Lie groups | Mathematical quantization | Group theory
In mathematics, the Heisenberg group , named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form under the operation of matrix multiplication. Elements a, b and c can be taken from any commutative ring with identity, often taken to be the ring of real numbers (resulting in the "continuous Heisenberg group") or the ring of integers (resulting in the "discrete Heisenberg group"). The continuous Heisenberg group arises in the description of one-dimensional quantum mechanical systems, especially in the context of the Stone–von Neumann theorem. More generally, one can consider Heisenberg groups associated to n-dimensional systems, and most generally, to any symplectic vector space. (Wikipedia).
Metric embeddings, uniform rectifiability, and the Sparsest Cut problem - Robert Young
Members' Seminar Topic: Metric embeddings, uniform rectifiability, and the Sparsest Cut problem Speaker: Robert Young Affiliation: New York University; von Neumann Fellow, School of Mathematics Date: November 2, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Lara Ismert: "Heisenberg Pairs on Hilbert C*-modules"
Actions of Tensor Categories on C*-algebras 2021 "Heisenberg Pairs on Hilbert C*-modules" Lara Ismert - Embry-Riddle Aeronautical University, Mathematics Abstract: Roughly speaking, a Heisenberg pair on a Hilbert space is a pair of self-adjoint operators (A,B) which satisfy the Heisenber
From playlist Actions of Tensor Categories on C*-algebras 2021
The Heisenberg Algebra in Symplectic Algebraic Geometry - Anthony Licata
Anthony Licata Institute for Advanced Study; Member, School of Mathematics April 2, 2012 Part of geometric representation theory involves constructing representations of algebras on the cohomology of algebraic varieties. A great example of such a construction is the work of Nakajima and Gr
From playlist Mathematics
Erik van Erp: Pseudodifferential Calculi and Groupoids
In recent work Debord and Skandalis realized pseudodifferential operators (on an arbitrary Lie groupoid G) as integrals of certain smooth kernels on the adiabatic groupoid of G. We propose an alternative definition of pseudodifferential calculi (including nonstandard calculi like the Heise
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Why Heisenberg Worked for Hitler
In 1939, Werner Heisenberg joined the "Uranium Club" to try to make a nuclear bomb for Hitler. Why? He didn't love the Nazis and he had plenty of opportunities to leave. This is the story of the moral failings of a brilliant man. My Patreon Page (thanks!): https://www.patreon.com/user?u=
From playlist History of Lighting (War of the Currents)
Robert Young - Self-similar solutions to extension and approximation problem
In 1979, Kaufman constructed a remarkable surjective Lipschitz map from a cube to a square whose derivative has rank 1 almost everywhere. In this talk, we will present some higher-dimensional generalizations of Kaufman's construction that lead to Lipschitz and Hölder maps with wild propert
From playlist Not Only Scalar Curvature Seminar
Equidistribution of Unipotent Random Walks on Homogeneous spaces by Emmanuel Breuillard
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
Heisenberg and Bohr's 1941 Copenhagen Meeting: What Happened?
I use letters, secret recordings and diaries to try to solve the mystery of why Heisenberg went to Nazi occupied Denmark and told Bohr that he was working on the military aspects of fission. The answer I came to is depressing about Heisenberg but surprisingly clear. See if you agree with
From playlist Early History of Quantum Mechanics
Group theory 24: Extra special groups
This lecture is part of an online mathematics course on group theory. It covers groups of order p^3. The non-abelian ones are examples of extra special groups, a sort of analog of the Heisenberg groups of quantum mechanics.
From playlist Group theory