Theory of numbers: Chevalley-Warning theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove the Chevalley-Warning theorem, which which gives conditions for a polynomial in several variables to have a solution modulo a prime. For the other lectures in the course see https://www.youtube.
From playlist Theory of numbers
Cayley-Hamilton Theorem Example 2
Matrix Theory: Let A be the 3x3 matrix A = [1 2 2 / 2 0 1 / 1 3 4] with entries in the field Z/5. We verify the Cayley-Hamilton Theorem for A and compute the inverse of I + A using a geometric power series.
From playlist Matrix Theory
Kevin Costello - A twisted form of the ADS/CFT correspondence
Kevin COSTELLO (Northwestern Univ., Evanston, USA)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
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
Proof that Cayley table row and column entries are unique and complete
In this video I show a proof of why all the row and column entries in a Cayley table are unique and why all of the elements in the group appear in each row and column. This proof goes a long way towards proving Cayley's theorem.
From playlist Abstract algebra
Introduction to number theory lecture 22. Chevalley-Warning theorem
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We discuss the Chevalley-Warning theorem, which says roughly that it is easy to find soluti
From playlist Introduction to number theory (Berkeley Math 115)
Theorem 1.10 - part 10.5 - Neron-Ogg-Shafarevich - Structure of m-Torsion of A mod p
Here we use the theory of Neron Models, Chevalley-Rosenlicht, and a handful of other things to determine the structure of the torsion of an Abelian variety with bad reduction modulo p. This is used in proving the hard part of the Neron-Ogg-Shafarevich criterion: if an abelian variety has a
From playlist Theorem 1.10
Simple grps 1 by N. S. Narasimha Sastry
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Cayley-Hamilton Theorem: General Case
Matrix Theory: We state and prove the Cayley-Hamilton Theorem over a general field F. That is, we show each square matrix with entries in F satisfies its characteristic polynomial. We consider the special cases of diagonal and companion matrices before giving the proof.
From playlist Matrix Theory
Spectral and scattering features of hyperbolic manifolds - Michael Magee
Michael Magee Member, School of Mathematics October 1, 2014 More videos on http://video.ias.edu
From playlist Mathematics
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)
Oksana Yakimova, Research talk - 30 January 2015
Oksana Yakimova (Universität Jena) - Research talk http://www.crm.sns.it/course/4158/ On symmetric invariants of semi-direct products. Let $\mathfrak g$ be a complex reductive Lie algebra. By the Chevalley restriction theorem, the subalgebra of symmetric invariants $S(\mathfrak g)^{\math
From playlist Lie Theory and Representation Theory - 2015
CurvesSurfaces3: De Casteljau Bezier Curves in Algebraic Calculus | N J Wildberger
We explain how to extend Archimedes' famous Parabolic Area Formula to the cubic situation. This formula was historically the first major calculation in Calculus, and gave an explicit and workable formula for the area of a slice of a parabola, cut off by a chord, in terms of the area of a p
From playlist MathSeminars
Peter Stevenhagen: The Chebotarev density theorem
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Jean-Morlet Chair - Shparlinski/Kohel
Ax-Katz-Chevalley-Warning Introduction
Take a smooth projective variety defined over a finite field FF_p. The number of FF_p points is actually congruent to one modulo p and actually how divisible by p this number is has to do with the Hodge diamond.
From playlist Newton above Hodge
PMSP - Approximate algebraic structure (groups, fields, homomorphisms, ...) II - Ben Green
Ben Green University of Cambridge June 14, 2010 For more videos, visit http://video.ias.edu
From playlist Mathematics
Homogeneous spaces, algebraic K-theory and cohomological(...) - Izquierdo - Workshop 2 - CEB T2 2019
Diego Izquierdo (MPIM Bonn) / 24.06.2019 Homogeneous spaces, algebraic K-theory and cohomological dimension of fields. In 1986, Kato and Kuzumaki stated a set of conjectures which aimed at giving a Diophantine characterization of the cohomological dimension of fields in terms of Milnor
From playlist 2019 - T2 - Reinventing rational points
Proof that the Sequence {1/n} is a Cauchy Sequence
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that the Sequence {1/n} is a Cauchy Sequence
From playlist Cauchy Sequences
Plenary lecture 2 by Emmanuel Breuillard - Part 1
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature