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HU Credits:
2
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Noam Lifshitz
Coordinator Office Hours:
The hour right after class
Teaching Staff:
Dr. Noam Lifshitz
Course/Module description:
In the course we will learn a variety of tools from different fields in order to solve problems that are very easy to state. These are called intersection problems for finite sets. They take the form: How large can a family of n/2-sized subsets of {1,...,n} be if the inersection of each two sets in the family is not of size n/4.
Course/Module aims:
The student will be able to use the recently developed tools in extremal combinatorics and attempt to solve open problems in the area using them.
Learning outcomes - On successful completion of this module, students should be able to:
The students will be able to use analytic and algebraic methods and then be able to attempt to solve the open problems presented in the course.
Attendance requirements(%):
Teaching arrangement and method of instruction:
Course/Module Content:
1) The EKR theorem and Katona's circle method
2) Shifting method
3) Spectral method/ Hoffman's bound
4) Sharp threshold results
5) Regularity method
6) The junta method
7) Ranks of matrices and tensors: the polynomial method
8) Huang's spectral dimension method
9) Methods from algebraic topology
10) Hyprcontractivity for global functions
11) The Frankl-Rodl theorem
12) Sunflower problem
Required Reading:
I'll send you notes with exercises that you are expected to go over and send me corrections
Additional Reading Material:
Course/Module evaluation:
End of year written/oral examination 80 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 20 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
Additional information:
Good control of probability and linear algebra.
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