Explore the fundamental concepts of additive combinatorics in this 54-minute lecture by David Grynkiewicz from the International Centre for Theoretical Sciences. Delve into set addition and sum sets before examining basic lower bounds and Kneser's Theorem. Follow along as the speaker presents and proves key theorems, including the Cauchy-Davenport theorem from 1813. Gain insights into special cases like complete torsion and field extensions. This talk, part of a workshop on Additive Combinatorics, offers a comprehensive introduction to essential topics in this dynamic field that intersects with number theory, ergodic theory, and harmonic analysis.
Basic Lower Bounds and Kneser's Theorem by David Grynkiewicz
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
Basic Lower Bounds and Kneser's Theorem
Set Addition Sum sets
Basic Lower Bounds and Kneser's Theorem
Theorem
Proof
Note
Theorem
Proof
Kneser's Theorem
Proof
Special Case Complete Torsion
Theorem 1813 Cauchy - Davenport theorem
Theorem
Proof
Theorem F/H field extension
Taught by
International Centre for Theoretical Sciences
