Thirty-first School: Bayrischzell, Germany
31.8.-11.9.2026
funded by the Wilhelm and Else Heraeus Foundation
Lecture Program:
| Riccardo Argurio (UBL Brussels) | Generalized Symmetries in Field Theory |
| Ilka Brunner (LMU Munich) | Topological Field Theory |
| Cliff Burgess (Perimeter Institute) | Effective Field Theory |
| Livia Ferro (Hertfordshire) | Positive Geometries |
| Christoph Nega (AEI Potsdam) | Scattering Amplitudes |
The instruction language is English.
Some lecture notes may appear later and will be made available here
Recommended Literature:
- Argurio:
Pedro R. S. Gomes : An Introduction to Higher-Form Symmetries https://arxiv.org/abs/2303.01817
T. Daniel Brennan, Sungwoo Hong: An Introduction to Higher-Form Symmetries https://arxiv.org/abs/2306.00912
Nabil Iqbal: Jena lectures on generalized global symmetries: principles and applications arxiv.org/abs/2407.20815
Riccardo Argurio: Saalburg Lecture Notes Saalburg-Lecture-Notes - Brunner:
https://saalburg.aei.mpg.de/wp-content/uploads/sites/25/2026/09/Brunner_TFT.pdf
https://www.math.uni-hamburg.de/home/schweigert/ULECT-80-author-vers.pdf - Burgess:
Original papers:
S. Weinberg, Phenomenological Lagrangians, Physica A96 (1979) 1-2, 327-340
S. Coleman, J. Wess and B.Zumino, Structure of Phenomenological Lagrangians I, Phys. Rev. 177 (1969) 2239
S. Coleman, C. Callan, J. Wess and B. Zumino, Structure of Phenomenological Lagrangians II, Phys. Rev. 177 (1969) 2247
J. Donoghue, General Relativity as and Effective Field Theory: the Leading Quantum Corrections,
Phys. Rev. D50 (1994) 3874 gr-qc/9405057
Reviews:
C.Burgess: Introduction to Effective Field Theory (CUP) (The introductory first 6 chapters can be found here:
https://physics.mcmaster.ca/~cburgess/Book/Ch1-6SnippetEFT.pdf)
D. Kaplan: Five Lectures on Effective Field Theory, nucl-th/0510023
C. Burgess: Quantum Gravity in Everyday Life, Living Reviews in Relativity 7 (2004) 5
gr-qc/0311082 - Ferro:
Original papers:
N. Arkani-Hamed, J. Trnka; The Amplituhedron:https://arxiv.org/abs/1312.2007
N. Arkani-Hamed, Y. Bai, T. Lam; Positive Geometries and Canonical Forms: https://arxiv.org/abs/1703.04541
N. Arkani-Hamed, Y. Bai, S. He, G. Yan; Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet: https://arxiv.org/abs/1711.09102
D. Damgaard, L. Ferro, T.Lukowski, M. Parisi; The Momentum Amplituhedron:https://arxiv.org/abs/1905.04216;
L. Ferro, T. Lukowski; The Loop Momentum Amplituhedron
Reviews:
L. Ferro, T. Lukowski; Amplituhedra, and Beyond:https://arxiv.org/abs/2007.04342
E. Herrmann, J. Trnka; The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes: https://arxiv.org/abs/2203.13018
T. Lam, An invitation to positive geometries:https://arxiv.org/abs/2208.05407 - Nega:
Stefan Weinzierl: Feynman integrals https://arxiv.org/abs/2201.03593
J. Henn, Lectures on differential equations for Feynman integrals, 1412.2296
S.Abreu, R, Britto and C. Duhr: Mathematical structures in Feynman integrals: 2203.13014
