**Time and place:** MWF 12-1, Science Center 310

**Professor:** Jacob Lurie

The
course
syllabus.

**Lecture Notes**:

Lecture 1:
Overview.

Lecture 2:
The Wall Finiteness
Obstruction.

Lecture 3:
Whitehead Torsion: Part I.

Lecture 4:
Whitehead Torsion: Part
II.

Lecture 5:
Cell-Like Maps.

Lecture 6:
Concordance of
Polyhedra.

Lecture 7:
Higher Simple Homotopy
Theory.

Lecture 8:
Fibrations of Polyhedra.

Lecture 9:
Fibrations of
Nonsingular Simplicial Sets.

Lecture 10:
Combinatorial Models for
Simple Homotopy Theory.

Lecture 11:
Equivalence of the
Combinatorial Definition.

Lecture 12:
Some Loose Ends.

Lecture 13:
Homotopy Types vs Simple
Homotopy Types.

Lecture 14:
(Lower) K-Theory
of infty-Categories.

Lecture 15:
The Wall Finiteness
Obstruction Revisited.

Lecture 16:
Higher K-Theory of
infty-Categories.

Lecture 17:
The Additivity Theorem.

Lecture 18:
Additive K-Theory.

Lecture 19:
K-Theory of Ring Spectra.

Lecture 20:
Lower K-Groups of Ring
Spectra.

Lecture 21:
The Algebraic K-Theory of
Spaces.

Lecture 22:
Constructible
Sheaves.

Lecture 23:
Universal Local Acyclicity.

Lecture 24:
The Assembly Map.

Lecture 25:
The Assembly Map II.

Lecture 26:
The Assembly Map III.

Lecture 27:
Higher Torsion.

Lecture 28:
Another Assembly Map.

Lecture 29:
Another Assembly Map II.

Lecture 30:
The Whitehead Space.

Lecture 31:
The Whitehead Space II.

Lecture 32:
Proof of the Main
Theorem.

Lecture 33:
Digression: Review of
Microbundles

Lecture 34:
Overview of Part 3

Lecture 35:
The Setup

Lecture 36:
The Combinatorial Step
(Part I)

Lecture 37:
The Combinatorial Step
(Part II)

Lecture 38:
Thickenings of a
Point

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