3-manifolds | Differential geometry | Surgery theory
In mathematics, Reidemeister torsion (or R-torsion, or Reidemeister–Franz torsion) is a topological invariant of manifolds introduced by Kurt Reidemeister for 3-manifolds and generalized to higher dimensions by Wolfgang Franz and Georges de Rham.Analytic torsion (or Ray–Singer torsion) is an invariant of Riemannian manifolds defined by Daniel B. Ray and Isadore M. Singer as an analytic analogue of Reidemeister torsion. Jeff Cheeger and Werner Müller proved Ray and Singer's conjecture that Reidemeister torsion and analytic torsion are the same for compact Riemannian manifolds. Reidemeister torsion was the first invariant in algebraic topology that could distinguish between closed manifolds which are homotopy equivalent but not homeomorphic, and can thus be seen as the birth of geometric topology as a distinct field. It can be used to classify lens spaces. Reidemeister torsion is closely related to Whitehead torsion; see. It has also given some important motivation to arithmetic topology; see. For more recent work on torsion see the books and (Nicolaescu , ). (Wikipedia).
Werner Müller : Analytic torsion for locally symmetric spaces of finite volume
Abstract : This is joint work with Jasmin Matz. The goal is to introduce a regularized version of the analytic torsion for locally symmetric spaces of finite volume and higher rank. Currently we are able to treat quotients of the symmetric space SL(n,ℝ)/SO(n) by congruence subgroups of SL(
From playlist Topology
Physics - Mechanics: Torsion (1 of 14) What is Torsion?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is torsion and the variables associated with twisting of a steel rod. Next video in this series can be found at: https://youtu.be/jlt6Jy59nJs
From playlist PHYSICS 16.6 TORSION
Physics - Mechanics: Torsion (11 of 14) Torsion and a Hollow Tube
Visit http://ilectureonline.com for more math and science lectures! In this video I will derive the equation of torque=? of the torsion of a hollow tube. Next video in this series can be found at: https://youtu.be/mQ-wseAfAlc
From playlist PHYSICS 16.6 TORSION
In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
Physics - Mechanics: Torsion (2 of 14) What is Torsional Constant?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is torsional constant or the “second momentum of area”. Next video in this series can be found at: https://youtu.be/Mr29GDA0jLE
From playlist PHYSICS 16.6 TORSION
In this video we will explore torsion, which is the twisting of an object caused by a moment. It is a type of deformation. A moment which tends to cause twisting is called torque. Some of the things covered in this video include how circular bars deform under torsion, how we can calculate
From playlist Mechanics of Materials / Strength of Materials
Physics - Mechanics: Torsion (6 of 14) Torsional Pendulum (Potential Equivalent of SHM)
Visit http://ilectureonline.com for more math and science lectures! In this video I will equate the simple harmonic motion of a block attached to a spring to the rotational equivalent of the torsional pendulum. Next video in this series can be found at: https://youtu.be/ahBEW8L0jjI
From playlist PHYSICS 16.6 TORSION
Akshay Venkatesh - 2/4 Analytic number theory around torsion homology
Akshay Venkatesh - Analytic number theory around torsion homology
From playlist École d'été 2014 - Théorie analytique des nombres
Pierre Albin : Extending the Cheeger-Müller theorem through degeneration
Abstract : Reidemeister torsion was the first topological invariant that could distinguish between spaces which were homotopy equivalent but not homeomorphic. The Cheeger-Müller theorem established that the Reidemeister torsion of a closed manifold can be computed analytically. I will repo
From playlist Topology
Physics - Mechanics: Torsion (7 of 14) The Torsional Pendulum: Example
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate f=? and theta(t)=? of a torsional pendulum. Next video in this series can be found at: https://youtu.be/4BhjMqa1oHo
From playlist PHYSICS 16.6 TORSION
Umberto Zannier - Ambients for the Betti map and the question of its rank
November 16, 2017 - This is the final talk of a series of three Fall 2017 Minerva Lectures In this last lecture we shall further consider some of the mentioned contexts involving the Betti map. We shall also discuss in short some recent work with Yves André and Pietro Corvaja, where we obt
From playlist Minerva Lectures Umberto Zannier
Umberto Zannier - Torsion values for sections in abelian schemes and the Betti map
November 14, 2017 - This is the second of three Fall 2017 Minerva Lectures We shall consider further variations in the games, obtaining more general Betti maps. We shall also illustrate some links of the Betti map with several other contexts (Manin's theorem of the kernel, linear different
From playlist Minerva Lectures Umberto Zannier
Gianluca Paolini: Torsion-free Abelian groups are Borel complete
HYBRID EVENT Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 14, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicia
From playlist Logic and Foundations
CTNT 2020 - Computations in Number Theory (by Alvaro Lozano-Robledo) - Lecture 4
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Computations in Number Theory Research
Pierre Albin: The sub-Riemannian limit of a contact manifold
Talk by Pierre Albin in the Global Noncommutative Geometry Seminar (Americas) on January 29, 2021. https://globalncgseminar.org/talks/tba-5/?utm_source=mailpoet&utm_medium=email&utm_campaign=global-noncommutative-geometry-seminar-americas-01292021_14
From playlist Global Noncommutative Geometry Seminar (Americas)
IGA: Singularities of Hermitian Yang Mills Connections
After introducing some background about stable bundles and HYM connections, I will explain both the analytic and algebraic sides when studying singularities of HYM connections. It turns out that local algebraic invariants can be extracted to characterize the analytic side. In particular, t
From playlist Informal Geometric Analysis Seminar
Gareth Jones: Improvements in the Pila-Wilkie theorem for curves
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 Logic and Foundations
Math 131 Spring 2022 042722 Properties of Analytic Functions, continued
Recall: analytic functions are infinitely (term-by-term) differentiable. Relation of coefficients and values of derivatives. Remark: analytic functions completely determined by values on an arbitrarily small interval. Analytic functions: convergence at an endpoint implies continuity the
From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)