, lattices, ordered algebraic structures

06A: Ordered Sets

  1. Noson S. Yanofsky, "Galois Theory of Algorithms."
    Eprint: arXiv:1011.0014v1 [math.RA] (2010) 22 pages.

11 Number theory

11-01: Elementary exposition, textbooks

  1. Tom Apostol, Introduction to analytic number theory.
    Undergraduate Texts in Mathematics. Springer-Verlag, New York-Heidelberg, 1976. xii+338 pages.
  2. Henri Cohen, Number Theory. Vol I. Tools and Diophantine Equations.
    Graduate Texts in Mathematics, 239. Springer, New York, 2007. xxiv+650 pages.
    DOI: 10.1007/978-0-387-49923-9.
  3. —————, Number theory. Vol. II. Analytic and modern tools.
    Graduate Texts in Mathematics, 240. Springer, New York, 2007. xxiv+596 pages.
    DOI: 10.1007/978-0-387-49894-2.

11F: Discontinuous groups and automorphic forms

  1. Scott Carnahan, "Generalized Moonshine I: Genus zero functions."
    Eprint: arXiv:0812.3440v3 [math.RT], 23 pages.
    Algebra and Number Theory 4 no. 6 (2010) pages 649–679.
  2. —————, "Generalized moonshine II: Borcherds products."
    Eprint: arXiv:0908.4223v2 [math.RT], 34 pages.
  3. Fred Diamon, Jerry Shurman, A First Course in Modular Forms.
    Graduate Texts in Mathematics, 228. Springer-Verlag, New York, 2005. xvi+436 pages.
    DOI: 10.1007/b138781.
  4. John F. Duncan, "Arithmetic groups and the affine E8 Dynkin diagram."
    Eprint: arXiv:0810.1465v2 [math.RT] 29 pages.
    In Groups and symmetries, pages 135–163, CRM Proc. Lecture Notes, 47, Amer. Math. Soc., Providence, RI, 2009.
  5. Suresh Govindarajan, "Brewing moonshine for Mathieu."
    Eprint: arXiv:1012.5732v1 [math.NT], 21 pages (2010).
  6. Jae-Hyun Yang, "Kac-Moody Algebras, the Monstrous Moonshine, Jacobi Forms and Infinite Products."
    Eprint: arXiv:math/0612474v2 [math.NT], 77 pages.
    In Proceedings of the 1995 symposium on number theory, geometry and related topics, edited by Jin-Woo Son and Jae-Hyun Yang, the Pyungsan Institute for Mathematical Sciences (1996), pages 13–82.

11H: Geometry of numbers

  1. John H. Conway, Neil J.A. Sloane, Sphere packings, lattices and groups.
    Third edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 290. Springer-Verlag, New York, 1999. lxxiv+703 pages.
    With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov.

11J: Diophantine approximation, transcendental number theory

  1. Yong-Cheol Kim, "ζ(5) is irrational."
    Eprint: arXiv:1105.0730v2 [math.CA], 7 pages. Revised 10 May 2011.

12 Field theory and polynomials

12-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Steve Roman, Field Theory.
    Second edition. Graduate Texts in Mathematics, 158. Springer, New York, 2006. xii+332 pages.
    DOI: 10.1007/0-387-27678-5.

12F: Field Extensions

  1. Andrew Baker, "An Introduction to Galois Theory."
    Eprint (pdf) Compiled Sunday 9 Jan. 2011 5:38:34 PM (PST). 130 pages.
  2. James S. Milne, "Fields and Galois Theory."
    Notes version 4.22 eprint (2011) 126 pages.
  3. Miles Reid, Galois Theory material on the course MA3D5 Galois Theory given as a lecture course January–March 2003, 2004 and 2005

13 Commutative rings and algebras

  1. Nicolas Bourbaki, Elements of Mathematics: Commutative Algebra.
    Translated from the French. Paris, Hermann; Reading, Mass., Addison-Wesley Publishing Co. (1972) xxiv+625 pages.

13-00: General Reference Works

  1. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra.
    Addison-Wesley Publishing Co. (1969) ix+128 pages.

13-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Ezra Miller and Bernd Sturmfels, Combinatorial Commutative Algebra.
    Graduate Texts in Mathematics, 227. Springer-Verlag, New York, 2005. xiv+417 pages.
    DOI: 10.1007/b138602.

13D: Homological methods

  1. David Eisenbud, The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry.
    Graduate Texts in Mathematics, 229. Springer-Verlag, New York, 2005. xvi+243 pages.
    DOI: 10.1007/b137572.

13P: Computational aspects of commutative algebra

  1. David A. Cox, John Little, Donal O'Shea, Using Algebraic Geometry.
    Second edition. Graduate Texts in Mathematics, 185. Springer, New York, 2005. xii+572 pages.

14 Algebraic geometry

14A: Foundations

  1. Nikolai Durov, "Classifying Vectoids and Generalisations of Operads."
    Eprint: arXiv:1105.3114v1 [math.AG], 23 pages. Submitted on 16 May 2011.
    Based on talk "Classifying vectoids and generalizations of operads", given at conference "Contemporary Mathematics", St.Petersburg, June 12, 2009.
  2. David Eisenbud, Joe Harris, The Geometry of Schemes.
    Graduate Texts in Mathematics, 197. Springer-Verlag, New York, 2000. x+294 pages.
    DOI: 10.1007/b97680.
  3. Sharon Hollander, "A Homotopy Theory for Stacks."
    Eprint: arXiv:math/0110247v2 [math.AT], 24 pages.
    Israel J. Math. 163 (2008), 93–124. DOI: 10.1007/s11856-008-0006-5.
  4. Ieke Moerdijk, "Introduction to the language of stacks and gerbes."
    Eprint: arXiv:math/0212266v1 [math.AT], 30 pages.
  5. Ravi Vakil, "Foundations of Algebraic Geometry."
    Eprint: Lecture Notes for Stanford Math course 216 "Foundations Of Algebraic Geometry."

14C: Cycles and subschemes

  1. Marc Levine, Mixed Motives.
    AMS Publishers eprint (1998), 515 pages.

14D: Families, fibrations

  1. Robin Hartshorne, Deformation Theory.
    Graduate Texts in Mathematics, 257. Springer, New York, 2010. viii+234 pages.
    DOI: 10.1007/978-1-4419-1596-2.

14F: Cohomology theory

  1. Dennis Gaitsgory, "Notes on Geometric Langlands: ind-coherent sheaves."
    Eprint: arXiv:1105.4857v1 [math.AG], 92 pages.
  2. Matvei Libine, "Lecture Notes on Equivariant Cohomology."
    Eprint: arXiv:0709.3615v3 [math.SG], 72 pages.

14L: Algebraic Groups

  1. P. E. Newstead, "Geometric Invariant Theory."
    Eprint: Lecture Notes, 17 pages, November 2006.
  2. R. P. Thomas, "Notes on GIT and symplectic reduction for bundles and varieties."
    Eprint: arXiv:math/0512411v3 [math.AG], 51 pages.
    Surveys in Differential Geometry, 10 (2006): A Tribute to Professor S.-S. Chern.

15 Linear and multilinear algebra; matrix theory

15A: Basic linear algebra

  1. Ilse C.F. Ipsen, Dean J. Lee, "Determinant Approximations."
    Eprint: arXiv:1105.0437v1 [math.NA], 14 pages.

16 Associative rings and algebras

16W: Rings and algebras with additional structure

  1. N. Andruskiewitsch, C. Vay, "On a family of Hopf algebras of dimension 72."
    Eprint: arXiv:1105.0394v1 [math.QA], 26 pages. Submitted on 2 May 2011.
  2. Pavel Etingof, Dmitri Nikshych, Viktor Ostrik, "On fusion categories."
    Eprint: arXiv:math/0203060v10 [math.QA], 50 pages.
    Ann. of Math. (2) 162 no. 2 (2005), 581–642. DOI: 10.4007/annals.2005.162.581

17 Nonassociative rings and algebras

17-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Nicolas Bourbaki, Lie Groups and Lie Algebras: Chapters 1–3.
    Second Edition. Springer (1989).
  2. —————, Lie Groups and Lie Algebras: Chapters 4–6.
    First Edition. Springer (2002).
  3. —————, Lie Groups and Lie Algebras: Chapters 7–9.
    First Edition. Springer (2005).

