18.156 | Spring 2025 | Graduate

Projection Theory

Lecture Notes

The lecture notes are available in PDF and LaTeX formats.
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18.156 (S25): Full Lecture Notes: Projection Theory
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18.156 (S25): Full Lecture Notes: Projection Theory (LaTeX version)
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18.156 (S25): Full Lecture Notes LaTeX Files.zip
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18.156 (S25): Lecture 01: Introduction and Overview
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18.156 (S25): Lecture 02: Fundamental Methods of Projection Theory
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18.156 (S25): Lecture 03: Projection Theory for Balls in Euclidean Space
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18.156 (S25): Lecture 04: The Fourier Method in Euclidean Space
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18.156 (S25): Lecture 05: The Large Sieve
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18.156 (S25): Lecture 06: Projections and Smoothing
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18.156 (S25): Lecture 07: Applications of the Large Sieve to Number Theory
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18.156 (S25): Lecture 08: The Szemeredi-Trotter Theorem
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18.156 (S25): Lecture 09: Reflections on the Szemeredi-Trotter Theorem
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18.156 (S25): Lecture 10: Sum-Product Theory
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18.156 (S25): Lecture 11: Contagious Structure in Projection Theory
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18.156 (S25): Lecture 12: Proof of the Bourgain-Katz-Tao Projection Theorem
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18.156 (S25): Lecture 13: Proof of the Balog-Szemeredi-Gowers Theorem
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18.156 (S25): Lecture 14: Bourgain's Projection Theorem over R, Part I
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18.156 (S25): Lecture 15: Bourgain's Projection Theorem II
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18.156 (S25): Lecture 16: Bourgain's Projection theorem III
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18.156 (S25): Lecture 17: Random Walks on Finite Groups I
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18.156 (S25): Lecture 18: Random Walks on Finite Groups II
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18.156 (S25): Lecture 19: Random Walks on Finite Groups III
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18.156 (S25): Lecture 20: Homogenenous Dynamics I
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18.156 (S25): Lecture 21: Homogeneous Dynamics II
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18.156 (S25): Lecture 22: Sharp Projection Theorems I: Introduction and Beck's Theorem
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18.156 (S25): Lecture 23: Sharp Projection Theorems II: AD Regular Case
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18.156 (S25): Lecture 24: Sharp Projection Theorems III: Combining Different Scales

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