The seminar meets Fridays from 18:00 to 19:30 (Princeton time).

Contact the organizer for the Zoom link.

For information please contact Joaquín Moraga.

- The seminar aims to train young graduate students on the techniques of the Minimal Model Program.
- The whole seminar will run over zoom (even if in person meetings are allowed at Princeton University in the future).
- This will be an extensive seminar that will cover a big portion of the existing literature, finishing with Birkar's boundedness of Fano varieties, so we expect that it will run for at least one year.
- We may cover some special topics depending on the interests of the assistants.
- As a starting point, we will read Kollár-Mori "Birational Geometry of Algebraic Varieties".
- This page will be updated as the seminar progresses.

**January 29th:** Overview of the Minimal Model Program. (Notes)

*Topics:*Overview of the Minimal Model Program.

**February 5th:** Kollár-Mori "Birational Geometry of Algebraic Varieties" Chapter 1. (Notes)

*Topics:*Bend and break, existence of rational curves, and the Cone Theorem.

**Febuary 12th:** Kollár-Mori "Birational Geometry of Algebraic Varieties" Chapter 2. (Notes)

*Topics:*Terminal, canonical, Kawamata log terminal, and log canonical singularities. Kodaira vanishing and generalizations.

**Febuary 19th:** Kollár-Mori "Birational Geometry of Algebraic Varieties" Chapter 3: Part 1. (Notes)

*Topics:*Basepoint-free Theorem and the Cone Theorem.

**Febuary 26th:** Kollár-Mori "Birational Geometry of Algebraic Varieties" Chapter 3: Part 2. (Notes)

*Topics:*The Rationality Theorem and the Non-vanishing Theorem.

**March 5th:** Kollár-Mori "Birational Geometry of Algebraic Varieties" Chapter 3 and Chapter 4: Section 1 & 2. (Notes)

*Topics:*The relative cone theorem, running the minimal model program, and surface klt singularities.

**March 12th:** Kollár-Mori "Birational Geometry of Algebraic Varieties" Chapter 5: Section 1, 2 & 3. (Notes)

*Topics:*Rational singularities, log terminal singularities, and canonical 3-fold singularities.

**March 19th:** Kollár-Mori "Birational Geometry of Algebraic Varieties" Chapter 5: Section 4 & 5. (Notes)

*Topics:*Inversion of adjunction and Duality Theory.

**March 26th:** Kollár-Mori "Birational Geometry of Algebraic Varieties" Chapter 6. (Notes)

*Topics:*Terminal 3-fold Minimal Model Program.

**April 2nd:** Lazarsfeld "Positivity in Algebraic Geometry" Chapter 9.1-9.4. (Notes)

*Topics:*Multiplier ideals and the Nadel Vanishing Theorem.

Here there are notes typed by one of the participants: Student Notes.