17B: Lie Algebras

  1. Claude Chevalley, Theory of Lie Groups I.
    Sixth printing. Princeton University Press (1965).
  2. C. Dong, R.L. Griess Jr., G. Hoehn, "Framed vertex operator algebras, codes and the moonshine module."
    Eprint: arXiv:q-alg/9707008v1, 54 pages.
    Comm. Math. Phys. 193 (1998), pages 407–448.
  3. John F. Duncan, "Super-moonshine for Conway's largest sporadic group."
    Eprint: arXiv:math/0502267v3 [math.RT] 41 pages, corrected ed. posted 14 September 2006.
    In Duke Math. J. 139 no. 2 (2007), pages 255–315.
  4. —————, "Moonshine for Rudvalis's sporadic group I."
    Eprint: arXiv:math/0609449v2 [math.RT], 56 pages.
  5. —————, "Moonshine for Rudvalis's sporadic group II."
    Eprint: arXiv:math/0611355v2 [math.RT], 31 pages.
  6. —————, Igor B. Frenkel, "Rademacher sums, moonshine and gravity."
    Eprint: arXiv:0907.4529v2 [math.RT] 102 pages, posted 25 October 2009.
  7. —————, "Vertex operators and sporadic groups."
    Eprint: arXiv:0811.1306v1 [math.RT] 14 pages, posted 2008.
    In Moonshine: the first quarter century and beyond, pages 188–203, London Math. Soc. Lecture Note Ser. 372, Cambridge Univ. Press, Cambridge, 2010.
  8. Alex J. Feingold, Igor B. Frenkel, John F. X. Ries, Spinor Construction of Vertex operator Algebras, Triality, and E8(1).
    AMS Publishers. Contemporary Mathematics 121 (1991), 146 pages.
  9. Igor Frenkel, James Lepowsky, Arne Meurman, Vertex operator algebras and the Monster.
    Pure and Applied Mathematics, 134. Academic Press, Inc., Boston, MA, 1988. liv+508 pages.
  10. Igor Frenkel, Naihuan Jing, Weiqiang Wang, "Twisted vertex representations via spin groups and the McKay correspondence."
    Eprint: arXiv:math/0007159v2 [math.QA] 45 pages, posted 27 July 2000.
    Published Duke Math. J. 111 (2002), pages 51–96.
  11. Terry Gannon, Moonshine beyond the Monster. The bridge connecting algebra, modular forms and physics.
    Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge, 2006. xiv+477 pages.
  12. Masaaki Harada, Ching Hung Lam, Akihiro Munemasa, "On the structure codes of the moonshine vertex operator algebra."
    Eprint: arXiv:1005.1144v1 [math.QA], 33 pages.
  13. Victor G. Kac, Infinite Dimensional Lie Algebras.
    Third Edition. Cambridge University Press (1990) xxi+400 pages.
    Shields library QA252.3 K33 1990.
  14. A. A. Kirillov (editor), Topics in Representation Theory.
    AMS Publishers. Advances in Soviet Mathematics 2 (1991) xi+247 pages.
  15. Liang Kong, "Open-closed field algebras."
    Eprint: arXiv:math/0610293v3 [math.QA], 55 pages.
    Commun. Math. Phys. 280 (2008) pages 207–261.
  16. Tom Lada, Jim Stasheff, "Introduction to sh Lie algebras for physicists."
    Eprint: arXiv:hep-th/9209099v1, 14 pages.
    Internat. J. Theoret. Phys. 32 no. 7 (1993), 1087–1103.
  17. James Lepowsky, Haisheng Li, Introduction to vertex operator algebras and their representations.
    Progress in Mathematics, 227. Birkhäuser Boston, Inc., Boston, MA, 2004. xiv+318 pages.
  18. James Lepowsky, "Some developments in vertex operator algebra theory, old and new."
    Eprint: arXiv:0706.4072v1 [math.QA], 41 pages.
    To appear in proceedings of conference on Lie Algebras, Vertex Operator Algebras and Their Applications, North Carolina State University, 2005, Contemporary Math.
  19. Bong H. Lian, Gregg J. Zuckerman, "Moonshine Cohomology."
    Eprint: arXiv:q-alg/9501015v1, 29 pages.
    Sūrikaisekikenkyūsho Kōkyūroku No. 904 (1995), pages 87–115.
  20. Marco Manetti, "Deformation theory via differential graded Lie algebras."
    Eprint: arXiv:math/0507284v1 [math.AG], 22 pages (in English).
    Algebraic Geometry Seminars, 1998–1999 (Italian) (Pisa), pages 21–48, Scuola Norm. Sup., Pisa, 1999.
  21. Christophe Nozaradan, "Introduction to Vertex Algebras."
    Eprint: arXiv:0809.1380v3 [math.QA], 94 pages.
    Introductory notes on Vertex algebras…a great complement to Kac's book.
  22. Michael Penkava, "L-infinity algebras and their cohomology."
    Eprint: arXiv:q-alg/9512014v1, 28 pages.
  23. Dmitry Roytenberg, "On weak Lie 2-algebras."
    Eprint: arXiv:0712.3461v1 [math.QA], 18 pages.

17C: Jordan Algebras

  1. Kevin McCrimmon, A taste of Jordan algebras.
    Eprint: doi:10.1007/b97489.
    Universitext. Springer-Verlag, New York, 2004. xxvi+562 pages.

18 Category theory, homological algebra

18-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. P. Achar, Basic Facts on Sheaves. Notes for Louisiana State University's Math Course 7280 "Applications of Homological Algebra" (2007)
  2. Steve Awodey, Lecture Notes on Categorical Logic. Parts I, II, and III.
  3. John Baez, Some Definitions Everyone Should Know from UC Riverside's Quantum Gravity Fall 2004 seminar.
  4. Maarten M. Fokkinga, A Gentle Introduction to Category Theory - the calculational approach.
    Eprint, 80 pages.
    In Lecture Notes of the 1992 Summerschool on Constructive Algorithmics pages 1–72 of Part 1, published by the University of Utrecht (1992).
  5. F. William Lawvere, Stephen H. Schanuel, Conceptual mathematics. A first introduction to categories.
    Second edition. Cambridge University Press, Cambridge, 2009. xviii+390 pages.
  6. James McKernan, Lecture 4 Lecture Notes, MIT Math Course 18.726 (2008).
  7. NLab entry, "Stuff, Structure, Properties" entry.
  8. Charles Siegel, Morphisms of Sheaves, Rigorous Trivialities Blog post (2008).
  9. The Catsters, Lectures on Products and Coproducts 1, 2, 3, 4.
  10. —————, "Lectures on Natural Transformations" Lecture 1, 2, 3, 3A.
  11. —————, Youtube lectures, Adjoint Functor Lecture Series.
  12. —————, Youtube Lectures, Adjunctions from Morphisms 1, 2, 3, 4, 5.

18-02: Research exposition (monographs, survey articles)

  1. Jiri Adámek, Horst Herrlich, George E. Strecker, Abstract and Concrete Categories: The Joy of Cats.
    Eprint freely available online (2004).
  2. Michael Barr, Charles Wells, Toposes, Triples and Theories.
    Corrected reprint of the 1985 original [MR0771116]. Repr. Theory Appl. Categ. No. 12 (2005), x+288 pages.
    Eprint: Wells' website.
  3. Saunders Mac Lane, Homology.
    Reprint of the 1975 edition. Classics in Mathematics 114. Springer-Verlag, Berlin, 1995. x+422 pages.
  4. —————, Categories for the Working Mathematician.
    Graduate Texts in Mathematics 5, Springer-Verlag, Second Edition (1998) xii+314 pages.

18A: General theory of categories and functors

  1. Ruggero Pagnan, "Concrete fibrations."
    Eprint: arXiv:1105.4710v1 [math.CT], 10 pages.

18B: Special Categories

  1. J.L. Bell, Toposes and local set theories: An introduction.
    Dover Publications Inc., Mineola, New York, 2008. xiii+267 pages.
    Reproduction of the Oxford Logic Guides, 14. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1988.
  2. Robert Goldblatt, The categorial analysis of logic.
    Second edition. Studies in Logic and the Foundations of Mathematics, 98. North-Holland Publishing Co., Amsterdam, 1984. xvi+551 pages.
    Eprint: Cornell library.
  3. Tom Leinster, "An informal introduction to topos theory."
    Eprint: arXiv:1012.5647v2 [math.CT], 25 pages.

18C: Categories and theories

  1. Nicola Gambino, Joachim Kock, "Polynomial functors and polynomial monads."
    Eprint: arXiv:0906.4931v2 [math.CT], 42 pages.
  2. E. Getzler, M.M. Kapranov, "Modular Operads."
    Eprint: arXiv:dg-ga/9408003v2, 46 pages.
    Compositio Math. 110 no. 1 (1998), pages 65–126.

18D: Categories with Structure

  1. Bruce Bartlett, "On unitary 2-representations of finite groups and topological quantum field theory."
    Eprint: arXiv:0901.3975v1 [math.QA], 243 pages.
  2. John Baez and J. Dolan, "From Finite Sets to Feynman Diagrams."
    Eprint: arXiv:math/0004133v1 [math.QA], 30 pages.
    In Mathematics unlimited—2001 and beyond, pages 29–50. Springer, Berlin (2001).
  3. Mikhail Khovanov, "Heisenberg algebra and a graphical calculus."
    Eprint: arXiv:1009.3295v1 [math.RT], 45 pages.
  4. Alexander Kirillov Jr, "On the modular functor associated with a finite group."
    Eprint: arXiv:math/0310087v1 [math.QA], 7 pages.
  5. Tom Leinster, "A Survey of Definitions of n-Category."
    Eprint: arXiv:math/0107188v1 [math.CT], 67 pages.
    Theory Appl. Categ. 10 (2002), 1–70.
  6. —————, Higher Operads, Higher Categories.
    Eprint: arXiv:math/0305049v1 [math.CT], 410 pages.
    London Mathematical Society Lecture Note Series, 298. Cambridge University Press, Cambridge, 2004. xiv+433 pages.
  7. —————, "Are operads algebraic theories?"
    Eprint: arXiv:math/0404016v1 [math.CT], 6 pages.
    Bull. London Math. Soc. 38 no. 2 (2006), 233–238. doi: 10.1112/S002460930601825X.
  8. Jacob Lurie, Higher Algebra.
    Eprint: Lurie's copy, 950 pages.
  9. Viktor Ostrik, "Module categories, weak Hopf algebras and modular invariants."
    Eprint: arXiv:math/0111139v1 [math.QA], 26 pages.
    Transform. Groups 8 no. 2 (2003), 177–206. DOI: 10.1007/s00031-003-0515-6
  10. Ingo Runkel, Jurgen Fuchs, Christoph Schweigert, "Categorification and correlation functions in conformal field theory."
    Eprint: arXiv:math/0602079v1 [math.CT], 16 pages.
    International Congress of Mathematicians. Vol. III, pages 443–458, Eur. Math. Soc., Zürich, 2006.

18E: Abelian Categories

  1. Josep Elgueta, "Generalized 2-vector spaces and general linear 2-groups."
    Eprint: arXiv:math/0606472v1 [math.CT], 35 pages.
    J. Pure Appl. Algebra 212 no. 9 (2008), pages 2069–2091.
  2. Bernhard Keller, "Introduction to A-infinity algebras and modules."
    Eprint: arXiv:math/9910179v2 [math.RA], 30 pages.
  3. Mikhail Khovanov, Volodymyr Mazorchuk, Catharina Stroppel, "A brief review of abelian categorifications."
    Eprint: arXiv:math/0702746v2 [math.RT], 35 pages.
  4. Maxim Kontsevich, Yan Soibelman, "Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I."
    Eprint: arXiv:math/0606241v2 [math.RA], 70 pages (2006).
  5. Jacob Lurie, "Stable Infinity Categories."
    Eprint: arXiv:math/0608228v5 [math.CT], 73 pages.
  6. Pierre Schapira, "Categories and Homological Algebra: An Introduction to Derived Categories."
    Lecture notes eprint (2010) 124 pages.

18F: Categories and geometry

  1. Tom Leinster, "The Euler characteristic of a category."
    Eprint: arXiv:math/0610260v1 [math.CT], 24 pages.
    Doc. Math. 13 (2008), 21–49.

18G: Homological Algebra

  1. John Baez and Michael Shulman, "Lectures on n-Categories and Cohomology."
    Eprint: arXiv:math/0608420v2 [math.CT] 66 pages, 2 eps figures.
    Towards higher categories, pages 1–68, IMA Vol. Math. Appl., 152. Springer, New York (2010).
  2. Mohamed Barakat, Markus Lange-Hegermann, "An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization."
    Eprint arXiv:1003.1943v3 [math.AC], 30 pages. Revised 2 May 2010.
  3. Clemens Berger, Tom Leinster, "The Euler characteristic of a category as the sum of a divergent series."
    Eprint: arXiv:0707.0835v1 [math.CT], 11 pages.
    Homology, Homotopy Appl. 10 no. 1 (2008), 41–51.
  4. Mikhail Khovanov, Radmila Sazdanovic, "Categorification of the polynomial ring."
    Eprint: arXiv:1101.0293v1 [math.QA], 29 pages.
  5. Carlos Simpson, "Homotopy theory of higher categories."
    Eprint: arXiv:1001.4071v1 [math.CT], 472 pages.

