**Time and place:** MWF 12-1, Science Center 113

**Professor:** Jacob Lurie

The
course
syllabus.

**Lecture Notes**:
Lecture 1: Tamagawa
Numbers and Weil's Conjecture.

Lecture 2: Weil's Conjecture for Function Fields.

Lecture 3: Cohomological Reformulation.

Lecture 4: Three Approaches from Topology.

Lecture 5: Higher Category Theory.

Lecture 6: l-adic Cohomology of Schemes.

Lecture 7: l-adic Cohomology of (Pre)stacks.

Lecture 8: Nonabelian Poincare Duality (in topology).

Lecture 9: Nonabelian Poincare Duality (in algebraic geometry).

Lecture 10: Acyclicity of the Ran Space.

Lecture 11: Universal Homology Equivalences.

Lecture 13: Generic Trivializations.

Lecture 14: Existence of Borel Reductions (I).

Lecture 15: Existence of Borel Reductions (II).

Lecture 16: Spaces of Rational Maps.

Lecture 17: The Main Calculation.

Lecture 17: The Main Calculation.

Lecture 19: Sheaves on the Ran Space.

Lecture 20: The Product Formula.

Lecture 23: Koszul Duality in Topology.

Lecture 24: Koszul Duality in Algebraic Geometry.

Lecture 25: Outline of the Local Calculation.

Lecture 26: Local Calculation: Reduction to Germs.

Lecture 27: Local Calculation: From Germs to Bundles.

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