Yinhuo Zhang: Braided autoequivalences, quantum commutative Galois objects and the Brauer groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebra
Ralph Kaufmann: Graph Hopf algebras and their framework
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: I will discuss recent results linking the Hopf algebras of Goncharov for multiple zetas, the Hopf algebra of Connes and Kreimer for renormalis
From playlist Workshop: "Amplitudes and Periods"
Computational Aspects in the Braid Group and Applications to Cryptography - Mina Teicher
Mina Teicher Bar-Ilan University; Member, School of Mathematics March 12, 2012 The braid group on n strands may be viewed as an infinite analog of the symmetric group on n elements with additional topological phenomena. It appears in several areas of mathematics, physics and computer scien
From playlist Mathematics
Matt SZCZESNY - Toric Hall Algebras and infinite-dimentional Lie algebras
The process of counting extensions in categories yields an associative (and sometimes Hopf) algebra called a Hall algebra. Applied to the category of Feynman graphs, this process recovers the Connes-Kreimer Hopf algebra. Other examples abound, yielding various combinatorial Hopf algebras.
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Piotr M. Hajac: Braided noncommutative join construction
We construct the join of noncommutative Galois objects (quantum torsors) over a Hopf algebra H. To ensure that the join algebra enjoys the natural (diagonal) coaction of H, we braid the tensor product of the Galois objects. Then we show that this coaction is principal. Our examples are bui
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/1mUo
From playlist 3D printing
Giovanni Landi: The Weil algebra of a Hopf algebra
We generalize the notion, due to H. Cartan, of an operation of a Lie algebra in a graded differential algebra. Firstly, for such an operation we give a natural extension to the universal enveloping algebra of the Lie algebra and analyze all of its properties. Building on this we define the
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
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
Perverse sheaves on configuration spaces, Hopf algebras and parabolic induction - Mikhail Kapranov
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Perverse sheaves on configuration spaces, Hopf algebras and parabolic induction Speaker: Mikhail Kapranov Affiliation: Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo Dat
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
TQFTs from non-semisimple modular categories and modified traces, Marco de Renzi, Lecture II
Lecture series on modified traces in algebra and topology Topological Quantum Field Theories (TQFTs for short) provide very sophisticated tools for the study of topology in dimension 2 and 3: they contain invariants of 3-manifolds that can be computed by cut-and-paste methods, and their e
From playlist Lecture series on modified traces in algebra and topology
Paul André Melliès - Dialogue Games and Logical Proofs in String Diagrams
After a short introduction to the functorial approach to logical proofs and programs initiated by Lambek in the late 1960s, based on the notion of free cartesian closed category, we will describe a recent convergence with the notion of ribbon category introduced in 1990 by Reshetikhin and
From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020
Cyclic Groups, Generators, and Cyclic Subgroups | Abstract Algebra
We introduce cyclic groups, generators of cyclic groups, and cyclic subgroups. We discuss an isomorphism from finite cyclic groups to the integers mod n, as well as an isomorphism from infinite cyclic groups to the integers. We establish a cyclic group of order n is isomorphic to Zn, and a
From playlist Abstract Algebra
Panorama of Mathematics: Andrei Okounkov
Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Andrei Okounkov: "Enumerati
From playlist Panorama of Mathematics
Geoffroy Horel - Knots and Motives
The pure braid group is the fundamental group of the space of configurations of points in the complex plane. This topological space is the Betti realization of a scheme defined over the integers. It follows, by work initiated by Deligne and Goncharov, that the pronilpotent completion of th
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
[BOURBAKI 2019] HOMFLY polynomials from the Hilbert schemes of a planar curve - Migliorini -30/03/19
Luca MIGLIORINI HOMFLY polynomials from the Hilbert schemes of a planar curve, after D. Maulik, A. Oblomkov, V. Shende... Among the most interesting invariants one can associate with a link L ⊂ S3 is its HOMFLY polynomial P(L, v, s) ∈ Z[v±1, (s – s–1)±1]. A. Oblomkov and V. Shende conjec
From playlist BOURBAKI - 2019
Walter Van SUIJLEKOM - Renormalization Hopf Algebras and Gauge Theories
We give an overview of the Hopf algebraic approach to renormalization, with a focus on gauge theories. We illustrate this with Kreimer's gauge theory theorem from 2006 and sketch a proof. It relates Hopf ideals generated by Slavnov-Taylor identities to the Hochschild cocycles that are give
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Pavel Safronov: Quantum character varieties at roots of unity
Abstract: Character varieties of closed surfaces have a natural Poisson structure whose quantization may be constructed in terms of the corresponding quantum group. When the quantum parameter is a root of unity, this quantization carries a central subalgebra isomorphic to the algebra of fu
From playlist Algebraic and Complex Geometry