Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
Math 060 101317C Linear Transformations: Isomorphisms
Lemma: Linear transformations that agree on a basis are identical. Definition: one-to-one (injective). Examples and non-examples. Lemma: T is one-to-one iff its kernel is {0}. Definition: onto (surjective). Examples and non-examples. Definition: isomorphism; isomorphic. Theorem: T
From playlist Course 4: Linear Algebra (Fall 2017)
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
Torsion units of integral group rings (Lecture 1) by Angel del Rio
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
Measure Equivalence, Negative Curvature, Rigidity (Lecture 3) by Camille Horbez
PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, India), Anish Ghosh (TIFR, Mumbai, India), Subhajit Goswami (TIFR, Mumbai, India) and Mahan M J (TIFR, Mumbai, India) DATE & TIME: 27 February 2023 to 10 March 2023 VENUE: Madhava Lecture Hall
From playlist PROBABILISTIC METHODS IN NEGATIVE CURVATURE - 2023
The Frobenius Problem - Method for Finding the Frobenius Number of Two Numbers
Goes over how to find the Frobenius Number of two Numbers.
From playlist ℕumber Theory
Berge's lemma, an animated proof
Berge's lemma is a mathematical theorem in graph theory which states that a matching in a graph is of maximum cardinality if and only if it has no augmenting paths. But what do those terms even mean? And how do we prove Berge's lemma to be true? == CORRECTION: at 7:50, the red text should
From playlist Summer of Math Exposition Youtube Videos
Mima Stanojkovski - Groups from determinantal curves
Groups are fundamental entities in mathematics and in the sciences, which, when viewed as symmetries of objects, can help understand better or tell the objects in question apart. As "most groups are p-groups", we are motivated to understand structure and symmetries of p-groups, even though
From playlist Research Spotlight
Giles Gardam: Kaplansky's conjectures
Talk by Giles Gardam in the Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/3580/ on September 17, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
This lecture is part of an online course on rings and modules. We continue the previous lecture on complete rings by discussing Hensel's lemma for finding roots of polynomials over p-adic rings or over power series rings. We sketch two proofs, by slowly improving a root one digit at a tim
From playlist Rings and modules
Nicholas Katz - Exponential sums and finite groups
Correction: The affiliation of Lei Fu is Tsinghua University. This is joint work with Antonio Rojas Leon and Pham Huu Tiep, where we look for “interesting” finite groups arising as monodromy groups of “simple to remember” families of exponential sums”.
From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021
Burnside's Lemma (Part 1) - combining group theory and combinatorics
A result often used in math competitions, Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be transformed into one another by rotation different, like in this cas
From playlist Traditional topics, explained in a new way
Giles Gardam - Kaplansky's conjectures
Kaplansky made various related conjectures about group rings, especially for torsion-free groups. For example, the zero divisors conjecture predicts that if K is a field and G is a torsion-free group, then the group ring K[G] has no zero divisors. I will survey what is known about the conj
From playlist Talks of Mathematics Münster's reseachers
Burnside's Lemma (Part 2) - combining math, science and music
Part 1 (previous video): https://youtu.be/6kfbotHL0fs Orbit-stabilizer theorem: https://youtu.be/BfgMdi0OkPU Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be
From playlist Traditional topics, explained in a new way
Laurent Bartholdi - Imbeddings in groups of subexponential growth
Laurent Bartholdi (University of Gottingen, Germany) A finitely generated group has subexponential growth if the number of group elements expressible as words of length $\le n$ grows subexponentially in $n$. I will show that every countable group that does not contain a subgroup of expone
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
Andrzej Zuk: Spectra of ultra-discrete limits
We present a computation of spectra of random walks on self-similar graphs. CIRM HYBRID EVENT Recorded during the meeting "Additive Combinatorics in Marseille" the September 08, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenf
From playlist Analysis and its Applications
Nicolás Matte Bon: Confined subgroups and high transitivity
A subgroup of a group is confined if the closure of its conjugacy class in the Chabauty space does not contain the trivial subgroup. Such subgroups arise naturally as stabilisers for non-free actions on compact spaces. I will explain a result establishing a relation between the confined su
From playlist Dynamical Systems and Ordinary Differential Equations
Graph regularity and counting lemmas - Jacob Fox
Conference on Graphs and Analysis Jacob Fox June 5, 2012 More videos on http://video.ias.edu
From playlist Mathematics
The Field With One Element and The Riemann Hypothesis (Full Video)
A crash course of Deninger's program to prove the Riemann Hypothesis using a cohomological interpretation of the Riemann Zeta Function. You can Deninger talk about this in more detail here: http://swc.math.arizona.edu/dls/ Leave some comments!
From playlist Riemann Hypothesis