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)
Multidimensional Bolzano Weierstraß
In this video, I prove the celebrated Bolzano-Weierstraß theorem in n dimensions, which says that a bounded sequence in R^n must have a convergent subsequence. This is the most important fact in analysis, and a lot of nice results follow from it Bolzano-Weierstraß: https://youtu.be/PapmU
From playlist Topology
Introduction to additive combinatorics lecture 10.1 --- the structure and properties of Bohr sets.
An important informal idea in additive combinatorics is that of a "structured" set. One example of a class of sets that are rich in additive structure is the class of Bohr sets, which play the role in general finite Abelian groups that subspaces play in the special case of groups of the fo
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Convolution Theorem: Fourier Transforms
Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.
From playlist Partial differential equations
Bolzano-Weierstrass Theorem (Direct Proof) In this video, I present a more direct proof of the Bolzano-Weierstrass Theorem, that does not use any facts about monotone subsequences, and instead uses the definition of a supremum. This proof is taken from Real Mathematical Analysis by Pugh,
From playlist Sequences
Here I prove the Heine-Borel Theorem, one of the most fundamental theorems in analysis. It says that in R^n, all boxes must be compact. The proof itself is very neat, and uses a bisection-type argument. Enjoy! Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHG
From playlist Topology
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
Kyle Broder -- Recent Developments Concerning the Schwarz Lemma
A lecture I gave at the Beijing International Center for Mathematical Research geometric analysis seminar. The title being Recent Developments Concerning the Schwarz Lemma with applications to the Wu--Yau Theorem. This contains some recent results concerning the Bochner technique for the G
From playlist Research Lectures
Gap and index estimates for Yang-Mills connections in 4-d - Matthew Gursky
Variational Methods in Geometry Seminar Topic: Gap and index estimates for Yang-Mills connections in 4-d Speaker: Matthew Gursky Affiliation: University of Notre Dame Date: March 19, 2019 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Dror Varolin - Minicourse - Lecture 5
No Audio Dror Varolin Variations of Holomorphic Hilbert spaces Traditional complex analysis focuses on a single space, like a domain in Euclidean space, or more generally a complex manifold, and studies holomorphic maps on that space, into some target space. The typical target space for
From playlist Maryland Analysis and Geometry Atelier
Modified Logarithmic Sobolev Inequalities: ... (Lecture 3) by Prasad Tetali
PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear
From playlist Advances in Applied Probability 2019
Dror Varolin - Minicourse - Lecture 2
Dror Varolin Variations of Holomorphic Hilbert spaces Traditional complex analysis focuses on a single space, like a domain in Euclidean space, or more generally a complex manifold, and studies holomorphic maps on that space, into some target space. The typical target space for a domain i
From playlist Maryland Analysis and Geometry Atelier
Hyperbolic geometry and the proof of Morrison-Kawamata... (Lecture - 01) by Misha Verbitsky
20 March 2017 to 25 March 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions between mathematics and theoretical physics, especially
From playlist Complex Geometry
Bourbaki - 24/01/15 - 3/4 - Gilles CARRON
De nouvelles utilisations du principe du maximum en géométrie [d'après B. Andrews, J. Clutterbuck et S. Brendle]
From playlist Bourbaki - 24 janvier 2015
Weil conjectures 4 Fermat hypersurfaces
This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T
From playlist Algebraic geometry: extra topics
Homogeneous holomorphic foliations on Kobayashi hyperbolic manifolds by Benjamin Mckay
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
[#SoME1] A simple statement with a remarkable proof ( + Proof of Bolzano-Weierstrass Theorem)
In this video, I present a very important statement that, at first, seems quite obvious, but whose proof requires some neat reasoning. I start off by explaining everything required in order to understand the problem, and then restate it in a more rigorous way. Then, I present two proofs f
From playlist Summer of Math Exposition Youtube Videos
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 4) by Dror Varolin
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Proving Bolzano-Weierstrass with Nested Interval Property | Real Analysis
We prove the Bolzano Weierstrass theorem using the Nested Interval Property. The Bolzano-Weierstrass theorem states every bounded sequence has a convergent subsequence. We will construct a subsequence by bounding our sequence between M and -M, then creating an infinite sequence of nested i
From playlist Real Analysis
Bo'az Klartag - Convexity in High Dimensions II
November 4, 2022 This is the second talk in the Minerva Mini-course of Bo'az Klartag, Weizmann Institute of Science and Princeton's Fall 2022 Minerva Distinguished Visitor We will discuss recent progress in the understanding of the isoperimetric problem for high-dimensional convex sets, a
From playlist Minerva Mini Course - Bo'az Klartag