**Time and place:** MWF 9:00 - 9:50, APM 5402

**Professor:** Jacob Lurie

The
course
syllabus.

**Lectures (Warning: these notes are sloppy. Use at own risk.)**:

Lecture 1:
Overview.

Lecture 2:
Tilting.

Lecture 3:
Untilting.

Lecture 4:
Holomorphic Functions of the Variable p.

Lecture 5:
Norms.

Lecture
6: Definition of the Fargues-Fontaine Curve.

Lecture
7: The Artin-Hasse Exponential.

Lecture
8: The de Rham Period Ring.

Lecture
9: Divisors.

Lecture
10: Structure of the Fargues-Fontaine Curve.

Lecture
11: Trivial Eigenspaces of the Frobenius.

Lecture
12: Detection of Zeroes.

Lecture
13: Digression-Jensen's Formula.

Lecture
14: The Metric Structure of Y.

Lecture
15: Zeroes of Primitive Elements.

Lecture
16: Converging to a Zero.

Lecture
17: Untilts of an Algebraically Closed Field.

Lecture
18: Bounded and Meromorphic Functions of p.

Lecture
19: Line Bundles on the Fargues-Fontaine Curve.

Lecture
20: The Harder-Narasimhan Filtration.

Lecture
21: Covers of the Fargues-Fontaine Curve.

Lecture
22: Line Bundles on Covers.

Lecture
23: Formal Groups.

Lecture
24: Lubin-Tate Formal Groups.

Lecture
25: Functions on Y_E.

Lecture
26: Isocrystals.

Lecture
27: Applications.

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