In this video I shed some light on a heavily alluded to and poorly explained object, the Hopf Fibration. The Hopf Fibration commonly shows up in discussions surrounding gauge theories and fundamental physics, though its construction is not so mysterious.
From playlist Summer of Math Exposition Youtube Videos
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
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"
Bertrand Eynard - An overview of the topological recursion
The "topological recursion" defines a double family of "invariants" $W_{g,n}$ associated to a "spectral curve" (which we shall define). The invariants $W_{g,n}$ are meromorphic $n$-forms defined by a universal recursion relation on $|\chi|=2g-2+n$, the initial terms $W_{0,1}$
From playlist Physique mathématique des nombres de Hurwitz pour débutants
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/3bz5
From playlist 3D printing
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
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
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
Homotopical effects of k-dilation - Larry Guth
Variational Methods in Geometry Seminar Topic: Homotopical effects of k-dilation Speaker: Larry Guth Affiliation: Massachusetts Institute of Technology Date: November 27, 2018 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Behavior of Welschinger Invariants Under Morse Simplification - Erwan Brugalle
Erwan Brugalle Universite de Paris 6 November 9, 2012 Welschinger invariants, real analogs of genus 0 Gromov-Witten invariants, provide non-trivial lower bounds in real algebraic geometry. In this talk I will explain how to get some wall-crossing formulas relating Welschinger invariants o
From playlist Mathematics
Dynamical systems evolving – Lai-Sang Young – ICM2018
Plenary Lecture 8 Dynamical systems evolving Lai-Sang Young Abstract: I will discuss a number of results taken from a cross-section of my work in Dynamical Systems theory and applications. The first topics are from the ergodic theory of chaotic dynamical systems. They include relation be
From playlist Plenary Lectures
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
Cylindrical contact homology as a well-defined homology? - Joanna Nelson
Joanna Nelson University of Wisconsin-Madison September 30, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
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
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
Symmetries of hamiltonian actions of reductive groups - David Ben-Zvi
Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound II - Amnon Ta-Shma Computer Science/Discrete Mathematics Seminar II Topic: Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound II Speaker: Amnon Ta-Shma Affiliation: Tel Aviv University Date: January 3
From playlist Mathematics
Francis Brown - 4/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)
In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of
From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)
Chapter 7 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Lagrangian Floer theory (Lecture – 02) by Sushmita Venugopalan
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants