This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for
From playlist Quaternions
Maxim Kazarian - 2/3 Mathematical Physics of Hurwitz numbers
Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num
From playlist Physique mathématique des nombres de Hurwitz pour débutants
Maxim Kazarian - 3/3 Mathematical Physics of Hurwitz numbers
Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num
From playlist Physique mathématique des nombres de Hurwitz pour débutants
Maxim Kazarian - 1/3 Mathematical Physics of Hurwitz numbers
Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num
From playlist Physique mathématique des nombres de Hurwitz pour débutants
Matrix Theory: For the quaternion alpha = 1 - i + j - k, find the norm N(alpha) and alpha^{-1}. Then write alpha as a product of a length and a direction.
From playlist Matrix Theory
Lie Groups and Lie Algebras: Lesson 2 - Quaternions
This video is about Lie Groups and Lie Algebras: Lesson 2 - Quaternions We study the algebraic nature of quaternions and cover the ideas of an algebra and a field. Later we will discover how quaternions fit into the description of the classical Lie Groups. NOTE: An astute viewer noted th
From playlist Lie Groups and Lie Algebras
Thermodynamical approach to the Markoff-Hurwitz equation - Michael Magee
Analysis Math-Physics Seminar Topic: Thermodynamical approach to the Markoff-Hurwitz equation Speaker: Michael Magee Affiliation: Yale University Date:April 19, 2017 For more info, please visit http://video.ias.edu
From playlist Mathematics
Dimitri Zvonkine - On two ELSV formulas
The ELSV formula (discovered by Ekedahl, Lando, Shapiro and Vainshtein) is an equality between two numbers. The first one is a Hurwitz number that can be defined as the number of factorizations of a given permutation into transpositions. The second is the integral of a characteristic class
From playlist 4th Itzykson Colloquium - Moduli Spaces and Quantum Curves
Quaternions as 4x4 Matrices - Connections to Linear Algebra
In math, it's usually possible to view an object or concept from many different (but equivalent) angles. In this video, we will see that the quaternions may be viewed as 4x4 real-valued matrices of a special form. What is interesting here is that if you know how to multiply matrices, you a
From playlist Quaternions
Recovering elliptic curves from their p-torsion - Benjamin Bakker
Benjamin Bakker New York University May 2, 2014 Given an elliptic curve EE over a field kk, its p-torsion EpEp gives a 2-dimensional representation of the Galois group GkGk over 𝔽pFp. The Frey-Mazur conjecture asserts that for k=ℚk=Q and p13p13, EE is in fact determined up to isogeny by th
From playlist Mathematics
Dimitri Zvonkine - Hurwitz numbers, the ELSV formula, and the topological recursion
We will use the example of Hurwitz numbers to make an introduction into the intersection theory of moduli spaces of curves and into the subject of topological recursion.
From playlist Physique mathématique des nombres de Hurwitz pour débutants
David Roberts, Hurwitz Belyi maps
VaNTAGe seminar, October 12, 2021 License: CC-BY-NC-SA
From playlist Belyi maps and Hurwitz spaces
History of representation theory in quantum mechanics
In this video I speak about the early history of group representation theory in quantum mechanics using the rather recent history book by Schneider on van der Waerden, called "Zwischen Zwei Disziplinen". Other names dropped are Frobenius, Burnside, Schur, Killing, Study, Cartan, Weyl, Brau
From playlist Physics
Transversality and super-rigidity in Gromov-Witten Theory (Lecture - 03) by Chris Wendl
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
An asymptotic for the growth of Markoff-Hurwitz tuples - Ryan Ronan
Special Seminar Topic: An asymptotic for the growth of Markoff-Hurwitz tuples Speaker: Ryan Ronan Affiliation: Baruch College, The City University of New York Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Algebraic geometry 45: Hurwitz curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It discusses Hurwitz curves and sketches a proof of Hurwitz's bound for the symmetry group of a complex curve.
From playlist Algebraic geometry I: Varieties
The Routh-Hurwitz Stability Criterion
In this video we explore the Routh Hurwitz Stability Criterion and investigate how it can be applied to control systems engineering. The Routh Hurwitz Stability Criterion can be used to determine how many roots of a polynomial are in the right half plane. Topics and time stamps: 0:00 –
From playlist Control Theory
Quaternion algebras via their Mat2x2(F) representations
In this video we talk about general quaternion algebras over a field, their most important properties and how to think about them. The exponential map into unitary groups are covered. I emphasize the Hamiltionion quaternions and motivate their relation to the complex numbers. I conclude wi
From playlist Algebra
Billiards in quadrilaterals, Hurwitz spaces, and real multiplication of Hecke type - Alex Wright
Members' Seminar Topic: Billiards in quadrilaterals, Hurwitz spaces, and real multiplication of Hecke type Speaker: Alexander Wright Affiliation: Stanford University; Member, School of Mathematics Monday, November 30 Video Link: https://video.ias.edu/membsem/2015/1130-Wright After a brief
From playlist Mathematics