# Affine root system

In mathematics, an affine root system is a root system of affine-linear functions on a Euclidean space. They are used in the classification of affine Lie algebras and superalgebras, and semisimple p-adic algebraic groups, and correspond to families of Macdonald polynomials. The reduced affine root systems were used by Kac and Moody in their work on Kac–Moody algebras. Possibly non-reduced affine root systems were introduced and classified by and (except that both these papers accidentally omitted the Dynkin diagram ). (Wikipedia).

In this video we look at the intersection between and linear and quadratic function

Finite Difference Method

Finite Difference Method for finding roots of functions including an example and visual representation. Also includes discussions of Forward, Backward, and Central Finite Difference as well as overview of higher order versions of Finite Difference. Chapters 0:00 Intro 0:04 Secant Method R

From playlist Root Finding

Multiplying & Dividing Radicals Properties of Roots

I introduce finding Real Roots of Numbers and then expand into using the Property of Roots to simplify algebraic expressions that involve variables. Special care is taken to explain the differences between taking an even root versus taking an odd root. Find free review test, useful notes

From playlist Algebra 2

Primitive Roots Solution - Applied Cryptography

This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.

From playlist Applied Cryptography

Parabolas 5 Algebra Regents

In this video we review the basic components of a parabola

From playlist Parabolas

Complex Conjugate Root Theorem (1 of 2: Conjugate of a sum)

More resources available at www.misterwootube.com

From playlist Using Complex Numbers

imaginary root of matrix

Imaginary root of matrix In this video, I'll find the imaginary root of a matrix! What is it and how will I do it? Watch this video to find out! Imaginary power of a matrix: https://youtu.be/lF9n50GxxSI Linear Algebra: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCM0HdpHbhWcKdM-oVXP

From playlist Eigenvalues

Gopal Prasad: Descent in Bruhat-Tits theory

Bruhat-Tits theory applies to a semisimple group G, defined over an henselian discretly valued field K, such that G admits a Borel K-subgroup after an extension of K. The construction of the theory goes then by a deep Galois descent argument for the building and also for the parahoric grou

From playlist Algebraic and Complex Geometry

Representations of Fuchsian groups, parahoric group schemes by Vikraman Balaji

DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif

From playlist Moduli Of Bundles And Related Structures 2020

Tropical Geometry - Lecture 3 - Fields and Varieties | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

Nexus Trimester - Alexandre d'Aspremont (École Normale Supérieure)

An Optimal Affine Invariant Smooth Minimization Algorithm Alexandre d'Aspremont (École Normale Supérieure) March 18, 2016 Abstract: We formulate an affine invariant implementation of the algorithm in (Nesterov, 1983). We show that the complexity bound is then proportional to an affine in

Parabolas 8 Algebra Regents

In this video we review the basic components of a parabola

From playlist Parabolas

João Lourenço: Twisted Kac-Moody groups over the integers

In geometric representation theory, one is interested in studying the geometry of affine Grassmannians of quasi-split simply-connected reductive groups. In this endeavor, one of the main techniques, introduced by Faltings in the split case, consists in constructing natural realisati

From playlist Algebraic and Complex Geometry

Primitive Roots - Applied Cryptography

This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.

From playlist Applied Cryptography

Joel Kamnitzer: Categorical g-actions for modules over truncated shifted Yangians

CIRM VIRTUAL CONFERENCE Given a representation V of a reductive group G, Braverman-Finkelberg-Nakajima defined a Poisson variety called the Coulomb branch, using a convolution algebra construction. This variety comes with a natural deformation quantization, called a Coulomb branch algebr

From playlist Virtual Conference

Yang Shi: Normalizer theory of Coxeter groups and discrete integrable systems

Abstract: Formulation of the Painleve equations and their generalisations as birational representations of affine Weyl groups provides us with an elegant and efficient way to study these highly transcendental, nonlinear equations. In particular, it is well-known that discrete evolutions of

From playlist Integrable Systems 9th Workshop

Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism... - Amit Hazi

Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism algebras Speaker: Amit Hazi Affiliation: University of London Date: November 17, 2020 For more video please visit http://vi

Robert Cass: Perverse mod p sheaves on the affine Grassmannian

28 September 2021 Abstract: The geometric Satake equivalence relates representations of a reductive group to perverse sheaves on an affine Grassmannian. Depending on the intended application, there are several versions of this equivalence for different sheaf theories and versions of the a

Monica Nevins: Representations of p-adic groups via their restrictions to compact open subgroups

SMRI Algebra and Geometry Online 'Characters and types: the personality of a representation of a p-adic group, revealed by branching to its compact open subgroups' Monica Nevins (University of Ottawa) Abstract: The theory of complex representations of p-adic groups can feel very technical

From playlist SMRI Algebra and Geometry Online