19 K-theory

19-00: General Reference Works

  1. Allen Hatcher, Vector Bundles and K-Theory.
    Eprint: (2009).

20 Group theory and generalizations

20-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. M. Aschbacher, Finite group theory.
    Second edition. Cambridge Studies in Advanced Mathematics, 10. Cambridge University Press, Cambridge, 2000. xii+304 pages.
  2. Pierre Grillet, Abstract Algebra.
    Second edition. Graduate Texts in Mathematics, 242. Springer, New York, 2007. xii+669 pages.
    DOI: 10.1007/978-0-387-71568-1.

20-06: Proceedings, Conferences, Collections, etc.

  1. E. I. Khukhro and V. D. Mazurov, The Kourovka Notebook.
    Number 15. Russian Academy of Sciences, Siberian Branch, Institute of Mathematics (2002) 163 pages.
    Shields QA 174.2 .K6813 2002.

20B: Permutation groups

  1. George M. Bergman, "Generating infinite symmetric groups."
    Eprint: arXiv:math/0401304v2 [math.GR], 9 pages.
    Bull. London Math. Soc. 38 (2006), pages 429–440.
  2. Andrei Okounkov, "On the representations of the infinite symmetric group."
    Eprint: arXiv:math/9803037v1 [math.RT], 50 pages.
    Zapiski Nauchnyh Seminarov POMI 240 (1997), pages 167–230.

20C: Representation Theory of Groups

  1. David M. Goldschmidt, Group Characters, Symmetric Functions, and the Hecke Algebra.
    American Mathematical Society Publishers eprint (1993) 73 pages.

20D: Abstract finite groups

  1. Michael Aschbacher, Sporadic groups.
    Cambridge Tracts in Mathematics, 104. Cambridge University Press, Cambridge, 1994. xii+314 pages.
  2. Luis J. Boya, "Introduction to Sporadic Groups."
    Eprint: arXiv:1101.3055v1 [math-ph], 18 pages.
    SIGMA 7 (2011), 009, 18 pages.
    An introduction "for physicists."
  3. John F. Duncan, "Moonshine for Rudvalis's sporadic group I."
    Eprint: arXiv:math/0609449v2 [math.RT] 56 pages, posted 3 November 2008.
  4. —————, "Moonshine for Rudvalis's sporadic group II."
    Eprint: arXiv:math/0611355v2 [math.RT] 31 pages, posted 3 November 2008.
  5. Robert L. Griess Jr., Twelve sporadic groups.
    Springer Monographs in Mathematics. Springer-Verlag, Berlin, 1998. iv+169 pages.
  6. Robert L. Griess Jr., Ching Hung Lam, "A moonshine path from E8 to the monster."
    Eprint: arXiv:0910.2057v2 [math.GR], 42 pages.
    J. Pure Appl. Algebra 215 no. 5 (2011), pages 927–948.
  7. A.A. Ivonov, Geometry of Sporadic Groups. I. Petersen and tilde geometries.
    Encyclopedia of Mathematics and its Applications, 76. Cambridge University Press, Cambridge, 1999. xiv+408 pages.
  8. A.A. Ivonov and S.V. Shpectorov, Geometry of sporadic groups. II. Representations and amalgams.
    Encyclopedia of Mathematics and its Applications, 91. Cambridge University Press, Cambridge, 2002. xviii+286 pages.
  9. A.A. Ivonov, The Monster group and Majorana involutions.
    Cambridge Tracts in Mathematics, 176. Cambridge University Press, Cambridge, 2009. xiv+252 pages.
  10. Robert A. Wilson, The finite simple groups.
    Graduate Texts in Mathematics 251. Springer-Verlag London, Ltd., London 2009. xvi+298 pages.

20E: Structure and classification of infinite or finite groups

  1. Peter Abramenko, Kenneth S. Brown, Buildings. Theory and applications.
    Graduate Texts in Mathematics, 248. Springer, New York, 2008. xxii+747 pages.
    DOI: 10.1007/978-0-387-78835-7.

20F: Special aspects of infinite or finite groups

  1. Marcelo Fiore, Tom Leinster, "An abstract characterization of Thompson's group F."
    Eprint: arXiv:math/0508617v2 [math.GR], 17 pages.
    Semigroup Forum 80 no. 2 (2010), 325–340. DOI: 10.1007/s00233-010-9209-2.
  2. Christian Kassel, Vladimir Turaev, Braid Groups.
    Graduate Texts in Mathematics, 247. Springer, New York, 2008. xii+340 pages.
    DOI: 10.1007/978-0-387-68548-9.

20J: Connections with homological algebra and category theory

  1. Conchita Martinez-Perez, Brita E.A. Nucinkis, "Bredon cohomological finiteness conditions for generalisations of Thompson's groups."
    Eprint: arXiv:1105.0189v2 [math.GR] 23 pages.

20L: Groupoids (i.e. small categories in which all morphisms are isomorphisms)

  1. Jeffrey C. Morton, "2-Vector Spaces and Groupoids."
    Eprint: arXiv:0810.2361v2 [math.QA], 44 pages.

22 Topological groups, Lie groups

22-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. John Frank Adams, Lectures on Lie Groups.
    New York: W. A. Benjamin (1969).
    Shields library QA287 A3
  2. —————, Lectures on Exceptional Lie Groups.
    University of Chicago Press (1996). xiv+122 pages.
    Shields library QA387 A299 1996
  3. Daniel Bump, Lie Groups.
    Graduate Texts in Mathematics, 225. Springer-Verlag, New York, 2004. xii+451 pages.
  4. Robert Gilmore, Lie groups, Lie algebras, and some of their applications.
    Reprint of the 1974 original. Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1994. xx+587 pages.
  5. Alexander Kirillov Jr, An introduction to Lie groups and Lie algebras.
    Eprint 136 pages.
    Cambridge Studies in Advanced Mathematics 113. Cambridge University Press, Cambridge, 2008. xii+222 pages.
  6. Anthony W. Knapp, Lie Groups Beyond an Introduction.
    Second Edition. Birkhäuser. Progress in Mathematics 140 (2002) 812 pages.
  7. V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations.
    Graduate Texts in Mathematics 102 Springer-Verlag (1984).

22-02: Research exposition (monographs, survey articles)

  1. Predrag Cvitanović, Group Theory: Birdtracks, Lie's, and exceptional groups.
    Princeton University Press, Princeton, NJ, 2008. xiv+273 pages. Eprint: available (version 9).

22A: Topological and differentiable algebraic systems

  1. Yu. A. Neretin, Categories of Symmetries and Infinite-Dimensional Groups.
    Oxford Science Publications. London Mathematical Society Monographs, New Series 16 (1996) xiv+417 pages.
    Shields library QA 252.3 N4713 1996.
  2. Vladimir Pestov, "Topological groups: where to from here?"
    Eprint: arXiv:math/9910144v4 [math.GN].
    Proceedings, 14th Summer Conf. on General Topology and its Appl. (C.W. Post Campus of Long Island University, August 1999), Topology Proceedings 24 (1999), pages 421–502.
  3. —————, "Forty-plus annotated questions about large topological groups."
    Eprint: arXiv:math/0512564v3 [math.GN], 11 pages.
    An invited contribution to the second edition of Open Problems In Topology (Elliott Pearl, editor).
  4. —————, Aleksandra Kwiatkowska, "An introduction to hyperlinear and sofic groups."
    Eprint: arXiv:0911.4266v2 [math.GR], 30 pages.
    A final submission to the volume Appalachian Set Theory 2006–2009 (James Cummings and Ernest Schimmerling, eds.), to appear in the Ontos-Verlag Mathematical Logic Series.

22D: Locally compact groups and their algebras

  1. Karl-Hermann Neeb, "A complex semigroup approach to group algebras of infinite dimensional Lie groups."
    Eprint: arXiv:0709.1062v1 [math.OA], 41 pages. Submitted on 7 Sep 2007.
    Semigroup Forum 77 no. 1 (2008) pages 5–35.
  2. Volker Runde, "Abstract harmonic analysis, homological algebra, and operator spaces."
    Eprint: arXiv:math/0206041v6 [math.FA] (2002) 12 pages.

22E: Lie Groups

  1. Edward Frenkel, "Gauge Theory and Langlands Duality."
    Eprint: arXiv:0906.2747v1 [math.RT], 32 pages.
    Séminaire Bourbaki. Volume 2008/2009. Exposés 997–1011.
    Astérisque No. 332 (2010), Exp. No. 1010, ix–x, 369–403.
  2. Helge Glockner, "Fundamentals of direct limit Lie theory."
    Eprint: arXiv:math/0403093v2 [math.GR], 33 pages.
    TU Darmstadt Preprint 2324, March 2004.
  3. —————, "Direct limits of infinite-dimensional Lie groups."
    Survey article, arXiv:0803.0045v2 [math.GR], 38 pages. Revised 1 April 2008.
  4. Brian C. Hall, "An Elementary Introduction to Groups and Representations."
    Eprint: arXiv:math-ph/0005032v1, 128 pages. Submitted on 31 May 2000.
  5. R. Michael Howe, Tuong Ton-That, "Multiplicity, Invariants and Tensor Product Decomposition of Tame Representations of U(∞)."
    Eprint: arXiv:math-ph/9910025v1, 48 pages.
    To appear in J. Math. Phys.
  6. A. A. Kirillov (editor), Topics in Representation Theory.
    AMS Publishers. Advances in Soviet Mathematics 2 (1991) xi+247 pages.
  7. Karl-Hermann Neeb, Friedrich Wagemann, "Lie group structures on groups of smooth and holomorphic maps on non-compact manifolds."
    Eprint: arXiv:math/0703460v2 [math.DG], 39 pages. Revised 16 March 2007.
    Geometriae Dedicata 134 (2008) pages 17–60.
  8. Karl-Hermann Neeb, "A complex semigroup approach to group algebras of infinite dimensional Lie groups."
    Eprint: arXiv:0709.1062v1 [math.OA], 41 pages.
  9. Mark R. Sepanski, Compact Lie Groups.
    Graduate Texts in Mathematics, 235. Springer, New York, 2007. xiv+198 pages.
    DOI: 10.1007/978-0-387-49158-5.
  10. Josef Teichmann, "Infinite dimensional Lie Theory from the point of view of Functional Analysis."
    Dissertation eprint (2001) x+100 pages.

