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"
Claudia Pinzari: "Weak quasi-Hopf algebras associated to Verlinde fusion categories"
Actions of Tensor Categories on C*-algebras 2021 "Weak quasi-Hopf algebras associated to Verlinde fusion categories" Claudia Pinzari - Sapienza Università di Roma Abstract: Unitary modular fusion categories arise in various frameworks. After a general overview on unitarity, we discuss th
From playlist Actions of Tensor Categories on C*-algebras 2021
Commutative algebra 31 (Nullstellensatz)
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. We describe the weak and strong Nullstellensatz, and give short proofs of them over the complex numbers using Rabinowitsch's
From playlist Commutative algebra
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
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"
algebraic geometry 7 weak nullstellensatz
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It describes the weak nullstellensatz, giving the maximal ideals of polynomial rings over algebraically closed fields.
From playlist Algebraic geometry I: Varieties
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Towards Strong Minimality and the Fuchsian Triangle Groups - J. Nagloo - Workshop 3 - CEB T1 2018
Joel Nagloo (City University of New York) / 29.03.2018 Towards Strong Minimality and the Fuchsian Triangle Groups From the work of Freitag and Scanlon, we have that the ODEs satisfied by the Hauptmoduls of arithmetic subgroups of SL2(Z) are strongly minimal and geometrically trivial. A c
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Lars Hesselholt: Around topological Hochschild homology (Lecture 4)
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" The resulting cohomology theory has had numerous applications to algebraic K-theory and, more recently, to integral p-adic Hodge theory. The goa
From playlist HIM Lectures: Junior Trimester Program "Topology"
MAE5790-12 Bifurcations in two dimensional systems
Bifurcations of fixed points: saddle-node, transcritical, pitchfork. Hopf bifurcations. Other bifurcations of periodic orbits. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 8.0--8.2.
From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University
Michael Atiyah, Seminars Geometry and Topology 1/2 [2009]
Seminars on The Geometry and Topology of the Freudenthal Magic Square Date: 9/10/2009 Video taken from: http://video.ust.hk/Watch.aspx?Video=98D80943627E7107
From playlist Mathematics
Marc Levine - "The Motivic Fundamental Group"
Research lecture at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Kurusch EBRAHIMI-FARD - Wick Products and Combinatorial Hopf Algebras
Wick products play a central role in both quantum field theory and stochastic calculus. They originated in Wick’s work from 1950. In this talk we will describe Wick products using combinatorial Hopf algebra. Based on joint work with F. Patras, N. Tapia, L. Zambotti. https://indico.math.c
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Lie groups: Baker Campbell Hausdorff formula
This lecture is part of an online graduate course on Lie groups. We state the Baker Campbell Hausdorff formula for exp(A)exp(B). As applications we show that a Lie group is determined up to local isomorphism by its Lie algebra, and homomorphisms from a simply connected Lie group are deter
From playlist Lie groups
Mathematical Biology. 21: Hopf Bifurcations
UCI Math 113B: Intro to Mathematical Modeling in Biology (Fall 2014) Lec 21. Intro to Mathematical Modeling in Biology: Hopf Bifurcations View the complete course: http://ocw.uci.edu/courses/math_113b_intro_to_mathematical_modeling_in_biology.html Instructor: German A. Enciso, Ph.D. Text
From playlist Math 113B: Mathematical Biology
Frédéric Patras - Noncommutative Wick Polynomials
Wick polynomials are at the foundations of QFT (they encode normal orderings) and probability (they encode chaos decompositions). In this lecture, we survey the construction and properties of noncommutative (or free) analogs using shuffle Hopf algebra techniques. Based on joint works wit
From playlist Combinatorics and Arithmetic for Physics: special days
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
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