Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
Higher Algebra 9: Symmetric monoidal infinity categories
In this video, we introduce the notion of a symmetric monoidal infinity categories and give some examples. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-mu
From playlist Higher Algebra
What is the definition of a monomial and polynomials with examples
👉 Learn how to classify polynomials based on the number of terms as well as the leading coefficient and the degree. When we are classifying polynomials by the number of terms we will focus on monomials, binomials, and trinomials, whereas classifying polynomials by the degree will focus on
From playlist Classify Polynomials
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Juliet Cooke: Skein categories
In this talk we will talk about skein categories which are a categorical analogue of skein algebras based on coloured ribbon tangles. We shall then see how these skein categories satisfy excision and therefore fit within the framework of factorisation homology as k-linear factorisation hom
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Damiano Mazza: Heterodox exponential modalities in linear logic
HYBRID EVENT Recorded during the meeting Linear Logic Winter School" the January 28, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual
From playlist Logic and Foundations
John R. Parker: Complex hyperbolic lattices
Lattices in SU(2,1) can be viewed in several different ways: via their geometry as holomorphic complex hyperbolic isometries, as monodromy groups of hypergeometric functions, via algebraic geometry as ball quotients and (sometimes) using arithmeticity. In this talk I will describe these di
From playlist Geometry
Calculus 3: Tensors (7 of 45) Tensors for Crystal Structures: Monoclinic
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the tensor matrix representing a MONOclinic crystal structure where 2 of the angles of the cube is 90 degrees and the 3rd angle is greater than 90 degrees-which means the cube leans in 1 direc
From playlist CALCULUS 3 CH 10 TENSORS
Richard Rimanyi - Stable Envelopes, Bow Varieties, 3d Mirror Symmetry
There are many bridges connecting geometry with representation theory. A key notion in one of these connections, defined by Maulik-Okounkov, Okounkov, Aganagic-Okounkov, is the "stable envelope (class)". The stable envelope fits into the story of characteristic classes of singularities as
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Lecture 7: Hochschild homology in ∞-categories
In this video, we construct Hochschild homology in an arbitrary symmetric-monoidal ∞-category. The most important special case is the ∞-category of spectra, in which we get Topological Hochschild homology. Feel free to post comments and questions at our public forum at https://www.uni-mu
From playlist Topological Cyclic Homology
Stable Homotopy Seminar, 13: The Smash Product
I describe a bunch of desirable properties of the smash product on spectra, and then prove Lewis's theorem that no category of spectra has them. However, there are ways of sacrificing one or the other of the properties and getting something fairly well-behaved. The earliest attempts are Bo
From playlist Stable Homotopy Seminar
Eugenia Cheng: "The periodic table of n-categories"
Speaker: Eugenia Cheng (University of Sheffield) Title: The periodic table of n-categories Event: Categories, Logic and Foundations of Physics IV (January 2009, Imperial College London) Slides: http://www.cs.ox.ac.uk/quantum/slides/clap4-eugeniacheng.pdf Abstract: Degenerate n-categories
From playlist Software Development Lectures
On the classification of fusion categories – Sonia Natale – ICM2018
Algebra Invited Lecture 2.5 On the classification of fusion categories Sonia Natale Abstract: We report, from an algebraic point of view, on some methods and results on the classification problem of fusion categories over an algebraically closed field of characteristic zero. © Interna
From playlist Algebra
Higher Algebra 10: E_n-Algebras
In this video we introduce E_n-Algebras in arbitrary symmetric monoidal infinity-categories. These interpolate between associated algebras (= E_1) and commutative algebras (= E_infinity). We also establish some categorical properties and investigate the case of the symmetric monoidal infin
From playlist Higher Algebra
Alon Nissan-Cohen: Towards an ∞-categorical version of real THH
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Following Hesselholt and Madsen's development of the so-called "real" (i.e. Z/2-equivariant) version of algebraic K-theory, Dotto developed a th
From playlist HIM Lectures: Junior Trimester Program "Topology"
Monodromy of nFn−1 hypergeometric functions and arithmetic groups I - T.N. Venkatara
Speaker: T. N. Venkataramana (TIFR) Title: Monodromy of nFn−1 hypergeometric functions and arithmetic groups I Abstract: We describe results of Levelt and Beukers-Heckman on the explicit computation of monodromy for generalised hypergeometric functions of one variable. We then discuss the
From playlist Mathematics
Matrix factorisations and quantum error correcting codes
In this talk Daniel Murfet gives a brief introduction to matrix factorisations, the bicategory of Landau-Ginzburg models, composition in this bicategory, the Clifford thickening of a supercategory and the cut operation, before coming to a simple example which shows the relationship between
From playlist Metauni