26 Real functions

26-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. R. Courant, Differential and integral calculus. Vol. I.
    Translated from the German by E. J. McShane. Reprint of the second edition (1937). Wiley Classics Library. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1988. xiv+616 pages.
    Shields Library QA303 C843 1988 v.1.
  2. Edward D. Gaughan, Introduction to Analysis.
    Fifth Edition. Brooks/Cole Publishing Co., Pacific Grove, CA, 1993. xi+240 pages.
    Shields Library QA300 .G34 2009.

30 Functions of a complex variable

30F: Riemann Surfaces

  1. Hermann Weyl, The concept of a Riemann surface.
    Dover unabridged republication, 2009. xi+189 pages.
    Translated from the third German edition by Gerald R. MacLane. ADIWES International Series in Mathematics Addison-Wesley Publishing Co., Inc., Reading, Mass.-London 1964.

30G: Generalized function theory

  1. Igor Frenkel, Matvei Libine, "Quaternionic Analysis, Representation Theory and Physics."
    Eprint: arXiv:0711.2699v4 [math.RT], 63 pages, 3 figures, posted 25 May 2008.
    Published in Adv. Math. 218 no. 6 (2008) pages 1806–1877.

32 Several complex variables and analytic spaces

32-01: Instructional exposition (textbooks, tutorial papers, etc)

  1. Raymond O. Wells, Differential Analysis on Complex Manifolds.
    Third edition. With a new appendix by Oscar Garcia-Prada. Graduate Texts in Mathematics, 65. Springer, New York, 2008. xiv+299 pages.
    DOI: 10.1007/978-0-387-73892-5.

34 Ordinary differential equations

34A: General theory

  1. V.I. Arnol'd, Ordinary differential equations.
    Translated from the Russian and edited by Richard A. Silverman. The M.I.T. Press, Cambridge, Mass.-London, 1973. ix+280 pages.
    Shields Library QA372 .A713.

35 Partial differential equations

35-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Jürgen Jost, Partial Differential Equations.
    Second edition. Graduate Texts in Mathematics, 214. Springer, New York, 2007. xiv+356 pages.
    DOI: 10.1007/b97312.

35-02: Research exposition (monographs, survey articles)

  1. Jared Wunsch, "Microlocal analysis and evolution equations."
    Eprint: arXiv:0812.3181v2 [math.AP], 98 pages.
    Lecture notes from 2008 CMI/ETH Summer School on Evolution Equations (2008).

35B: Qualitative properties of solutions

  1. Sepideh Mirrahimi, Gael Raoul, "Population structured by a space variable and a phenotypical trait."
    Eprint: arXiv:1105.1936v1 [math.AP], 31 pages. Submitted on 10 May 2011.

35P: Spectral theory and eigenvalue problems

  1. Johannes Sjoestrand, "PT symmetry and Weyl asymptotics."
    Eprint: arXiv:1105.4746v1 [math.SP], 11 pages.

37 Dynamical systems and ergodic theory

37K: Infinite-dimensional Hamiltonian systems

  1. Alberto De Sole, Victor G. Kac, "The variational Poisson cohomolgy."
    Eprint: arXiv:1106.0082v1 [math-ph], 130 pages. Submitted on 1 June 2011.

39 Difference and functional equations

39-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Victor Kac, Pokman Cheung, Quantum Calculus.
    Universitext. Springer-Verlag, New York, 2002. x+112 pages.

39A: Difference Equations

  1. Nelson Faustino, Uwe Kaehler, "On a correspondence principle between discrete differential forms, graph structure and multi-vector calculus on symmetric lattices."
    Eprint: arXiv:0712.1004v4 [math.CV], 23 pages.

40 Sequences, series, summability

40C: General Summability Methods

  1. Armen Bagdasaryan, "A new general method of summation."
    Eprint: arXiv:1105.2787v1 [math.CA], 35 pages. Submitted on 11 May 2011.

42 Fourier analysis

42-02: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Loukas Grafakos, Modern Fourier Analysis.
    Second edition. Graduate Texts in Mathematics, 250. Springer, New York, 2009. xvi+504 pages.
    DOI: 10.1007/978-0-387-09434-2.

42A: Harmonic analysis in one variable

  1. Alexander Wurm, Nurit Krausz, Cecile DeWitt-Morette, Marcus Berg, "Fourier Transforms of Lorentz Invariant Functions."
    Eprint: arXiv:math-ph/0212040v1, 15 pages.
    J. Math. Phys. 44 no. 1 (2003), pages 352–365.

43 Abstract harmonic analysis

43-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Russell Brown, Lecture Notes on Harmonic Analysis.
    Eprint (2001). Compiled Wed. 8 Aug. 2001 1:47:00 PM PDT.
  2. Gerald B. Folland, A course in abstract harmonic analysis.
    Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1995. x+276 pages.

43A: Abstract harmonic analysis

  1. Sergei Kerov, Grigori Olshanski, Anatoly Vershik, "Harmonic analysis on the infinite symmetric group."
    Eprint: arXiv:math/0312270v1 [math.RT], 80 pages.
    Invent. Math. 158 no. 3 (2004), pages 551–642.
  2. Grigori Olshanski, "An introduction to harmonic analysis on the infinite symmetric group."
    Eprint: arXiv:math/0311369v1 [math.RT], 35 pages.
    Asymptotic combinatorics with applications to mathematical physics (St. Petersburg, 2001), pages 127–160, Lecture Notes in Math., 1815, Springer, Berlin 2003.
  3. Jae-Hyun Yang, "Harmonic Analysis on Homogeneous Spaces."
    Eprint: arXiv:math/0601655v2 [math.NT], 52 pages.

46 Functional analysis

46-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. John Hunter and Bruno Nachtergaele, Applied Analysis.
    World Scientific Publishing Company, eprint (2005). xiv+439 pages.
  2. Richard V. Kadison, John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. I. Elementary theory.
    Pure and Applied Mathematics, 100. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. xv+398 pages.
    Shields Library QA3 .P8 v.100 no.1.
  3. —————, —————, Fundamentals of the theory of operator algebras. Vol. II. Advanced theory.
    Pure and Applied Mathematics, 100. Academic Press, Inc., Orlando, FL, 1986. pp. i–xiv and 399–1074.
    Shields Library QA3 .P8 v.100 no.2.

46-02: Research exposition (monographs, survey articles)

  1. Nicolas Bourbaki, Topological vector spaces. Chapters 1–5.
    Translated from the French by H. G. Eggleston and S. Madan. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 1987. viii+364 pages.

46B: Normed linear spaces and Banach spaces; Banach lattices

  1. Fernando Albiac and Nigel J. Kalton, Topics in Banach Space Theory.
    Graduate Texts in Mathematics, 233. Springer, New York, 2006. xii+373 pages.
    DOI: 10.1007/0-387-28142-8.
  2. Gilles Pisier, "Grothendieck's Theorem, past and present."
    Eprint: arXiv:1101.4195v3 [math.FA], 87 pages.

46F: Distributions, generalized functions, distribution spaces

  1. I.M. Gel'fand, G.E. Shilov, Generalized functions. Vol. 1. Properties and operations.
    Translated from the Russian by Eugene Saletan. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1964. xviii+423 pages.
    Shields Library QA331 G4413 v.1.
  2. Werner Westerkamp, "Recent Results in Infinite Dimensional Analysis and Applications to Feynman Integrals."
    Eprint: arXiv:math-ph/0302066v1, 140 pages.

46L: Selfadjoint operator algebras

  1. Alain Connes, Noncommutative Geometry.
    Academic Press, Inc., San Diego, CA, 1994. xiv+661 pages.
    Eprint:, 654 pages. Created Fri 24 Feb 2006 11:12:05 PM PST.
  2. Fernando Lledó, "Operator algebras: an informal overview."
    Eprint: arXiv:0901.0232v1 [math.OA], 15 pages.

46T: Nonlinear Functional Analysis

  1. Alberto Abbondandolo, Pietro Majer, "Infinite dimensional Grassmannians."
    Eprint: arXiv:math/0307192v2 [math.AT], 35 pages.
    J. Operator Theory 61 no. 1 (2009), pages 19–62.

52 Convex and discrete geometry

52A: General convexity

  1. Feng Luo, "A combinatorial curvature flow for compact 3-manifolds with boundary."
    Eprint: arXiv:math/0405295v2 [math.GT], 6 pages.
    Also electronic research announcements, AMS, Volume 11, Pages 12–20 (January 28, 2005)

52C: Discrete Geometry

  1. Bennett Chow, Feng Luo, "Combinatorial Ricci Flows on Surfaces."
    Eprint: arXiv:math/0211256v1 [math.DG], 25 pages. Submitted on 17 November 2002.
  2. David Glickenstein, "A combinatorial Yamabe flow in three dimensions."
    Eprint: arXiv:math/0506182v1 [math.MG], 20 pages.
    Published version: Topology 44 (2005) pages 791–808.
  3. Xianfeng David Gu, Ren Guo, Feng Luo, Wei Zeng, "Discrete Laplace-Beltrami Operator Determines Discrete Riemannian Metric."
    Eprint: arXiv:1010.4070v1 [cs.DM], 10 pages. Submitted on 19 October 2010.

53 Differential geometry

53-01: Instructional Exposition (textbooks, tutorial papers, etc.)

  1. Serge Lang, Fundamentals of Differential Geometry.
    Graduate Texts in Mathematics 191, Springer–Verlag (1999). xviii+535 pages.
    Shields Library QA11.A1 G73 no.191
  2. John Lee, Riemannian Manifolds: An introduction to curvature.
    Graduate Texts in Mathematics, 176. Springer-Verlag, New York, 1997. xvi+224 pages.
    DOI: 10.1007/b98852.
  3. Peter Petersen, Riemannian Geometry.
    Second edition. Graduate Texts in Mathematics, 171. Springer, New York, 2006. xvi+401 pages.
    DOI: 10.1007/978-0-387-29403-2.
  4. Theodore Shifrin, "Differential Geometry: A First Course in Curves and Surfaces."
    Eprint:, 127 pages.
    Notes for University of Georgia Math course 4250/6250 "Differential Geometry" Spring 2011.
  5. Michael Spivak, A comprehensive introduction to differential geometry. Vol. I.
    Third edition. Publish or Perish, Inc., Wilmington, Del., 2005. xvi+489 pages.
  6. —————, A comprehensive introduction to differential geometry. Vol. II.
    Third edition, second printing. Publish or Perish, Inc., Wilmington, Del., 1999. xii+363 pages.
  7. —————, A comprehensive introduction to differential geometry. Vol. III.
    Third edition. Publish or Perish, Inc., Wilmington, Del., 1999. ix+314 pages.
  8. —————, A comprehensive introduction to differential geometry. Vol. IV.
    Third edition. Publish or Perish, Inc., Wilmington, Del., 1999. vii+390 pages.
  9. —————, A comprehensive introduction to differential geometry. Vol. V.
    Third edition. Publish or Perish, Inc., Wilmington, Del., 1999. viii+467 pages.

