Basic Information
Boolean Functions, Boolean Cube, Fourier Expansion. Noise Operator. Influence. Hypercontractivity. Biased Fourier Analysis. Sharp Threshold Theorems. Invariance Principle. Global Hypercontractivity. Analysis On Slice. Learning Outcomes# By The End of The Course, The Student Will# 1. Be Familiar With Basic Concepts, Such As# Fourier Expansion, Noise Operator, Influence, Biased Fourier Analysis. 2. Understand and Be Able to Apply The Main Techniques in The Area# Classical and Global Hypercontractivity, Invariance Principle. 3. Be Able to Apply The Tools Covered in Class to Various Areas In Theoretical Computer Science and Mathematics# Property Testing, Combinatorics, Random Graphs and Others. 4. Be Familiar With Open Problems in The Area, and Be Able To Tackle Them.
Faculty: Computer Science
|Undergraduate Studies
|Graduate Studies
Pre-required courses
(94412 - Probability (advanced) and 104016 - Algebra 1/extended) or (94412 - Probability (advanced) and 104166 - Algebra Am) or (104016 - Algebra 1/extended and 104222 - Probability Theory) or (104166 - Algebra Am and 104222 - Probability Theory)