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18.156 | Spring 2025 | Graduate

# Projection Theory

##### Lecture 01: Introduction to Projection Theory

##### Lecture 02: Fundamental Methods of Projection Theory

##### Lecture 03: Projection Theory in Euclidean Space

##### Lecture 04: The Fourier Method in Euclidean Space

##### Lecture 05: The Large Sieve

##### Lecture 06: Projections and Smoothing

##### Lecture 07: Applications of the Large Sieve to Number Theory

##### Lecture 08: The Szemeredi-Trotter Theorem

##### Lecture 09: Reflections on the Szemeredi-Trotter Theorem

##### Lecture 10: Sum-Product Theory

##### Lecture 11: Contagious Structure in Projection Theory

##### Lecture 12: The Bourgain-Katz-Tao Projection Theorem

##### Lecture 13: The Balog-Szemeredi-Gowers Theorem

##### Lecture 14: The Bourgain Projection Theorem Part 1 (over the Real Numbers)

##### Lecture 15: The Bourgain Projection Theorem, Part 2

##### Lecture 16: The Bourgain Projection Theorem, Part 3

##### Lecture 17: Random Walks on Finite Groups, Part 1

##### Lecture 18: Random Walks on Finite Groups, Part 2

##### Lecture 19: Random Walks on Finite Groups, Part 3

##### Lecture 20: Homogeneous Dynamics, Part 1

##### Lecture 21: Homogeneous Dynamics, Part 2

##### Lecture 22: Sharp Projection Theorems, Part 1: Introduction and Beck's Theorem.

##### Lecture 23: Sharp Projection Theorems, Part 2: AD Regular Case

##### Lecture 24: Sharp Projection Theorems, Part 3: Combining Different Scales

## Course Info

##### Instructor

- Prof. Lawrence D Guth

##### Departments

- Mathematics

##### As Taught In

Spring 2025

##### Level

Graduate

##### Topics

- Mathematics
  - Differential Equations
  - Mathematical Analysis

##### Learning Resource Types

theaters Lecture Videos
notes Lecture Notes
assignment Problem Sets
group_work Projects
Editable Files

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