53-02: Research exposition (monographs, survey articles)

  1. H. Blaine Lawson Jr., and Marie-Louise Michelsohn, Spin Geometry.
    Princeton Mathematical Series, 38. Princeton University Press, Princeton, NJ, 1989. xii+427 pages.
    Phy. Sci. Eng. Library QC793.3.S6 L39 1989.

53A: Classical differential geometry

  1. Arthur L. Besse, Manifolds all of whose geodesics are closed.
    Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], 93. Springer-Verlag, Berlin-New York, 1978. ix+262 pages.

53C: Global differential geometry

  1. Antonio N. Bernal, Miguel Sánchez, "On smooth Cauchy hypersurfaces and Geroch's splitting theorem."
    Eprint: arXiv:gr-qc/0306108v2, 12 pages. Revised 26 July 2003.
    Comm. Math. Phys. 243 no. 3 (2003) pages 461–470.
  2. Arthur L. Besse, Einstein Manifolds.
    Reprint of the 1987 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2008. xii+516 pages.
    Shields library QA649 B49 1987.
  3. David Bleecker, Gauge theory and variational principles.
    Global Analysis Pure and Applied Series A, 1. Addison-Wesley Publishing Co., Reading, Mass., 1981. xviii+179 pages.
    Phy Sci Engr Library QC793.3.F5 B55.
  4. Xianzhe Dai, Xiaodong Wang, Guofang Wei, "On the Stability of Riemannian Manifold with Parallel Spinors."
    Eprint: arXiv:math/0311253v3 [math.DG], 21 pages. Revised 1 March 2004.
    Invent. Math. 161 no. 1 (2005), pages 151–176.
  5. C.T.J. Dodson, Categories, bundles and spacetime topology.
    Second edition. Mathematics and its Applications, 45. Kluwer Academic Publishers Group, Dordrecht, 1988. xviii+243 pages.
    Shields QA 611 D58 1988.
  6. Maxim Kontsevich, "Deformation quantization of Poisson manifolds, I."
    Eprint: arXiv:q-alg/9709040v1, 46 pages. Submitted on 29 September 1997.
    Lett. Math. Phys. 66 no. 3 (2003) 157–216.
  7. Felipe Leitner, "Imaginary Killing spinors in Lorentzian geometry."
    Eprint: arXiv:math/0302024v1 [math.DG], 15 pages. Submitted on 3 February 2003.
    J. Math. Phys. 44 no. 10 (2003), pages 4795–4806.
  8. Gregory L. Naber, Topology, Geometry and Gauge fields: Interactions.
    DOI: 10.1007/978-1-4419-7895-0.
    Applied Mathematical Sciences, 141. Springer-Verlag, New York, 2000. xiv+443 pages.
    Shields Library QC20.7.T65 N332 2000.

53D: Symplectic geometry, contact geometry

  1. Barney Bramham, Helmut Hofer, "First Steps Towards a Symplectic Dynamics."
    Eprint: arXiv:1102.3723v1 [math.DS], 60 pages.
  2. Joe Johns, "The Picard-Lefschetz theory of complexified Morse functions."
    Eprint: arXiv:0906.1218v1 [math.SG] 54 pages, 11 figures (2009).
  3. Maxim Kontsevich, "Operads and Motives in Deformation Quantization."
    Eprint: arXiv:math/9904055v1 [math.QA], 37 pages.
    Lett. Math. Phys. 48 no. 1 (1999) pages 35–72.
  4. —————, "Deformation quantization of algebraic varieties."
    Eprint: arXiv:math/0106006v1 [math.AG] 30 pages.
    Lett. Math. Phys. 56 no. 3 (2006) pages 271–294.
  5. Paul Seidel, Fukaya categories and Picard-Lefschetz theory.
    Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich, 2008. viii+326 pages.
    Shields Library QA665 .S45 2008.
  6. Marco Zambon, "L-infinity algebras and higher analogues of Dirac structures and Courant algebroids."
    Eprint: arXiv:1003.1004v5 [math.SG], 29 pages.

53J: Partial differential equations on manifolds; differential operators

  1. Lars Andersson, "The global existence problem in general relativity."
    Eprint: arXiv:gr-qc/9911032v4, 49 pages. Revised 28 April 2006.
    In The Einstein equations and the large scale behavior of gravitational fields, pages 71–120, Birkhäuser, Basel, 2004.

55 Algebraic topology

55-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Wlliam F. Basener, Topology and its applications.
    Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. xxxviii+339 pages.
  2. James F. Davis, Paul Kirk,
    Lecture Notes in Algebraic Topology.
    Eprint: Revised Edition, 395 pages. Modified Wednesday 1 June 2011 2:09:42 PM (PDT).

55-02: Research exposition (monographs, survey articles)

  1. Norman Steenrod, The topology of fibre bundles.
    Reprint of the 1957 edition. Princeton Landmarks in Mathematics. Princeton Paperbacks. Princeton University Press, Princeton, NJ, 1999. viii+229 pages.
    Shields library QA612.6 S74 1999 c.1.

55P: Homotopy Theory

  1. Javier J. Gutiérrez, "Cellularization of structures in stable homotopy categories."
    Eprint: arXiv:1105.1997v1 [math.AT], 19 pages.
  2. Max Karoubi, "K-Theory. An Elementary introduction."
    Eprint: arXiv:math/0602082v1 [math.KT], 22 pages.
    Clay Mathematics Academy Lecture notes.

55U: Applied homological algebra and category theory

  1. Jacob Lurie, Higher Topos Theory.
    Up-to-date Eprint: Lurie's copy, 943 pages.
    Eprint: arXiv:math/0608040v4 [math.CT], 735 pages.
    Annals of Mathematics Studies, 170. Princeton University Press, Princeton, NJ, 2009. xviii+925 pages.

57 Manifolds and cell complexes

57-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. John M. Lee, Introduction to topological manifolds.
    Second edition. Graduate Texts in Mathematics, 202. Springer, New York, 2011. xviii+433 pages.
    DOI: 10.1007/b98853.

57M: Low-dimensional topology

  1. Dror Bar-Natan, "On Khovanov's categorification of the Jones polynomial."
    Eprint: arXiv:math/0201043v3 [math.QA], 34 pages.
    Algebraic and Geometric Topology 2 (2002) 337–370.
  2. —————, "Khovanov's homology for tangles and cobordisms."
    Eprint: arXiv:math/0410495v2 [math.GT], 57 pages.
    Geom. Topol. 9 (2005) 1443–1499.
  3. Louis Funar, Christophe Kapoudjian, Vlad Sergiescu, "Asymptotically rigid mapping class groups and Thompson's groups."
    Eprint: arXiv:1105.0559v1 [math.GR], 77 pages. A survey paper.
  4. Stavros Garoufalidis, "Chern-Simons theory, analytic continuation and arithmetic."
    Eprint: arXiv:0711.1716v3 [math.GT], 22 pages.
  5. Mikhail Khovanov, "A categorification of the Jones polynomial."
    Eprint: arXiv:math/9908171v2 [math.QA], 51 pages.
    Duke Math. J. 101 no. 3 (2000), 359–426.
    Original paper where Jones polynomial is categorified.
  6. Ross Geoghegan, Topological Methods in Group Theory.
    Graduate Texts in Mathematics, 243. Springer, New York, 2008. xiv+473 pages.
    DOI: 10.1007/978-0-387-74614-2.
  7. Paul Turner, "Five Lectures on Khovanov Homology."
    Eprint: arXiv:math/0606464v1 [math.GT], 38 pages.

58 Global analysis, analysis on manifolds

58-01: Instructional Exposition (textbooks, tutorial papers, etc.)

  1. Vladimir G. Ivancevic, Tijana T. Ivancevic, "Undergraduate Lecture Notes in De Rham–Hodge Theory."
    Eprint: arXiv:0807.4991v4 [math.DG], 28 pages.
  2. Serge Lang, Fundamentals of Differential Geometry.
    Graduate Texts in Mathematics 191, Springer–Verlag (1999). xviii+535 pages.
    Shields Library QA11.A1 G73 no.191.
  3. Gregory L. Naber, Topology, geometry and Gauge fields: Foundations.
    DOI: 10.1007/978-1-4419-7254-5.
    Second edition. Texts in Applied Mathematics, 25. Springer, New York, 2011. xx+437 pages.
    Phy Sci Engr Library QC20.7.T65 N33 1997.

58A: General Theory of Differentiable Manifolds

  1. G. Sardanashvily, "Fibre Bundles, Jet Manifolds and Lagrangian Theory. Lectures for Theoreticians."
    Eprint: arXiv:0908.1886v2 [math-ph], 158 pages.

58B: Infinite-Dimensional Manifolds

  1. Masoud Khalkhali, "Very Basic Noncommutative Geometry."
    Eprint: arXiv:math/0408416v1 [math.KT], 104 pages.
  2. Boris Khesin, Robert Wendt, The geometry of infinite-dimensional groups.
    Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 51. Springer-Verlag, Berlin, 2009. xii+304 pages.
    DOI: 10.1007/978-3-540-77263-7.
  3. Andreas Kriegl, Peter W. Michor, "Aspects of the theory of infinite dimensional manifolds."
    Eprint: arXiv:math/9202206v1 [math.DG], 17 pages. Submitted on 1 February 1992.
    Diff. Geom. Appl. 1 (1991) pages 159–176.
  4. —————, —————, The Convenient Setting of Global Analysis.
    AMS publishers ebook (1997) 618 pages.
  5. G. Sardanashvily, "Lectures on Differential Geometry of Modules and Rings."
    Eprint: arXiv:0910.1515v2 [math-ph], 137 pages.

58C: Calculus on manifolds; nonlinear operators

  1. Wolfgang Bertram, Helge Glockner, Karl-Hermann Neeb, "Differential Calculus, Manifolds and Lie Groups over Arbitrary Infinite Fields."
    Eprint: arXiv:math/0303300v1 [math.GM], 70 pages.
  2. Pierre Cartier, Cecile DeWitt-Morette, Matthias Ihl, Christian Saemann, Maria E. Bell, "Supermanifolds - Application to Supersymmetry."
    Eprint: arXiv:math-ph/0202026v1, 48 pages.
    In Multiple facets of quantization and supersymmetry, pages 412–457, World Sci. Publ., River Edge, NJ, 2002.
  3. Ted Jacobson, Joseph D. Romano, "The Spin Holonomy Group In General Relativity."
    Eprint: arXiv:gr-qc/9207006v1, 21 pages.
    Comm. Math. Phys. 155 no. 2 (1993), pages 261–276.
  4. Danny Stevenson, "Geometry of infinite dimensional Grassmannians and the Mickelsson-Rajeev cocycle."
    Eprint: arXiv:0802.3608v1 [math.DG], 21 pages.

58D: Spaces and manifolds of mappings

  1. Pierre Cartier, Cécile DeWitt-Morette, "A new perspective on Functional Integration." Eprint: arXiv:funct-an/9602005v1, 102 pages.
    Journal of Mathematical Physics 36 (1995) pages 2137–2340.
  2. Daniel S. Freed, "Higher algebraic structures and quantization."
    Eprint: arXiv:hep-th/9212115v2, 62 pages.
    Comm. Math. Phys. 159 no. 2 (1994) pages 343–398.
  3. Emil Mottola, "Functional Integration Over Geometries."
    Eprint: arXiv:hep-th/9502109v1, 68 pages.
    J. Math. Phys. 36 no. 5 (1995), pages 2470–2511.

58E: Variational problems in infinite-dimensional spaces

  1. John Milnor, Morse theory.
    Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51 Princeton University Press, Princeton, N.J. 1963 vi+153 pages.
  2. G. Sardanashvily, "Classical field theory. Advanced mathematical formulation."
    Eprint: arXiv:0811.0331v2 [math-ph], 30 pages.
    Int. J. Geom. Methods Mod. Phys. v5 (2008) pages 1163–1189.

58F: Ordinary differential equations on manifolds; dynamical systems

  1. Ernst Binz, Jędrzej Śniatycki, Hans Fischer, Geoemtry of Classical Fields.
    Dover, Elsevier Science Publishers B.V., New York, 1988. xviii+450 pages.
  2. Mark J. Gotay, Hendrik B. Grundling, Gijs M. Tuynman, "Obstruction results in quantization theory."
    Eprint: arXiv:dg-ga/9605001v1, 34 pages.
    J. Nonlinear Sci. 6 no. 5 (1996), pages 469–498.

58G: Partial differential equations on manifolds; differential operators

  1. Erik Aurell, Per Salomonson, "On Functional Determinants of Laplacians in Polygons and Simplices."
    Eprint: arXiv:hep-th/9304031v1, 40 pages.
    Comm. Math. Phys. 165 no. 2 (1994), pages 233–259.
  2. —————, —————, "Further results on Functional Determinants of Laplacians in Simplicial Complexes."
    Eprint: arXiv:hep-th/9405140v1, 30 pages.
  3. M. Bordag, B. Geyer, K. Kirsten, E. Elizalde, "Zeta function determinant of the Laplace operator on the D-dimensional ball."
    Eprint: arXiv:hep-th/9505157v1, 22 pages.
    Comm. Math. Phys. 179 no. 1 (1996), pages 215–234.
  4. Anton Deitmar, "Regularized and L2-determinants."
    Eprint: arXiv:dg-ga/9511009v2, 30 pages.
    Proc. London Math. Soc. (3) 76 no. 1 (1998), 150–174.
  5. Gerald Dunne, "Functional Determinants in Quantum Field Theory."
    Eprint, 56 pages. Dated 21 May 2009.
    Lecture notes on Functional Determinants in Quantum Field Theory given at the 14th WE Heraeus Saalburg summer school in Wolfersdorf, Thuringia, in September 2008.
  6. Giampiero Esposito, "Dirac Operator and Eigenvalues in Riemannian Geometry."
    Eprint: arXiv:gr-qc/9507046v1, 105 pages. Submitted on 24 July 1995.
  7. —————, "Dirac Operator and Spectral Geometry."
    Eprint: arXiv:hep-th/9704016v3, 205 pages. Revised 16 December 2000.
    Cambridge Lecture Notes in Physics, 12. Cambridge University Press, Cambridge (1998). xiv+209 pages.
  8. Victor Guillemin and Shlomo Sternberg, Geometric Asymptotics.
    AMS Publishers, eprint (1977) 480 pages.
  9. Maxim Kontsevich, Simeon Vishik, "Determinants of elliptic pseudo-differential operators."
    Eprint: arXiv:hep-th/9404046v1, 155 pages.
  10. —————, —————, "Geometry of determinants of elliptic operators."
    Eprint: arXiv:hep-th/9406140v1, 25 pages.
    In Functional analysis on the eve of the 21st century, Vol. 1 (New Brunswick, NJ, 1993), pages 173–197, Progr. Math. 131, Birkhäuser Boston, Boston, MA, 1995.
  11. D. V. Vassilevich, "Heat kernel expansion: user's manual."
    Eprint: arXiv:hep-th/0306138v3, 113 pages. Revised 6 September 2003.
    Phys. Rep. 388, no. 5–6 (2003) pages 279–360.

58J: Partial differential equations on manifolds; differential operators

  1. Christian Baer, Nicolas Ginoux, Frank Pfaeffle, "Wave Equations on Lorentzian Manifolds and Quantization."
    Eprint: arXiv:0806.1036v1 [math.DG], 199 pages and 43 figures.
    ESI Lectures in Mathematics and Physics. European Mathematical Society (EMS), Zürich, 2007. viii+194 pages.
  2. G. Chinta, J. Jorgenson, A. Karlsson, "Zeta functions, heat kernels and spectral asymptotics on degenerating families of discrete tori."
    Eprint: arXiv:0806.2014v2 [math.CO], 34 pages.
    Nagoya Math. J. 198 (2010), pages 121–172.
  3. Giampiero Esposito, "Spectral Geometry and Quantum Gravity."
    Eprint: arXiv:hep-th/9708128v1, 6 pages.
    An invited talk given at the Tomsk Conference: Quantum Field Theory and Gravity (July-August 1997).
  4. —————, "Euclidean Quantum Gravity in Light of Spectral Geometry."
    Eprint: arXiv:hep-th/0307226v1, 31 pages.
    In Spectral geometry of manifolds with boundary and decomposition of manifolds, pages 23–42, Contemp. Math., 366, Amer. Math. Soc., Providence, RI, 2005.
  5. Daniel S. Freed, Dirac Charge Quantization and Generalized Differential Cohomology.
    Eprint: arXiv:hep-th/0011220v2, 62 pages.
    In Surveys in Differential Geometry, Int. Press, Somerville, MA, 2000, pages 129–194.
  6. Gerd Grubb, "A resolvent approach to traces and zeta Laurent expansions."
    Eprint: arXiv:math/0311081v4 [math.AP], 27 pages. Updated with known corrections. The paper has appeared in AMS Contemporary Math. Proceedings, vol. 366 "Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds", 2005, pp. 67–93.
  7. Klaus Kirsten, Alan McKane, "Functional determinants by contour integration methods."
    Eprint: arXiv:math-ph/0305010v1, 29 pages.
    Ann. Physics 308 no. 2 (2003), pages 502–527.
  8. Simon Scott, "Zeta determinants on manifolds with boundary."
    Eprint: arXiv:math/0406315v1 [math.AP], 62 pages.
    J. Funct. Anal. 192 no. 1 (2002), pages 112–185.
  9. —————, "The residue determinant."
    Eprint: arXiv:math/0406268v7 [math.AP], 26 pages.
    Comm. Partial Differential Equations 30 no. 4-6 (2005), pages 483–507.

65 Numerical Analysis

65-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Mark Holmes, Introduction to numerical methods in differential equations.
    Texts in Applied Mathematics, 52. Springer, New York, 2007. xii+238 pages.
    Shields Library QA371 .H66 2007.
    DOI: 10.1007/978-0-387-68121-4.
  2. Arieh Iserles, A first course in the numerical analysis of differential equations.
    Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, 1996. xviii+378 pages.
  3. Tim Sauer, Numerical Analysis.
    San Francisco: Addison Wesley, 2006. xiv+669 pages.

65L: Ordinary differential equations

  1. Saied Abbasbandy, Jose-Luis Lopez, Ricardo Lopez-Ruiz, "The homotopy analysis method and the Lienard equation."
    Eprint: arXiv:0805.3916v1 [nlin.PS], 16 pages.
    Int. J. Comput. Math. 88 no. 1 (2011), pages 121–134.

68 Computer Science

68A: Computers and computer systems

  1. Douglas Comer, Operating System Design: The XINU Approach.
    Prentice-Hall Inc., Upper Saddle River, New Jersey, 1984. xxi+486 pages.
  2. —————, Operating System Design, Volume II: Internetworking with XINU.
    Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1984. xxi+567 pages.
  3. Donald E. Knuth, The Art of Computer Programming. Volume 1: Fundamental Algorithms.
    Third Edition. Addison-Wesley Series in Computer Science and Information Processing. Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1997.
  4. —————, The Art of Computer Programming. Volume 2: Seminumerical Algorithms.
    Third Edition. Addison-Wesley Series in Computer Science and Information Processing. Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1997.

68T: Artificial intelligence

  1. John Harrison, Handbook of practical logic and automated reasoning.
    Cambridge University Press, Cambridge, (2009) xx+681 pages.
    Shields Library QA76.9.L63 H38 2009.
  2. Judea Pearl, Causality. Models, reasoning, and inference.
    Second edition. Cambridge University Press, Cambridge, 2009. xx+464 pages.

70 Mechanics of particles and systems

70-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. Michael Spivak, "Elementary mechanics from a mathematician's viewpoint."
    Eprint: available, 102 pages.
    Seminar on Mathematical Sciences, 29. Keio University, Department of Mathematics, Yokohama, 2004. vi+101 pages.
  2. —————, Physics for mathematicians—mechanics I.
    Publish or Perish, Inc., Houston, TX, 2010. xvi+733 pages.

70G: General models, approaches, and methods

  1. V. Gerdt, A. Khvedelidze, Yu. Palii, "Towards an algorithmisation of the Dirac constraint formalism."
    Eprint: arXiv:math-ph/0611021v1, 15 pages.
    Global Integrability of Field Theories / Proceedings of GIFT 2006. J.Calmet, W.M.Seiler, R.W.Tucker (Eds.), Cocroft Institute, Daresbury (UK), 2006, pp. 135–154.

70H: Hamiltonian and Lagrangian mechanics

  1. Julian Barbour, Brendan Z. Foster, "Constraints and gauge transformations: Dirac's theorem is not always valid."
    Eprint: arXiv:0808.1223v1 [gr-qc], 14 pages.

78 Optics, electromagnetic theory

78M: Basic Methods

  1. Ari Stern, Yiying Tong, Mathieu Desbrun, Jerrold E. Marsden, "Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms."
    Eprint: arXiv:0707.4470v3 [math.NA], 37 pages.

81 Quantum Theory

81-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. R. Ticciati, Quantum Field Theory for Mathematicians.
    Encyclopedia of Mathematics and its Applications 72. Cambridge University Press, Cambridge (1999). xvi+699 pp.
    Phy. Sci. Engr. Library QC174.45 .T53 1999.

81-02: Research exposition (monographs, survey articles)

  1. James Glimm and Arthur Jaffe, Quantum physics: A functional integral point of view.
    Second edition. Springer-Verlag, New York (1987). xxii+535 pages.
    Phy. Sci. Engr. Library QC174.45 .G49 1987.
  2. Marc Henneaux, Claudio Teitelboim, Quantization of Gauge Systems.
    [Paperback edition.] Princeton University Press, Princeton, NJ, 1992. xxvii+520 pages
  3. Lawrence S. Schulman, Techniques and Applications of Path Integration.
    Dover Publications Inc., Mineola, New York, 2005. xiii+416 pages.
    Reproduction of the Wiley 1981 edition. Mathematical rigor is traded for physical insightfulness.
  4. Albert S. Schwarz, Quantum field theory and topology.
    Translated from the 1989 Russian original by Eugene Yankowsky [E. M. Yankovskiĭ] and Silvio Levy. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 307. Springer-Verlag, Berlin, 1993. viii+274 pages.

81-06: Proceedings, conferences, collections, etc.

  1. Quantum fields and strings: a course for mathematicians. Vol. 2.
    Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997.
    Edited by Pierre Deligne, Pavel Etingof, Daniel S. Freed, Lisa C. Jeffrey, David Kazhdan, John W. Morgan, David R. Morrison and Edward Witten. American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 1999.
    Vol. 2: pages i–xxiv and 727–1501.

81-08: Computational Methods

  1. Kurt Langfeld, "Computational Methods in Quantum Field Theory."
    Eprint: arXiv:0711.3004v1, 50 pages.
    Notes based on a lecture presented at the XIX Physics Graduate Days at the University of Heidelberg, 8th–12th October 2007.

81E: Quantum field theory

  1. Matthias R Gaberdiel, "An Introduction to Conformal Field Theory."
    Eprint: arXiv:hep-th/9910156v2, 69 pages.
    Rept.Prog.Phys. 63 (2000) 607–667.
  2. Alexander Makhlin, "Localized Matter and Geometry of the Dirac Field."
    Eprint: arXiv:0911.3671v1 [math-ph], 22 pages.
  3. Ron K. Unz, "Path integration and the functional measure."
    Eprint, 41 pages.
    Nuovo Cimento A series 11 92 no. 4 (1986), pages 397–426.

81P: Axiomatics, Foundations, Philosophy

  1. John Baez, "Quantum Quandaries: A Category Theoretic Perspective."
    Eprint arXiv:quant-ph/0404040v2, 21 pages, 2 encapsulated Postscript figures.
    The structural foundations of quantum gravity, pages 240–265. Oxford Univ. Press, Oxford (2006).
  2. Philip Goyal, "From Information Geometry to Quantum Theory."
    Eprint: arXiv:0805.2770v4 [quant-ph], 5 pages.
    New J. Phys. 12 (2010), February, 023012, 9 pages.
  3. Samuel J. Lomonaco, Louis H. Kauffman, "Quantizing Braids and Other Mathematical Objects: The General Quantization Procedure."
    Eprint: arXiv:1105.0371v1 [quant-ph], 15 pages. Submitted on 2 May 2011.

81Q: General mathematical topics and methods in quantum theory

  1. Emerson Sadurni, "Klein-Gordon and Dirac gyroscopes."
    Eprint: arXiv:0805.3127v3 [quant-ph], 13 pages.
    J. Phys. A 42 no. 1 (2009), 015209, 10 pages.

81R: Groups and algebras in quantum theory

  1. Ken Barnes, Group theory for the standard model of particle physics and beyond.
    Series in High Energy Physics, Cosmology and Gravitation. CRC Press, Boca Raton, FL, 2010. xiv+241 pages.
  2. M. Berg, C. DeWitt-Morette, S. Gwo, E. Kramer, "The Pin Groups in Physics: C, P, and T."
    Eprint: arXiv:math-ph/0012006v1, 109 pages.
    Rev. Math. Phys. 13 no. 8 (2001), pages 953–1034.
  3. Nathan Berkovits, "Pure spinors, twistors, and emergent supersymmetry."
    Eprint: arXiv:1105.1147v2 [hep-th], 10 pages. Revised 6 May 2011.
  4. Alain Connes, Dirk Kreimer, "Hopf Algebras, Renormalization and Noncommutative Geometry."
    Eprint: arXiv:hep-th/9808042v1, 49 pages.
    Comm. Math. Phys. 199 no. 1 (1998), pages 203–242.
  5. K.Kanakoglou, A. Herrera-Aguilar, "Graded Fock–like representations for a system of algebraically interacting paraparticles."
    Eprint: arXiv:1105.4819v1 [math-ph], 4 pages.
    Journ. of Phys.: Conf. Ser., v.287 (2011) 012037.
  6. Frédéric Paugam, "Towards the mathematics of quantum field theory."
    Eprint: Course Notes, 334 pages. Compiled on Tuesday 31 May 2011 10:24:46 PM (PDT).
  7. G.Sardanashvily, "Mathematical models of spontaneous symmetry breaking."
    Eprint: arXiv:0802.2382v1 [math-ph], 14 pages.
    The Preface to the special issue "Higgs Mechanism and Spontaneous Symmetry Breaking" of International Journal of Geometric Methods in Modern Physics (v5, N2 2008).

81S: General quantum mechanics and problems of quantization

  1. Arthur Jabs, "General quantum mechanics and problems of quantization."
    Eprint: arXiv:0810.2399v3 [quant-ph], 18 pages.
    Extended version of a talk given at the international workshop on theoretical and experimental aspects of the spin-statistics connection and related symmetries (SpinStat2008), Trieste, Italy, 21–25 October 2008.

81T: Quantum field theory; related classical field theories

81T05: Axiomatic quantum field theory; operator algebras
  1. Hellmut Baumgaertel, Hendrik Grundling, "Superselection in the presence of constraints."
    Eprint: arXiv:math-ph/0405038v1, 38 pages.
    J.Math.Phys. 46 (2005) 082303.
  2. Christoph Bergbauer, Dirk Kreimer, "New algebraic aspects of perturbative and non-perturbative Quantum Field Theory."
    Eprint: arXiv:0704.0232v2 [hep-th], 15 pages.
    In "New Trends in Mathematical Physics; Selected contributions of the XVth International Congress on Mathematical Physics", V. Sidoravicius (Ed.), Springer (2009)
  3. Romeo Brunetti, Klaus Fredenhagen, "Algebraic approach to Quantum Field Theory."
    Eprint: arXiv:math-ph/0411072v1, 21 pages.
    To appear on Elsevier Encyclopedia of Mathematical Physics.
  4. Romeo Brunetti, Martin Porrmann, Giuseppe Ruzzi, "General Covariance in Algebraic Quantum Field Theory."
    Eprint: arXiv:math-ph/0512059v1, 61 pages.
  5. Romeo Brunetti, Giuseppe Ruzzi, "Superselection Sectors and General Covariance. I."
    Eprint: arXiv:gr-qc/0511118v2, 66 pages.
    Commun.Math.Phys. 270 (2007), pages 69–108.
  6. Detlev Buchholz, "Current trends in axiomatic quantum field theory."
    Eprint: arXiv:hep-th/9811233v2, 22 pages.
    Lect.Notes Phys. 558 (2000) pages 43–64.
  7. —————, "Algebraic Quantum Field Theory: A Status Report."
    Eprint: arXiv:math-ph/0011044v1, 18 pages.
    Plenary talk given at XIIIth International Congress on Mathematical Physics, London, 18 pages, 3 figures.
  8. Detlev Buchholz, Hendrik Grundling, "Algebraic Supersymmetry: A case study."
    Eprint: arXiv:math-ph/0604044v2, 55 pages.
    Commun.Math.Phys. 272 (2007), pages 699–750.
  9. M. Duetsch, K. Fredenhagen, "Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion."
    Eprint: arXiv:hep-th/0001129v1, 29 pages.
    Comm. Math. Phys. 219 no. 1 (2001), pages 5–30.
  10. Hendrik Grundling, Fernando Lledo, "Local Quantum Constraints."
    Eprint: arXiv:math-ph/9812022v2, 52 pages.
    Rev.Math.Phys. 12 (2000), pages 1159–1218.
  11. Hans Halvorson, Michael Mueger, "Algebraic Quantum Field Theory."
    Eprint: arXiv:math-ph/0602036v1, 202 pages.
    To appear in Handbook of the Philosophy of Physics, North Holland, 2006.
  12. N.P. Landsman, "Constrained quantization in algebraic field theory."
    Eprint: arXiv:math-ph/9807029v1, 5 pages.
    XIIth International Congress of Mathematical Physics (ICMP '97) (Brisbane), 191–196, Int. Press, Cambridge, MA, 1999.
  13. Urs Schreiber, "AQFT from n-functorial QFT."
    Eprint: arXiv:0806.1079v2 [math.CT], 39 pages.
    Commun.Math.Phys. 291 (2009), pages 357–401.
  14. Bert Schroer, "Lectures on Algebraic Quantum Field Theory and Operator Algebras."
    Eprint: arXiv:math-ph/0102018v4, 72 pages.
81T08: Constructive quantum field theory
  1. G. Sardanashvily, "True Functional Integrals in Algebraic Quantum Field Theory."
    Eprint: arXiv:hep-th/9410107v1, 16 pages.
  2. Raymond F. Streaker and Arthur S. Wightman, PCT, Spin and Statistics, and All That.
    Corrected third printing of the 1978 edition. Princeton Landmarks in Physics. Princeton University Press, Princeton, NJ (2000). x+207 pages.
81T13: Yang-Mills and other gauge theories
  1. T.S. Biro, C. Gong, B. Mueller, A. Trayanov, "Hamiltonian Dynamics of Yang-Mills Fields on a Lattice."
    Eprint: arXiv:nucl-th/9306002v2, 51 pages.
    Int.J.Mod.Phys.C 5 (1994) 113–149.
  2. Giampiero Esposito, Diego N. Pelliccia, Francesco Zaccaria, "Gribov Problem for Gauge Theories: a Pedagogical Introduction."
    Eprint: arXiv:hep-th/0404240v2, 24 pages.
    Int. J. Geom. Methods Mod. Phys. 1 no. 4 (2004), pages 423–441.
  3. N. Reshetikhin, "Lectures on quantization of gauge systems."
    Eprint: arXiv:1008.1411v1 [math-ph], 63 pages.
    In Proceedings of the Summer School "New paths towards quantum gravity". Holbaek, Denmark; B. Booss-Bavnbek, G. Esposito and M. Lesch, eds. Springer, Berlin, 2010; pp. 3–58.
  4. Alexander Torres-Gomez, Kirill Krasnov, "Gravity-Yang-Mills-Higgs unification by enlarging the gauge group."
    Eprint: arXiv:0911.3793v2 [hep-th], 61 pages.
    Phys. Rev. D 81 no. 8 (2010), 085003.
81T15: Perturbative methods of renormalization
  1. K. Ebrahimi-Fard, J.M. Gracia-Bondia, F. Patras, "A Lie theoretic approach to renormalization."
    Eprint: arXiv:hep-th/0609035v3, 28 pages.
    Comm. Math. Phys. 276 no. 2 (2007), pages 519–549.
81T16: Nonperturbative methods of renormalization
  1. Gerald V. Dunne, "Functional Determinants in Quantum Field Theory."
    Eprint: arXiv:0711.1178v1 [hep-th], 16 pages.
    J. Phys. A 41 no. 30 (2008), 304006.
81T17: Renormalization group methods
  1. Romeo Brunetti, Michael Duetsch, Klaus Fredenhagen, "Perturbative Algebraic Quantum Field Theory and the Renormalization Groups."
    Eprint arXiv:0901.2038v2 [math-ph], 56 pages. Revised 15 July 2009.
    Adv. Theor. Math. Phys. 13 no. 5, (2009). Pages 1541–1599.
81T18: Feynman diagrams
  1. Dirk Kreimer, "Anatomy of a gauge theory."
    Eprint: arXiv:hep-th/0509135v3, 25 pages.
    Ann. Physics 321 no. 12 (2006), 2757–2781.
81T20: Quantum field theory on curved space backgrounds
  1. Giampiero Esposito, "Boundary operators in quantum field theory."
    Eprint: arXiv:hep-th/0001086v2, 23 pages.
    Internat. J. Modern Phys. A 15 no. 28 (2000), pages 4539–4555.
  2. —————, "Quantum field theory from first principles."
    Eprint: arXiv:hep-th/0006040v1, 16 pages.
    In Geometrical aspects of quantum fields (Londrina, 2000), pages 80–92, World Sci. Publ., River Edge, NJ, 2001.
  3. R. Percacci, "Mixing internal and spacetime transformations: some examples and counterexamples."
    Eprint: arXiv:0803.0303v1 [hep-th], 6 pages.
    J. Phys. A 41 no. 33 (2008), 335403, 8 pages.
81T25: Quantum field theory on lattices
  1. Brendan Z. Foster, Ted Jacobson, "Quantum field theory on a growing lattice."
    Eprint: arXiv:hep-th/0407019v2, 28 pages JHEP 0408 (2004) 024.
81T40: Two-dimensional field theories, conformal field theories, etc.
  1. Ingo Runkel, Jurgen Fuchs, Christoph Schweigert, "Categorification and correlation functions in conformal field theory."
    Eprint: arXiv:math/0602079v1 [math.CT], 16 pages.
    International Congress of Mathematicians. Vol. III, pages 443–458, Eur. Math. Soc., Zürich, 2006.
81T70: Quantization in field theory; cohomological methods
  1. Marc Henneaux, "Homological Algebra and Yang-Mills Theory."
    Eprint: arXiv:hep-th/9412141v1, 20 pages.
    J.Pure Appl.Algebra 100 (1995) pages 3–18.
  2. M. Kachkachi, A. Lamine, M. Sarih, "Gauge Theories: Geometry and cohomological invariants."
    Eprint: arXiv:hep-th/9707106v1, 15 pages.
    Internat. J. Theoret. Phys. 37 no. 6 (1998), 1681–1692.

