
Lecture 05: The Large Sieve
Lawrence D. Guth teaches the large sieve, a classical number theory tool, as part of MIT's 18.156 Projection Theory course. Guth frames the sieve method as a topic closely tied to projection theory, the course's broader subject, showing how bounds on exponential sums and integer point distributions connect back to geometric projection problems. The lecture runs seventy-nine minutes and builds on earlier sessions in the sequence, working through the underlying inequalities and their number-theoretic applications on the board. It is aimed at students already following the course rather than general viewers, with Guth moving at a graduate level through definitions, lemmas, and proofs that link sieve theory to the projection-theoretic framework developed earlier in the term.