Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
The Schrodinger Equation is (Almost) Impossible to Solve.
Sure, the equation is easily solvable for perfect / idealized systems, but almost impossible for any real systems. The Schrodinger equation is the governing equation of quantum mechanics, and determines the relationship between a system, its surroundings, and a system's wave function. Th
From playlist Quantum Physics by Parth G
Busemann Functions in Random Growth and Polymer Models by Timo Seppäläinen
PROGRAM FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS: Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE: 11 July 2022 to 29 July 2022 VENUE: Ramanujan Lecture Hall and online This
From playlist First-Passage Percolation and Related Models 2022 Edited
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation
Geodesics of FPP (Lecture 3) by Michael Damron
PROGRAM FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS: Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE: 11 July 2022 to 29 July 2022 VENUE: Ramanujan Lecture Hall and online This
From playlist First-Passage Percolation and Related Models 2022 Edited
Evan Sorensen (UWM) -- Busemann functions and semi-infinite geodesics in a semi-discrete space
In the last 10-15 years, Busemann functions have been a key tool for studying semi-infinite geodesics in planar first and last-passage percolation. We study Busemann functions in the semi-discrete Brownian last-passage percolation (BLPP) model and use these to derive geometric properties o
From playlist Northeastern Probability Seminar 2021
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
In Planar First-Passage Percolation, Non-Crossing Geodesics Tend to Coalesce by Daniel Ahlberg
PROGRAM FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE & TIME 11 July 2022 to 29 July 2022 VENUE Ramanujan Lecture Hall and online Th
From playlist First-Passage Percolation and Related Models 2022 Edited
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
Change of variables and the derivative -- Calculus I
This lecture is on Calculus I. It follows Part I of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus I
Geodesics of FPP (Lecture 2) by Michael Damron
PROGRAM FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS: Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE: 11 July 2022 to 29 July 2022 VENUE: Ramanujan Lecture Hall and online This
From playlist First-Passage Percolation and Related Models 2022 Edited
Riemann Sum Defined w/ 2 Limit of Sums Examples Calculus 1
I show how the Definition of Area of a Plane is a special case of the Riemann Sum. When finding the area of a plane bound by a function and an axis on a closed interval, the width of the partitions (probably rectangles) does not have to be equal. I work through two examples that are rela
From playlist Calculus
Martin Kell: Sectional curvature like conditions on metric spaces
In this talk I present two concavity assumptions on the distance. The first one is the non-negative curvature analogue of Busemann’s non-positive curvature condition and resembles a sectional curvature-like condition comparable to the measure contraction property. It holds for certain non-
From playlist HIM Lectures: Follow-up Workshop to JTP "Optimal Transportation"
Timo Seppäläinen: Variational formulas, Busemann functions, and fluctuation exponents - Part 2
Abstract: Busemann functions for the two-dimensional corner growth model with exponential weights. Derivation of the stationary corner growth model and its use for calculating the limit shape and proving existence of Busemann functions. Recording during the meeting : "Random Structures in
From playlist Probability and Statistics
Convergence of Limit Shapes for 2D Near-Critical First-Passage Percolation by Chang-Long Yao
PROGRAM FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE: 11 July 2022 to 29 July 2022 VENUE: Ramanujan Lecture Hall and online This p
From playlist First-Passage Percolation and Related Models 2022 Edited
Solvable LPP (Lecture 1) by Márton Balázs
PROGRAM FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS: Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE: 11 July 2022 to 29 July 2022 VENUE: Ramanujan Lecture Hall and online This
From playlist First-Passage Percolation and Related Models 2022 Edited
Vlad Yaskin: A solution to the 5th and 8th Busemann-Petty problems near the Euclidean ball
We show that the 5th and the 8th Busemann-Petty problems have positive solutions for bodies that are sufficiently close to the Euclidean ball in the Banach-Mazur distance. Joint work with M. Angeles Alfonseca, Fedor Nazarov, and Dmitry Ryabogin.
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Weil conjectures 2: Functional equation
This is the second lecture about the Weil conjectures. We show that the Riemann-Roch theorem implies the rationality and functional equation of the zeta function of a curve over a finite field.
From playlist Algebraic geometry: extra topics