May 12th – May 30th, 2025
Gran Sasso Science Institute, L'Aquila (IT)
The course will introduce Penrose’s incompleteness theorem to a broad mathematical audience. The course will be delivered in the format of a reading seminar and will include introductory modules on the basics of differential geometry and general relativity, to which no prior exposure will be assumed.
Calendar
Lecture 1 (12/05, ex-INPS P2.6, 2--4pm)
Angia Lauri & Eugenio Turchet
Manifolds, tensors and flows
Sec 2.1--2.3, 2.5, 2.14
Lecture 2 (14/05, ex-INPS Conference Room -1, 2--4pm)
Francesco Tornabene
Connection and curvature
Sec 2.6--2.12, 2.15--2.16
Lecture 3 (16/05, ex-INPS P2.6, 2--4pm)
Martino Caliaro
Lorentzian geometry and Einstein equations
Sec 2.4, 2.13, 2.17
Lecture 4 (19/05, ex-INPS P2.6, 2--4pm)
Martina Giachello
Minkowski space and Schwarzschild geometry
Sec 3.1 (excl. 3.1.4), 3.2 (excl. 3.2.1)
Lecture 5 (21/05, ex-INPS Conference Room -1, 2--4pm)
Ginevra Braga
Global hyperbolicity and well-posedness for geometric wave equations
Sec 4.5--4.7
Lecture 6 (23/05, ex-INPS P2.6, 2:30--4:30pm)
Vishnu Sanjay
Well-posedness for Einstein equations
Sec 4.8--4.11 (perhaps excl. Sec 4.9)
Lecture 7 (26/05, ex-INPS P2.6, 2--4pm)
Flavio Rossetti
Penrose's Incompleteness Theorem I
Sec 6.1--6.2 + extra
Lecture 8 (28/05, ex-INPS Conference Room -1, 2--4pm)
Pierfrancesco Martini
Penrose's Incompleteness Theorem II
Sec 6.3
Lecture 9 (29/05, ex-INPS P2.6, 2--4pm)
Gabriele Benomio
Penrose's Incompleteness Theorem III
Sec 6.4--6.7
Lecture 10 (30/05, ex-INPS P2.6, 2--4pm)
Gabriele Benomio
Q&A and outlook
Reading material: G. Holzegel, General Relativity and the Analysis of Black Hole Spacetimes
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