Gabriele Benomio, "SHORT Course: Topics in General Relativity"

12 May 2025, 14:00 → 30 May 2025, 16:00 Europe/Rome

GSSI

Lecturer Gabriele Benomio gabriele.benomio@gssi.it

Course description and outcomes

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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