Surgery theory | Differential topology
In mathematics, the Kervaire invariant is an invariant of a framed -dimensional manifold that measures whether the manifold could be surgically converted into a sphere. This invariant evaluates to 0 if the manifold can be converted to a sphere, and 1 otherwise. This invariant was named after Michel Kervaire who built on work of Cahit Arf. The Kervaire invariant is defined as the Arf invariant of the skew-quadratic form on the middle dimensional homology group. It can be thought of as the simply-connected quadratic L-group , and thus analogous to the other invariants from L-theory: the signature, a -dimensional invariant (either symmetric or quadratic, ), and the De Rham invariant, a -dimensional symmetric invariant . In any given dimension, there are only two possibilities: either all manifolds have Arf–Kervaire invariant equal to 0, or half have Arf–Kervaire invariant 0 and the other half have Arf–Kervaire invariant 1. The Kervaire invariant problem is the problem of determining in which dimensions the Kervaire invariant can be nonzero. For differentiable manifolds, this can happen in dimensions 2, 6, 14, 30, 62, and possibly 126, and in no other dimensions. The final case of dimension 126 remains open. (Wikipedia).
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
Lorentz Covariance VS Lorentz Invariance: What's the Difference? | Special Relativity
In special relativity, Lorentz covariance and Lorentz invariance are two very important concepts. But what exactly are these concepts? In this video, we will find out! Contents: 00:00 Definitions 00:51 Examples If you want to help us get rid of ads on YouTube, you can support us on Patr
From playlist Special Relativity, General Relativity
An introduction to Invariant Theory - Harm Derksen
Optimization, Complexity and Invariant Theory Topic: An introduction to Invariant Theory Speaker: Harm Derksen Affiliation: University of Michigan Date: June 4, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Invariant measure for quantum trajectories - Y.Pautrat - Workshop 2 - CEB T3 2017
Yan Pautrat / 23.10.17 Invariant measure for quantum trajectories Quantum trajectories represent the state of a quantum system undergoing repeated indirect measurements. A quantum trajectory is therefore a sequence of density matrices, and a natural question is to describe its asymptotic
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Symmetry in Physics | Noether's theorem
▶ Topics ◀ Global / Local Symmetries, Continuous / Discrete Symmetries ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on
From playlist Symmetry
Michael Hopkins: Bernoulli numbers, homotopy groups, and Milnor
Abstract: In his address at the 1958 International Congress of Mathematicians Milnor described his joint work with Kervaire, relating Bernoulli numbers, homotopy groups, and the theory of manifolds. These ideas soon led them to one of the most remarkable formulas in mathematics, relating f
From playlist Abel Lectures
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
Symmetries show up everywhere in physics. But what is a symmetry? While the symmetries of shapes can be interesting, a lot of times, we are more interested in symmetries of space or symmetries of spacetime. To describe these, we need to build "invariants" which give a mathematical represen
From playlist Relativity
Floer theory by Mohammed Abouzaid
DATE & TIME: 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 structure. The moduli space of these curves (
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Lagrangian Floer theory 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
Nonlinear algebra, Lecture 10: "Invariant Theory", by Bernd Sturmfels
This is the tenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Algorithmic invariant theory - Visu Makam
Optimization, Complexity and Invariant Theory Topic: Algorithmic invariant theory Speaker: Visu Makam Affiliation: University of Michigan Date: June 6. 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Iwasawa invariants for elliptic curves in a family by Sujatha Ramdorai
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Invariant theory and optimization by Ankit Garg
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019
Rod Gover - An introduction to conformal geometry and tractor calculus (Part 1)
After recalling some features (and the value of) the invariant « Ricci calculus » of pseudo‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
This lecture is part of an online graduate course on Lie groups. We show the existence of a left-invariant measure (Haar measure) on a Lie group. and work out several explicit examples of it. Correction: At 21:40 There is an exponent of -1 missing: the parametrization of the unitary gro
From playlist Lie groups
Invariant Points (New 9-1 GCSE Topic!) | Transformations | Grade 7-9 | GCSE Maths Tutor
Check out the new merchandise shop here: https://the-gcse-maths-tutor.myspreadshop.co.uk/ Join this channel to get access to perks: https://www.youtube.com/channel/UCStPzCGyt5tlwdpDXffobxA/join A video revising the techniques and strategies for working with invariant points (Higher Only)
From playlist GCSE Maths Videos
Gregory Cherlin: The Relational Complexity of a Finite Permutation Group
The lecture was held within the framework of the Hausdorff Trimester Program: Logic and Algorithms in Group Theory. Abstract: I am interested in a numerical invariant of finite permutation groups called the {\it relational complexity} which is suggested by the model theoretic point of vie
From playlist HIM Lectures: Trimester Program "Logic and Algorithms in Group Theory"