**Instructor: **Ivo Terek.

**Syllabus:** The mini-course has three parts.

- Brief review of linear algebra on pseudo-Euclidean vector spaces. Conditions for the existence of a Lorentz metric on a smooth manifold. Existence and uniqueness of the time-orientable double-cover of a Lorentz manifold.
- Spacetimes and examples (Minkowski, Schwarzschild, Reissner-Nordström, FLRW). Chronological, causal, and horismos precedence relations, and some basic properties.
- Local causality and the push-up lemma. Future and past sets. Achronal boundaries and edge points.

**Schedule:** We will have three lectures per week, on Mondays, Wednesdays, and Fridays, from 2 p.m. to 3 p.m., starting on **June 27th**, and ending on **July 15th**, in room MW154. ~~We also have a Zoom link for online attendance~~.

**Main reference:** Mainly chapter 3 of my book draft with Paolo Piccione (which we’ll share with the participants). Any feedback and corrections will be much appreciated.

**Recordings and weekly notes:**

- Week 1: lecture 1, lecture 2, lecture 3, written notes (1/3);
- Week 2: lecture 4, lecture 5, lecture 6, written notes (2/3);
- Week 3: lecture 7, lecture 8, lecture 9, written notes (3/3).

**Extra references:**

- O’Neill, B.;
**Semi-Riemannian geometry. With applications to relativity.**Pure and Applied Mathematics, 103.*Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York,*1983. xiii+468 pp. ISBN: 0-12-526740-1*.* - Penrose, R.;
**Techniques of differential topology in relativity.**Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 7.*Society for Industrial and Applied Mathematics, Philadelphia, Pa.,*1972. viii+72 pp. - Beem, J. K.; Ehrlich, P. E.; Easley, K. L;
**Global Lorentzian geometry.**Second edition. Monographs and Textbooks in Pure and Applied Mathematics, 202.*Marcel Dekker, Inc., New York,*1996. xiv+635 pp. ISBN: 0-8247-9324-2.