Abstract Algebra | Irreducible polynomials
We introduce the notion of an irreducible polynomial over the ring k[x] where k is any field. A proof that p(x) is irreducible if and only if (p(x)) is maximal is also given, along with some examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal W
From playlist Abstract Algebra
RT8.2. Finite Groups: Classification of Irreducibles
Representation Theory: Using the Schur orthogonality relations, we obtain an orthonormal basis of L^2(G) using matrix coefficients of irreducible representations. This shows the sum of squares of dimensions of irreducibles equals |G|. We also obtain an orthonormal basis of Class(G) usin
From playlist Representation Theory
Abstract Algebra | Irreducibles and Primes in Integral Domains
We define the notion of an irreducible element and a prime element in the context of an arbitrary integral domain. Further, we give examples of irreducible elements that are not prime. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://
From playlist Abstract Algebra
Schemes 14: Irreducible, reduced, integral, connected
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We discuss the 4 properties of schemes: reduced, irreducible, integral, and connected.
From playlist Algebraic geometry II: Schemes
Commutative algebra 14 (Irreducible subsets of Spec R)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we show that the irreducible closed subsets of Spec R are just the closures of points. We do this using the
From playlist Commutative algebra
In this video I discuss irreducible polynomials and tests for irreducibility. Note that this video is intended for students in abstract algebra and is not appropriate for high-school or early college level algebra courses.
From playlist Abstract Algebra
RT7.3. Finite Abelian Groups: Convolution
Representation Theory: We define convolution of two functions on L^2(G) and note general properties. Three themes: convolution as an analogue of matrix multiplication, convolution with character as an orthogonal projection on L^2(G), and using using convolution to project onto irreduci
From playlist Representation Theory
Alina Ostafe: Dynamical irreducibility of polynomials modulo primes
Abstract: In this talk we look at polynomials having the property that all compositional iterates are irreducible, which we call dynamical irreducible. After surveying some previous results (mostly over finite fields), we will concentrate on the question of the dynamical irreducibility of
From playlist Number Theory Down Under 9
Schemes 26: Abstract and projective varieties
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We discuss the relation between abstract, projective, and complete varieties, and given an example found by Hironaka of a complete variety that is not projecti
From playlist Algebraic geometry II: Schemes
Mirko Mauri : The essential skeletons of pairs and the geometric P=W conjecture
The geometric P=W conjecture is a conjectural description of the asymptotic behavior of a celebrated correspondence in non-abelian Hodge theory. In particular, it is expected that the dual boundary complex of the compactification of character varieties is a sphere. In a joint work with Enr
From playlist Algebraic and Complex Geometry
Christian Lehn: Symplectic varieties from cubic fourfolds
I will explain a construction of a family of 8-dimensional projective complex symplectic manifolds starting from the moduli space of twisted cubics on a general cubic fourfold. The relation to \mathrm{Hilb}^4 of a K3-surface is still open. This is a joint work with Manfred Lehn, Christoph
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Representation Theory & Categorification - Catharina Stroppel
2021 Women and Mathematics - Uhlenbeck Course Lecture Topic: Representation Theory & Categorification Speaker: Catharina Stroppel Affiliation: University of Bonn Date: May 24, 2021 For more video please visit https://www.ias.edu/video
From playlist Mathematics
Anthony Henderson: Hilbert Schemes Lecture 9
SMRI Seminar Series: 'Hilbert Schemes' Lecture 9 Correspondences in homology Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students intereste
From playlist SMRI Course: Hilbert Schemes
Olivier Benoist: Algebraic approximation of submanifolds of real algebraic varieties
CONFERENCE Recording during the thematic meeting : "Real Aspects of Geometry" the November 1, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audi
From playlist Algebraic and Complex Geometry
Pre-recorded lecture 3: Analytic functions of Nijenhuis operators and Splitting theorem
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). These lectures w
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Andrew Putman - The Steinberg representation is irreducible
The Steinberg representation is a topologically-defined representation of groups like GL_n(k) that plays a fundamental role in the cohomology of arithmetic groups. The main theorem I will discuss says that for infinite fields k, the Steinberg representation is irreducible. For finite field
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
On the existence of minimal Heegaard splittings - Dan Ketover
Variational Methods in Geometry Seminar Topic: On the existence of minimal Heegaard splittings Speaker: Dan Ketover Affiliation: Princeton University; Member, School of Mathematics Date: Oct 2, 2018 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Complex surfaces 5: Kodaira dimension 0
This talk is an informal survey of the complex projective surfaces of Kodaira number 0. We first explain why there are 4 types of such surfaces (Enriques, K3, hyperelliptic, and abelian) and then give a few examples of each type.
From playlist Algebraic geometry: extra topics