Homological algebra | Group theory
In abstract algebra, cohomological dimension is an invariant of a group which measures the homological complexity of its representations. It has important applications in geometric group theory, topology, and algebraic number theory. (Wikipedia).
From playlist Courses and Series
Trigonometry 5 The Cosine Relationship
A geometrical explanation of the law of cosines.
From playlist Trigonometry
Dimensions (1 of 3: The Traditional Definition - Directions)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
Covariance (1 of 17) What is Covariance? in Relation to Variance and Correlation
Visit http://ilectureonline.com for more math and science lectures! To donate:a http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the difference between the variance and the covariance. A variance (s^2) is a measure of how spread out the numbers of
From playlist COVARIANCE AND VARIANCE
http://www.teachastronomy.com/ Cosmology is the study of the universe, its history, and everything in it. It comes from the Greek root of the word cosmos for order and harmony which reflected the Greek belief that the universe was a harmonious entity where everything worked in concert to
From playlist 22. The Big Bang, Inflation, and General Cosmology
Leslie Saper : L2-cohomology and the theory of weights
Abstract : The intersection cohomology of a complex projective variety X agrees with the usual cohomology if X is smooth and satisfies Poincare duality even if X is singular. It has been proven in various contexts (and conjectured in more) that the intersection cohomology may be represente
From playlist Topology
How Big is the Universe? Part 1 of 2
An explanation of the size of the observable universe and why we cannot see beyond it. together with a forward look to a time when distant galaxies will no longer be visible.
From playlist Cosmology
From playlist Courses and Series
Trigonometry 7 The Cosine of the Sum and Difference of Two Angles
A geometric proof of the cosine of the sum and difference of two angles identity.
From playlist Trigonometry
Cohomological decomposition of the diagonal in small dimension (Lecture - 05) by Claire Voisin
Infosys-ICTS Ramanujan Lectures Some new results on rationality Speaker: Claire Voisin (College de France) Date: 01 October 2018, 16:00 Venue: Madhava Lecture Hall, ICTS campus Resources Lecture 1: Some new results on rationality Date & Time: Monday, 1 October 2018, 04:00 PM Abstra
From playlist Infosys-ICTS Ramanujan Lectures
Alexandru Dimca: Betti numbers of hypersurfaces and defects of linear systems IV
Abstract: Our approach is a generalization of Griffiths' results expressing the cohomology ofa smooth hypersurface V: f=0 in a projective space \mathbb{P}^n in terms of some graded pieces of the Jacobian algebra of f. We will start by recalling these classical results. Then we explain t
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Bettina EICK - Computational group theory, cohomology of groups and topological methods 5
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Nero Budur: Cohomology jump loci and singularities
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 Algebraic and Complex Geometry
Jennifer WILSON - High dimensional cohomology of SL_n(Z) and its principal congruence subgroups 1
Group cohomology of arithmetic groups is ubiquitous in the study of arithmetic K-theory and algebraic number theory. Rationally, SL_n(Z) and its finite index subgroups don't have cohomology above dimension n choose 2. Using Borel-Serre duality, one has access to the high dimensions. Church
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Peter PATZT - High dimensional cohomology of SL_n(Z) and its principal congruence subgroups 2
Group cohomology of arithmetic groups is ubiquitous in the study of arithmetic K-theory and algebraic number theory. Rationally, SL_n(Z) and its finite index subgroups don't have cohomology above dimension n choose 2. Using Borel-Serre duality, one has access to the high dimensions. Church
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Tim Perutz: From categories to curve-counts in mirror symmetry
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 Jean-Morlet Chair - Lalonde/Teleman
Jose Perea (10/7/22): A topological study of the space of planar pentagons
Conformation spaces of molecules are known to have non-trivial topology, which can complicate tasks like dimensionality reduction for dynamics modeling with intrinsic variables. In this talk, I'll describe the space of planar pentagons -- a toy model for conformation spaces -- and general
From playlist AATRN/STMS
Cup Products in Automorphic Cohomology - Matthew Kerr
Matthew Kerr Washington University in St. Louis March 30, 2012 In three very interesting and suggestive papers, H. Carayol introduced new aspects of complex geometry and Hodge theory into the study of non-classical automorphic representations -- in particular, those involving the totally d
From playlist Mathematics
Nero Budur: Absolute sets and the Decomposition Theorem
Abstract: We give a new, more conceptual proof of the Decomposition Theorem for semisimple perverse sheaves of rank-one origin, assuming it for those of constant-sheaf origin, that is, assuming the geometric case proven by Beilinson-Bernstein-Deligne-Gabber. Joint work with Botong Wang. R
From playlist Algebraic and Complex Geometry
Physics 35 Coulomb's Law (1 of 8)
Visit http://ilectureonline.com for more math and science lectures! In this three part lecture, I will introduce you to Coulomb's law, which describes the electric force between two charged particles or objects. It's format is similar to Newton's law of gravity, though Coulomb's constant
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