AGMP-literature

The literature for current topics will be suggested by the lecturer. The literature especially relevant for 2018/2019 edition:

Fioresi's "Supergeometry Lectures" (the Zuerich version), https://www.dm.unibo.it/~fioresi/

Dumtirescu's "Superconnections and parallel transport".

Hohnhold et al.'s "Differential forms and 0-dimensional supersymmetric field theories".

Freed's "Five Lectures on Supersymmetry".

Varadarajan's "Supersymmetry for Mathematicians: An Introduction" (Chapters 3,4 and 7).

Some literature on spinors (relevant especially in the winter term 2014/2015):

T. Frankel,
The Geometry of Physics,
Cambridge University Press, 1997.

H. Lawson, M. Michelsohn,
Spin Geometry,
Princeton University Press (1990).

M. Atiyah, R. Bott, A. Shapiro,
Clifford modules.

José Figueroa-O'Farrill,
PG course on Spin Geometry.

Participants of the Colloquium are also urged to consult any of the following background references:

B. Bakalov and A. Kirillov, Jr.,
Lectures on Tensor Categories and Modular Functors,
University Lecture Series, vol. 21, American Mathematical Society, 2001.

J.‐L. Brylinski,
Loop spaces, characteristic classes and geometric quantization,
Progress in Mathematics, vol. 107, Birkhäuser, 1993.

A. Connes,
Noncommutative Geometry,
Academic Press, 1994.

P. Deligne, P. Etingof, D.S. Freed, L. Jeffrey, D. Kazhdan, J. Morgan, D.R. Morrison and E. Witten (Eds.),
Quantum Fields and Strings: A Course For Mathematicians, vols. I, II,
American Mathematical Society, 1999.

P. Di Francesco, P. Mathieu and D. Sénéchal,
Conformal Field Theory,
Graduate Texts in Contemporary Physics, Springer, 1997.

G. Folland,
Quantum Field Theory,
American Mathematical Society, 2008.

T. Frankel,
The Geometry of Physics,
Cambridge University Press, 1997.

E. Frenkel,
``Lectures on the Langlands Program and Conformal Field Theory'',
In: Frontiers in Number Theory, Physics, and Geometry II,
Springer, 2007, pp. 387–533 [arXiv:hep-th/0512172].

J. Fröhlich and K. Gawędzki,
``Conformal Field Theory and Geometry of Strings'',
In: Vancouver 1993, Proceedings, Mathematical Quantum Theory I: Field Theory and Many-Body Theory,
J. Feldman, R. Froese and L.M. Rosen (Eds.),
CRM Proceedings & Lecture Notes vol. 7, American Mathematical Society, 1994, pp. 57–97 [arXiv:hep-th/9310187].

J.A. Fuchs,
Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory,
Cambridge Monographs on Mathematical Physics, Cambridge University Press, 1992.

K. Gawędzki,
``Conformal field theory: A case study'',
1999 [arXiv:hep-th/9904145].

M. Green, J. Schwarz, E. Witten,
Superstring theory, vols. I, II,
Cambridge University Press, 1987.

K. Hori et al. (Eds.),
Mirror symmetry,
Clay Mathematics Monographs, 2003.

S. Hu,
Lecture Notes on Chern–Simons–Witten Theory,
World Scientific, 2001.

J. Lurie,
``On the Classification of Topological Field Theories'',
In: Current Developments in Mathematics, Volume 2008,
International Press, 2009, pp. 129–280 [arXiv:0905.0465].

S. Mac Lane,
Categories for the Working Mathematician,
Graduate Texts in Mathematics vol. 5, Springer, 1971.

M. Mariño,
Chern–Simons Theory, Matrix Models, and Topological Strings,
Oxford University Press, 2005.

M. Nakahara,
Geometry, Topology and Physics,
Institute of Physics Publishing, 2003.

J. Polchinski,
String theory, vols. I, II,
Cambridge University Press, 1998.

H. Sati and U. Schreiber (Eds.),
Mathematical Foundations of Quantum Field and Perturbative String Theory,
Proceedings of Symposia in Pure Mathematics vol. 83, American, Mathematical Society, 2011.

G.B. Segal,
``The Definition of Conformal Field Theory'',
In: Symposium On Topology, Geometry And Quantum Field Theory (Segalfest),
G.B. Segal and U. Tillmann (Eds.),
London Mathematical Society Lecture Note Series vol. 308, Cambridge University Press, 2004, pp. 421–575.

L.A. Takhtajan,
Quantum Mechanics for Mathematicians,
American Mathematical Society, 2008.

R. Ticciati,
Quantum Field Theory for Mathematicians,
Cambridge University Press, 1999.

V.G. Turaev,
Quantum Invariants of Knots and 3‐Manifolds,
de Gruyter Studies in Mathematics vol. 8, Walter de Gruyter, 1994.

N.M.J. Woodhouse,
Geometric Quantization,
Oxford Mathematical Monographs, Oxford University Press, 1992.