Geometric incidences are a family of combinatorial problems. While these problems existed for several decades, in the past few years they have been experiencing a renaissance: Many new incidence results are being derived by using algebraic methods, while at the same time interesting connections between incidences and other parts of mathematics are being exposed (such as Harmonic Analysis and Theoretical Computer Science). This is currently an active research field which seems to attract the interest of various prominent mathematicians. In this class we will study this subfield and some of its connections to other parts of mathematics.
Each course participant is expected to read one related paper and to present it in class. This webpage will contain a list of possible papers. If more than a few students enroll, some of the undergrad participants would instead submit 3 homework assignments. Students are also expected to attend most of the classes.
The class requires a basic mathematical understanding, such as basic familiarity with combinatorics, probability, and linear algebra. We will go over most of the mathematical concepts that we rely on.
HARRY BATEMAN INSTRUCTOR IN MATHEMATICS
Detailed lecture notes would be uploaded before each class (for example, see last year's additive combinatorics lecture notes). Other related sources are Larry Guth's book on polynomial methods in combinatorics and Ze'ev Dvir's survey.