In mathematics, and especially differential geometry, the Quillen metric is a metric on the determinant line bundle of a family of operators. It was introduced by Daniel Quillen for certain elliptic operators over a Riemann surface, and generalized to higher-dimensional manifolds by Jean-Michel Bismut and Dan Freed. The Quillen metric was used by Quillen to give a differential-geometric interpretation of the ample line bundle over the moduli space of vector bundles on a compact Riemann surface, known as the Quillen determinant line bundle. It can be seen as defining the Chern–Weil representative of the first Chern class of this ample line bundle. The Quillen metric construction and its generalizations were used by Bismut and Freed to compute the holonomy of certain determinant line bundles of Dirac operators, and this holonomy is associated to certain anomaly cancellations in Chern–Simons theory predicted by Edward Witten. The Quillen metric was also used by Simon Donaldson in 1987 in a new inductive proof of the Hitchin–Kobayashi correspondence for projective algebraic manifolds, published one year after the resolution of the correspondence by Shing-Tung Yau and Karen Uhlenbeck for arbitrary compact Kähler manifolds. (Wikipedia).
Examples: Converting Between Metric Units
This video provides several examples of converting between different metric units of measure.
From playlist Unit Conversions: Metric Units
Vernier caliper / diameter and length of daily used objects.
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From playlist Fine Measurements
Micrometer/diameter of daily used objects.
What was the diameter? music: https://www.bensound.com/
From playlist Fine Measurements
Micrometer / diameter of daily used objects
What was the diameter? music: https://www.bensound.com/
From playlist Fine Measurements
This video explains how to convert to different metric units of measure for length, capacity, and mass. http://mathispower4u.wordpress.com/
From playlist Unit Conversions: Metric Units
The Quillen Determinant Bundle and Geometric Quantization of Various Moduli Spaces by Rukmini Dey
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Ex: Metric Conversions Using Unit Fractions - Length
This video provides three examples of how to perform metric conversions involving length using unit fractions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Unit Conversions: Metric Units
Masoud Khalkhali: Curvature of the determinant line bundle for noncommutative tori
I shall first survey recent progress in understanding differential and conformal geometry of curved noncommutative tori. This is based on work of Connes-Tretkoff, Connes-Moscovici, and Fathizadeh and myself. Among other results I shall recall the computation of spectral invariants, includi
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Percentiles, Deciles, Quartiles
Understanding percentiles, quartiles, and deciles through definitions and examples
From playlist Unit 1: Descriptive Statistics
G. Freixas i Montplet - Automorphic forms and arithmetic intersections (part 2)
In these lectures I will focus on the Riemann-Roch theorem in Arakelov geometry, in the specific context of some simple Shimura varieties. For suitable data, the cohomological part of the theorem affords an interpretation in terms of both holomorphic and non-holomorphic modular forms. The
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Damian Rössler: The arithmetic Riemann Roch Theorem and Bernoulli numbers
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: (with V. Maillot) We shall show that integrality properties of the zero part of the abelian polylogarithm can be investigated using the arithme
From playlist HIM Lectures: Trimester Program "Periods in Number Theory, Algebraic Geometry and Physics"
Soft Astronomy - Alice Quillen
Institute for Advanced Study / Princeton University Joint Astrophysics Colloquium Topic: Soft Astronomy Speaker: Alice Quillen Affiliation: University of Rochester Date: September 14, 2021 Compact mass-spring models can measure remarkably small deformations while conserving angular mom
From playlist Natural Sciences
This video shows how to use unit scale to determine the actual dimensions of a model and how to determine the dimensions of a model from an actual dimensions. http://mathispower4u.yolasite.com/
From playlist Unit Scale and Scale Factor
Erik Pedersen Bounded K and L theory
The lecture was held within the framework of Follow-up Workshop TP Rigidity. 29.4.2015
From playlist HIM Lectures 2015
Constructive Type Theory and Homotopy - Steve Awodey
Steve Awodey Institute for Advanced Study December 3, 2010 In recent research it has become clear that there are fascinating connections between constructive mathematics, especially as formulated in the type theory of Martin-Löf, and homotopy theory, especially in the modern treatment in
From playlist Mathematics
Alexander RAHM - Verification of the Quillen conjecture in the rank 2 imaginary quadratic case
We confirm a conjecture of Quillen in the case of the mod 2 cohomology of arithmetic groups SL(2, A[1/2]), where A is an imaginary quadratic ring of integers. To make explicit the free module structure on the cohomology ring conjectured by Quillen, we compute the mod 2 cohomology of SL(2,
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Introduction to standard deviation, IQR [Inter-Quartile Range], and range
From playlist Unit 1: Descriptive Statistics
Geometry of Vortices on Riemann Surfaces (Lecture 4) by Oscar García-Prada
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Finding the x and y coordinates for a given point on the unit circle
👉 Learn how to find the point on the unit circle given the angle of the point. A unit circle is a circle whose radius is 1. Given an angle in radians, to find the coordinate of points on the unit circle made by the given angle with the x-axis at the center of the unit circle, we plot the a
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
Euler classes transgressions and Eistenstein cohomology of GL(N) - Nicolas Bergeron
Workshop on Representation Theory and Analysis on Locally Symmetric Spaces Topic: Euler classes transgressions and Eistenstein cohomology of GL(N) Speaker: Nicolas Bergeron Affiliation: IMJ PRG Date: March 8, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics