Measures (measure theory) | Dynamical systems
In mathematics, an invariant measure is a measure that is preserved by some function. The function may be a geometric transformation. For examples, circular angle is invariant under rotation, hyperbolic angle is invariant under squeeze mapping, and a difference of slopes is invariant under shear mapping. Ergodic theory is the study of invariant measures in dynamical systems. The Krylov–Bogolyubov theorem proves the existence of invariant measures under certain conditions on the function and space under consideration. (Wikipedia).
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
F-measure is a harmonic mean of recall and precision. Think of it as accuracy, but without the effect of true negatives (which made accuracy meaningless for evaluating search algorithms). F-measure can also be interpreted as the Dice coefficient between the relevant set and the retrieved s
From playlist IR13 Evaluating Search Engines
Percentiles, Deciles, Quartiles
Understanding percentiles, quartiles, and deciles through definitions and examples
From playlist Unit 1: Descriptive Statistics
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
Joe Neeman: Gaussian isoperimetry and related topics II
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
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
Introduction to standard deviation, IQR [Inter-Quartile Range], and range
From playlist Unit 1: Descriptive Statistics
Dynamics on the Moduli Spaces of Curves, III - Maryam Mirzakhani
Maryam Mirzakhani Stanford University March 30, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
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
Denis Osin: Invariant random subgroups of acylindrically hyperbolic 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
Invariant measure of quantum trajectories: product (...) - C. Pellegrini - Workshop 1 - CEB T2 2018
Clément Pellegrini (Univ. Paul Sabatier, Toulouse) / 16.05.2018 Invariant measure of quantum trajectories: product of random matrices. Quantum trajectories are Markov processes with singular transition which prevent to use usual Markov Theorems in order to study their large time behaviou
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
Some Lattice Subgroups that cannot Act on the line(after Deroin and Hurtado) by Dave Morris
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Measure Equivalence, Negative Curvature, Rigidity (Lecture 2) by Camille Horbez
PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, India), Anish Ghosh (TIFR, Mumbai, India), Subhajit Goswami (TIFR, Mumbai, India) and Mahan M J (TIFR, Mumbai, India) DATE & TIME: 27 February 2023 to 10 March 2023 VENUE: Madhava Lecture Hall
From playlist PROBABILISTIC METHODS IN NEGATIVE CURVATURE - 2023
J. Smillie - Horocycle dynamics (Part 2)
A major challenge in dynamics on moduli spaces is to understand the behavior of the horocycle flow. We will motivate this problem and discuss what is known and what is not known about it, focusing on the genus 2 case. Specific topics to be covered include: * SL_2(R) orbit closures and inva
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Invariant Measures for Horospherical Flows by Hee Oh
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Amos Nevo: Representation theory, effective ergodic theorems, and applications - Lecture 1
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 Dynamical Systems and Ordinary Differential Equations
Karma Dajani - An introduction to Ergodic Theory of Numbers (Part 2)
In this course we give an introduction to the ergodic theory behind common number expansions, like expansions to integer and non-integer bases, Luroth series and continued fraction expansion. Starting with basic ideas in ergodic theory such as ergodicity, the ergodic theorem and natural ex
From playlist École d’été 2013 - Théorie des nombres et dynamique
Joe Neeman: Gaussian isoperimetry and related topics III
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
57 Sundar - Invariant measures and ergodicity for stochastic Navier-Stokes equations
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow