Dates and locations of exams: to be fixed in consultation with the Students and announced during lectures.
Conditions of admission to the exam: -
Assessment conditions: In order to pass the exam, the Student must achieve a pass grade either during the oral exam or for the completion, documented by a written report submitted to the Lecturer by the pre-determined deadline, of an individual theoretical project from a list to be linked hereunder.
Individual theoretical projects:
Non-linear realisations of symmetries and the inverse Higgs effect.
Defects and dualities in field theory -- a case study
The Wess--Zumino--Witten σ-model as an example of a (Sugawara-extended) conformal field theory.
Topological charges, Lie-algebra cohomology and the slim L∞-algebras.
Principal bundles with a structural groupoid and compatible connective structure in the description of gauged symmetries.
...
Lecture notes (with accompanying exercises and problems to be solved):
Motto: "As ye saw, saw shall ye reap." And saw I give thee...
Giovanni Giachetta, Luigi Mangiarotti i Геннадий А. Сарданашвили, Advanced Classical Field Theory, World Scientific, 2009.
Shoshichi Kobayashi i Katsumi Nomizu, Foundations of Differential Geometry", vol. I, vol. II, John Wiley & Sons, 1963-69.
Peter W. Michor, Topics in Differential Geometry, Graduate Studies in Mathematics, Vol. 93, American Mathematical Society, 2008.
Yvonne Choquet-Bruhat, Cécile DeWitt-Morette i Margaret Dillard Bleick, Analysis, Manifolds and Physics, Part I, II, Elsevier, 1996-2000.
Борис А. Дубровин, Сергей П. Новиков, Анатолий Т. Фоменко, Modern Geometry - Methods and Applications", vol. 1,2,3, Graduate Texts in Mathematics, Vol. 93, 104, 124, Springer, 1984-90 (a translation of the original work Современная геометрия, Методы и приложения, Том 1, 2, 3, Наука, 1979).
Saunders Mac Lane, Homology, Classics in Mathematics, Springer, 1995.
Christian A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, Vol. 38, Cambridge University Press, 1995.
Виктор В. Прасолов, Elements of Homology Theory, Graduate Studies in Mathematics, Vol. 81, American Mathematical Society, 2007 (a translation of the original work Элементы Теории Гомологий, Издательство МЦНМО, 2006).
José A. de Azcárraga i José M. Izquierdo, Lie groups, Lie algebras, cohomology and some applications in physics, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 1995.
Philippe Francesco, Pierre Mathieu i David Sénéchal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer, 2011.
Saunders Mac Lane, Categories for the Working Mathematician, Graduate Texts in Mathematics, Vol. 5, Springer, 1971.
Henri Cartan i Samuel Eilenberg, Homological Algebra, Princeton Mathematical Series, Vol. 19, Princeton University Press, 1956.
Joseph J. Rotman, An Introduction to Homological Algebra, Universitext, Springer, 2009.
Сергей И. Гельфанд i Юрий И. Манин, Methods of Homological Algebra, Springer Monographs in Mathematics, Springer, 2003 (a translation of the original work Методы гомологической алгебры. Введение в когомологии и производные категории, Наука, 1988).
R.R.S., „Algebra. Podstawy”, skrypt do wykładu z „Algebry I i II R” (a pre-final version in - alas - Polish, comments and corrections are much welcome).
Retro