Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

YouTube

Marina Iliopoulou - Three Polynomial Methods for Point Counting, Lecture I

Hausdorff Center for Mathematics via YouTube

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Explore three powerful polynomial methods for point counting in this lecture by Marina Iliopoulou. Dive into Dvir's polynomial method for solving the Kakeya problem in finite fields, Guth and Katz's polynomial partitioning technique for addressing the Erdös distinct distances problem in the plane, and the slice rank method developed by Croot, Lev, Pach, Ellenberg, and Gijswijt for demonstrating the small size of sets with no 3-term arithmetic progressions in finite-field settings. Learn about key concepts such as the Kakeya problem, Kakeya universe, vanishing quality, zero polynomials, and gain insights through proofs and sketches. Enhance your understanding of advanced mathematical techniques in this comprehensive 54-minute lecture from the Hausdorff Center for Mathematics.

Syllabus

Introduction
Notation
Kaiga problem
Kaiga universe
The polynomial method
Vanishing quality
Zero polynomials
Proof
Sketch
First method

Taught by

Hausdorff Center for Mathematics

Reviews

Start your review of Marina Iliopoulou - Three Polynomial Methods for Point Counting, Lecture I

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.