Localization (mathematics) | Mathematical principles | Diophantine equations | Algebraic number theory
In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the p-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in the real numbers and in the p-adic numbers for each prime p. (Wikipedia).
The Atom C2 The Pauli Exclusion Principle
The Pauli exclusion principle.
From playlist Physics - The Atom
The Atom C3 The Pauli Exclusion Principle
The Pauli exclusion principle.
From playlist Physics - The Atom
What Heisenberg's Uncertainty Principle *Actually* Means
Let's talk about one of the most misunderstood but awesome concepts in physics. The Heisenberg uncertainty principle. Or maybe it should be the Heisenberg 'fuzziness' principle instead? Would that confuse less people?
From playlist Some Quantum Mechanics
The Atom C1 The Pauli Exclusion Principle
The Pauli exclusion principle.
From playlist Physics - The Atom
Robert Harrison and Adrian Daub discuss Georg Wilhelm Friedrich Hegel and his heirs a few years back in an episode of Entitled Opinions, a KZSU Stanford University program. http://french-italian.stanford.edu/op... Hegel was one of the most important and influential 19th century German phi
From playlist Hegel
Francesca Balestrieri, The arithmetic of zero-cycles on products of K3 surfaces and Kummer varieties
VaNTAGe seminar, March 9, 2021
From playlist Arithmetic of K3 Surfaces
Light and Optics 7_1 Interference
Using Huygen's Principle to derive Snel's Law.
From playlist Physics - Light and Optics
The Atom A4 The Bohr Model of the Hydrogen Atom
The Bohr model of the atom.
From playlist Physics - The Atom
What is the Heisenberg Uncertainty Principle? A wave packet approach
In this video I would like to answer a simple question: according to quantum mechanics, how do you describe a freely moving particle? It sounds simple, but what we will discover is that by attempting to answer this question, we will actually uncover one of the most profound ideas in physic
From playlist Quantum Physics
Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions
VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Fred Diamond, Geometric Serre weight conjectures and theta operators
VaNTAGe Seminar, April 26, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in the talk: Ash-Sinott: https://arxiv.org/abs/math/9906216 Ash-Doud-Pollack: https://arxiv.org/abs/math/0102233 Buzzard-Diamond-Jarvis: https://www.ma.imperial.ac.uk/~buzzard/maths/research/paper
From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)
Origin and Development of Valuation Theory by Sudesh Khanduja
DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (
From playlist The Legacy of Emmy Noether
The Atom A5 The Bohr Model of the Hydrogen Atom
The Bohr model of the atom.
From playlist Physics - The Atom
Zorn's Lemma, The Well-Ordering Theorem, and Undefinability (Version 2.0)
Zorn's Lemma and The Well-ordering Theorem are seemingly straightforward statements, but they give incredibly mind-bending results. Orderings, Hasse Diagrams, and the Ordinals / set theory will come up in this video as tools to get a better view of where the "proof" of Zorn's lemma comes f
From playlist The New CHALKboard
Commutators in SL_2 and Markoff Surfaces - Chen Meiri
Arithmetic Groups Topic: Commutators in SL_2 and Markoff Surfaces Speaker: Chen Meiri Affiliation: Technion Date: December 15, 2021 We discuss a local to global profinite principle for being a commutator in some arithmetic groups. Specifically we show that SL2(Z) satisfies such a princip
From playlist Mathematics
Zorn's Lemma, The Well-Ordering Theorem, and Undefinability | Nathan Dalaklis
Zorn's Lemma and The Well-ordering Theorem are seemingly straightforward statements, but they give incredibly mind-bending results. Orderings, Hasse Diagrams, and the Ordinals will come up in this video as tools to get a better view of where the proof of Zorn's lemma comes from. ***Corre
From playlist The First CHALKboard
PARTIAL ORDERS - DISCRETE MATHEMATICS
In this video we discuss partial orders and Hasse Diagrams. Support me on Patreon: http://bit.ly/2EUdAl3 Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-
From playlist Discrete Math 1
On a conjecture of Poonen and Voloch I: Probabilistic models(...) - Sawin - Workshop 1 - CEB T2 2019
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From playlist 2019 - T2 - Reinventing rational points
The Atom A3 The Bohr Model of the Hydrogen Atom
The Bohr model of the atom.
From playlist Physics - The Atom
Hanneke Wiersema, Minimal weights of mod-p Galois representations
VaNTAGe Seminar, April 12, 2022 License: CC-BY-NC-SA
From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)