In mathematics, a Hadamard manifold, named after Jacques Hadamard — more often called a Cartan–Hadamard manifold, after Élie Cartan — is a Riemannian manifold that is complete and simply connected and has everywhere non-positive sectional curvature. By Cartan–Hadamard theorem all Cartan–Hadamard manifolds are diffeomorphic to the Euclidean space Furthermore it follows from the Hopf–Rinow theorem that every pairs of points in a Cartan–Hadamard manifold may be connected by a unique geodesic segment. Thus Cartan–Hadamard manifolds are some of the closest relatives of (Wikipedia).
How was it Made? Jacquard weaving
From playlist Engineering
Christian Bär: Local index theory for Lorentzian manifolds
HYBRID EVENT We prove a local version of the index theorem for Dirac-type operators on globally hyperbolic Lorentzian manifolds with Cauchy boundary. In case the Cauchy hypersurface is compact, we do not assume self-adjointness of the Dirac operator on the spacetime or of the associated el
From playlist Mathematical Physics
Klaus Fredenhagen - Quantum Field Theory and Gravitation
The incorporation of gravity into quantum physics is still an essentially open problem. Quantum field theory under the influence of an external gravitational field, on the other side, is by now well understood. I is remarkable that, nevertheless, its consistent treatment required a careful
From playlist Trimestre: Le Monde Quantique - Colloque de clôture
Thomas Weighill - Coarse homotopy groups of warped cones
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Thomas Weighill, University of North Carolina at Greensboro Title: Coarse homotopy groups of warped cones Abstract: Various versions of coarse homotopy theory have been around since the beginning of coarse geometry, and s
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
I give a proof of the Cartan-Hadamard theorem on non-positively curved complete Riemannian manifolds. For more details see Chapter 7 of do Carmo's "Riemannian geomety". If you find any typos or mistakes, please point them out in the comments.
From playlist Differential geometry
Kevin Kelly - Machine Learning Enhanced Compressive Hyperspectral Imaging - IPAM at UCLA
Recorded 02 December 2022. Kevin Kelly of Rice University Electrical and Computer Engineering presents "Machine Learning Enhanced Compressive Hyperspectral Imaging" at IPAM's Multi-Modal Imaging with Deep Learning and Modeling Workshop. Abstract: This talk reviews approaches to combine com
From playlist 2022 Multi-Modal Imaging with Deep Learning and Modeling
Mathematical Research Lecture -- Kyle Broder -- Curvature and Moduli
A recent talk I gave concerning the link between the curvature of the total space of a family of compact complex manifolds and the moduli-theoretic behaviour of the fibres. Part of this research appears in my Ph.D. thesis, and will appear in an upcoming preprint. 💪🙏 Support the channel b
From playlist Research Lectures
Complex Analysis (Advanced) -- The Schwarz Lemma
A talk I gave concerning my recent results on the Schwarz Lemma in Kähler and non-Kähler geometry. The talk details the classical Schwarz Lemma and discusses André Bloch. This is part 1 of a multi-part series. Part 1 -- https://youtu.be/AWqeIPMNhoA Part 2 -- https://youtu.be/hd7-iio77kc P
From playlist Complex Analysis
Jialong Deng - Enlargeable Length-structures and Scalar Curvatures
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Jialong Deng, University of Goettingen Title: Enlargeable Length-structures and Scalar Curvatures Abstract: We define enlargeable length-structures on closed topological manifolds and then show that the connected sum of a
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
J. Wu: The Novikov conjecture and C*-algebras of infinite dimensional nonpositively curved spaces
Talk by Jianchao Wu in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on June 10, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Jürgen Jost (5/13/22): Geometry and Topology of Data
We link the basic concept of topological data analysis, intersection patterns of distance balls, with geometric concepts. The key notion is hyperconvexity, and we also explore some variants. Hyperconvexity in turn leads us to a new concept of generalized curvature for metric spaces. Curvat
From playlist Bridging Applied and Quantitative Topology 2022