GIVE NOW about ocw help & faqs contact us
18.156 | Spring 2025 | Graduate

# Projection Theory

The lecture notes are available in PDF and LaTeX formats.
pdf
2 MB
18.156 (S25): Full Lecture Notes: Projection Theory
file
300 kB
18.156 (S25): Full Lecture Notes: Projection Theory (LaTeX version)
file
6 MB
18.156 (S25): Full Lecture Notes LaTeX Files.zip
pdf
796 kB
18.156 (S25): Lecture 01: Introduction and Overview
pdf
950 kB
18.156 (S25): Lecture 02: Fundamental Methods of Projection Theory
pdf
951 kB
18.156 (S25): Lecture 03: Projection Theory for Balls in Euclidean Space
pdf
537 kB
18.156 (S25): Lecture 04: The Fourier Method in Euclidean Space
pdf
642 kB
18.156 (S25): Lecture 05: The Large Sieve
pdf
414 kB
18.156 (S25): Lecture 06: Projections and Smoothing
pdf
485 kB
18.156 (S25): Lecture 07: Applications of the Large Sieve to Number Theory
pdf
484 kB
18.156 (S25): Lecture 08: The Szemeredi-Trotter Theorem
pdf
399 kB
18.156 (S25): Lecture 09: Reflections on the Szemeredi-Trotter Theorem
pdf
474 kB
18.156 (S25): Lecture 10: Sum-Product Theory
pdf
380 kB
18.156 (S25): Lecture 11: Contagious Structure in Projection Theory
pdf
437 kB
18.156 (S25): Lecture 12: Proof of the Bourgain-Katz-Tao Projection Theorem
pdf
438 kB
18.156 (S25): Lecture 13: Proof of the Balog-Szemeredi-Gowers Theorem
pdf
441 kB
18.156 (S25): Lecture 14: Bourgain's Projection Theorem over R, Part I
pdf
479 kB
18.156 (S25): Lecture 15: Bourgain's Projection Theorem II
pdf
420 kB
18.156 (S25): Lecture 16: Bourgain's Projection theorem III
pdf
521 kB
18.156 (S25): Lecture 17: Random Walks on Finite Groups I
pdf
557 kB
18.156 (S25): Lecture 18: Random Walks on Finite Groups II
pdf
180 kB
18.156 (S25): Lecture 19: Random Walks on Finite Groups III
pdf
420 kB
18.156 (S25): Lecture 20: Homogenenous Dynamics I
pdf
484 kB
18.156 (S25): Lecture 21: Homogeneous Dynamics II
pdf
474 kB
18.156 (S25): Lecture 22: Sharp Projection Theorems I: Introduction and Beck's Theorem
pdf
503 kB
18.156 (S25): Lecture 23: Sharp Projection Theorems II: AD Regular Case
pdf
580 kB
18.156 (S25): Lecture 24: Sharp Projection Theorems III: 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

Browse Resources

# You are leaving MIT OpenCourseWare

Please be advised that external sites may have terms and conditions, including license rights, that differ from ours. MIT OCW is not responsible for any content on third party sites, nor does a link suggest an endorsement of those sites and/or their content.