81U: Scattering theory

  1. Detlev Buchholz, Stephen J. Summers, "Scattering in Relativistic Quantum Field Theory: Fundamental Concepts and Tools."
    Eprint: arXiv:math-ph/0509047v1, 14 pages.
  2. Mahiko Suzuki, "Approximate gauge symmetry of composite vector bosons."
    Eprint: arXiv:1006.1319v5 [hep-ph], 26 pages.
    Phys. Rev. D 82, 045026 (2010).

81V: Applications to specific physical systems

  1. Giampiero Esposito, Cosimo Stornaiolo, "Nonlocality and ellipticity in a gauge-invariant quantization."
    Eprint: arXiv:hep-th/9907212v1, 17 pages.
    Internat. J. Modern Phys. A 15 no. 3 (2000), pages 449–460.

83 Relativity and gravitational theory

83-01: Instructional exposition (textbooks, tutorial papers, etc.)

  1. John Stewart, Advanced general relativity.
    Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (1990). viii+228 pages.

83-02: Research exposition (monographs, survey articles)

  1. Yvonne Choquet-Bruhat, General relativity and the Einstein equations.
    Oxford Mathematical Monographs. Oxford University Press, Oxford (2009). xxvi+785 pages.
  2. Roger Penrose, The Road to Reality: A complete guide to the laws of the universe.
    Alfred A. Knopf, Inc., New York, 2005. xxviii+1099 pages.

83-08: Computational Methods

  1. Thomas W. Baumgarte, Stuart L. Shapiro, Numerical Relativity: Solving Einstein's Equations on the Computer.
    Cambridge University Press (2010). Hardback, xviii+698 pages.
  2. Philippe Grandclement, Jérôme Novak, "Spectral Methods for Numerical Relativity."
    Eprint: arXiv:0706.2286v2 [gr-qc], 98 pages.
    Living Reviews in Relativity (2009) lrr-1009-1.
    NB: that spectral methods are ones "where, typically, the various functions are expanded onto sets of orthogonal polynomials or functions."

83C: Spinor and Twistor Methods; Newman-Penrose formalism

83C05: Einstein's equations (general structure, canonical formalism, Cauchy problems)
  1. Edward Anderson, "Foundations of Relational Particle Dynamics."
    Eprint: arXiv:0706.3934v4 [gr-qc], 21 pages.
    Classical Quantum Gravity 25 no. 2 (2008), 025003, 29 pages.
  2. Andrew Randono, "Canonical Lagrangian Dynamics and General Relativity."
    Eprint: arXiv:0802.2230v2 [gr-qc], 26 pages.
    Classical Quantum Gravity 25 no. 20 (2008), 205017, 21 pages.
83C45: Quantization of the gravitational field
  1. Edward Anderson, "Records Theory."
    Eprint: arXiv:0709.1892v6 [gr-qc], 29 pages.
    Internat. J. Modern Phys. D 18 no. 4 (2009), pages 635–667.
  2. —————, "Seminar on Records Theory."
    Eprint: arXiv:0711.3174v2 [gr-qc], 16 pages.
    Proceedings of the Second Conference on Time and Matter Eds. M O' Loughlin, S Stanic and D Veberic (Nova Gorica: University 2008).
  3. Alfio Bonanno, Giampiero Esposito, Claudio Rubano, "Improved Action Functionals in Non-Perturbative Quantum Gravity."
    Eprint: arXiv:hep-th/0511188v1, 5 pages.
    Internat. J. Modern Phys. A 20 no. 11 (2005), pages 2358–2363.
  4. Bryce DeWitt, Giampiero Esposito, "An Introduction to Quantum Gravity." Eprint: arXiv:0711.2445v1 [hep-th], 68 pages. Submitted on 15 November 2007.
    Reprinted from Recent developments in gravitation [275–322, Plenum, New York, 1979]. Int. J. Geom. Methods Mod. Phys. 5 no. 1 (2008), pages 101–156.
  5. Giampiero Esposito, "New kernels in quantum gravity."
    Eprint: arXiv:hep-th/9906169v2, 19 pages.
    Classical Quantum Gravity 16 no. 12 (1999), pages 3999–4010.
  6. E. Guadagnini, "Gravitons scattering from classical matter."
    Eprint: arXiv:0803.2855v1 [gr-qc], 15 pages.
    Classical Quantum Gravity 25 no. 9 (2008), 095012, 11 pages.
  7. Claus Kiefer, Quantum Gravity.
    Second edition. International Series of Monographs on Physics, 136. Oxford University Press, Oxford, 2007. xii+361 pages.
83C47: Methods of quantum field theory
  1. Gabor Helesfai, "Spontaneous symmetry breaking in Loop Quantum Gravity."
    Eprint: arXiv:0806.3356v2 [gr-qc], 28 pages.
    Classical Quantum Gravity 25 no. 23 (2008), 235010, 22 pages.
83C60: Spinor and twistor methods; Newman-Penrose formalism
  1. Giampiero Esposito, "From spinor geometry to complex general relativity."
    Eprint: arXiv:hep-th/0504089v2, 59 pages.
    Int. J. Geom. Methods Mod. Phys. 2 no. 4 (2005), pages 675–731.
  2. Robert J. Low, "Twistor linking and causal relations."
    Classical Quantum Gravity 7 no. 2, (1990) pages 177–187.
  3. —————, "Twistor linking and causal relations in exterior Schwarzschild space."
    Classical Quantum Gravity 11 no. 2 (1994) pages 453–456.
83C75: Space-time singularities, cosmic censorship, etc.
  1. Fay Dowker, Lydia Philpott, Rafael Sorkin, "Energy-momentum diffusion from spacetime discreteness."
    Eprint: arXiv:0810.5591v3 [gr-qc], 13 pages.
    Phys. Rev. D 79 no. 12 (2009), 124047, 13 pp.
  2. Robert J. Low "Spaces of causal paths and naked singularities."
    Classical Quantum Gravity 7 no. 6 (1990) pages 943–954.

83D: Relativistic Gravitational Theories other than Einstein's, including asymmetric field theories

  1. Alfio Bonanno, Giampiero Esposito, Claudio Rubano, "Arnowitt-Deser-Misner gravity with variable G and Lambda and fixed point cosmologies from the renormalization group."
    Eprint: arXiv:gr-qc/0403115v2, 17 pages.
    Classical Quantum Gravity 21 no. 21 (2004), pages 5005–5016.
  2. Henrique Gomes, "Gauge Theory in Riem: Classical."
    Eprint: arXiv:0807.4405v6 [gr-qc], 29 pages.
    To appear in Journal of Math. Phys. July issue.
  3. R. Percacci, "Gravity from a Particle Physicists' perspective."
    Eprint: arXiv:0910.5167v1 [hep-th], 27 pages.
    Lectures given at the Fifth International School on Field Theory and Gravitation, Cuiaba, Brazil 20–24 April 2009.

94 Information and communication, circuits

94A: Communication, information

  1. Joseph T. Lizier, Mikhail Prokopenko, Albert Y. Zomaya, "Local information transfer as a spatiotemporal filter for complex systems."
    Eprint: arXiv:0809.3275v1 [nlin.CG], 12 pages.
    Phys. Rev. E (3) 77 no. 2 (2008), 026110, 11 pages.


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