Diophantine equations | Theorems in number theory

Tunnell's theorem

In number theory, Tunnell's theorem gives a partial resolution to the congruent number problem, and under the Birch and Swinnerton-Dyer conjecture, a full resolution. (Wikipedia).

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Dimitri Zvonkine - On two ELSV formulas

The ELSV formula (discovered by Ekedahl, Lando, Shapiro and Vainshtein) is an equality between two numbers. The first one is a Hurwitz number that can be defined as the number of factorizations of a given permutation into transpositions. The second is the integral of a characteristic class

From playlist 4th Itzykson Colloquium - Moduli Spaces and Quantum Curves

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Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem

In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

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C73 Introducing the theorem of Frobenius

The theorem of Frobenius allows us to calculate a solution around a regular singular point.

From playlist Differential Equations

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Every Subset of a Linearly Independent Set is also Linearly Independent Proof

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A proof that every subset of a linearly independent set is also linearly independent.

From playlist Proofs

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Determining if a vector is a linear combination of other vectors

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determining if a vector is a linear combination of other vectors

From playlist Linear Algebra

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How to Determine if Functions are Linearly Independent or Dependent using the Definition

How to Determine if Functions are Linearly Independent or Dependent using the Definition If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Th

From playlist Zill DE 4.1 Preliminary Theory - Linear Equations

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Bernoulli ode

Illustrates the solution of a Bernoulli first-order differential equation. Free books: http://bookboon.com/en/differential-equations-with-youtube-examples-ebook http://www.math.ust.hk/~machas/differential-equations.pdf

From playlist Differential Equations with YouTube Examples

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C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 2

We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 2 (version temporaire)

We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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Christina Sormani - Sequences of manifolds with lower bounds on their scalar curvature

If one has a weakly converging sequence of manifolds with a uniform lower bound on their scalar curvature, what properties of scalar curvature persist on the limit space? What additional hypotheses might be added to provide stronger controls on the limit space? What hypotheses are requ

From playlist Not Only Scalar Curvature Seminar

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Solve a Bernoulli Differential Equation Initial Value Problem

This video provides an example of how to solve an Bernoulli Differential Equations Initial Value Problem. The solution is verified graphically. Library: http://mathispower4u.com

From playlist Bernoulli Differential Equations

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Luca Giorgetti: "Distortion for II_1 multifactor inclusions and bimodules"

Actions of Tensor Categories on C*-algebras 2021 "Distortion for II_1 multifactor inclusions and bimodules" Luca Giorgetti - Università degli Studi di Roma "Tor Vergata" Abstract: We introduce an invariant, called distortion, for inclusions of II_1 von Neumann algebras with finite index

From playlist Actions of Tensor Categories on C*-algebras 2021

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C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 4

We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 4 (version temporaire)

We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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Christina Sormani: A Course on Intrinsic Flat Convergence part 1

Intrinsic Flat Convergence was first introduced in joint work with Stefan Wenger building upon work of Ambrosio-Kirchheim to address a question proposed by Tom Ilmanen. In this talk, I will present an overview of the initial paper on the topic [JDG 2011]. I will briefly describe key examp

From playlist HIM Lectures 2015

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Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem

In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

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Universal quantum noise in adiabatic pumping by Kyrylo Snizhko

DISCUSSION MEETING : EDGE DYNAMICS IN TOPOLOGICAL PHASES ORGANIZERS : Subhro Bhattacharjee, Yuval Gefen, Ganpathy Murthy and Sumathi Rao DATE & TIME : 10 June 2019 to 14 June 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore Topological phases of matter have been at the forefront of r

From playlist Edge dynamics in topological phases 2019

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AQC2016 - Classical Modeling of Quantum Tunneling

A Google TechTalk, June 29, 2016, presented by Itay Hen (USC) ABSTRACT: Tunneling is widely believed to be the main advantage quantum annealers have over their classical counterparts. With neither provable speedups nor no-go theorems demonstrated, the true power of quantum annealers remai

From playlist Adiabatic Quantum Computing Conference 2016

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Theory of numbers: Congruences: Euler's theorem

This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim

From playlist Theory of numbers

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Some Aspects of Space Fractional Quantum Mechanics by Bhabani Prasad Mandal

PROGRAM NON-HERMITIAN PHYSICS - PHHQP XVIII DATE :04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Qua

From playlist Non-Hermitian Physics - PHHQP XVIII

Related pages

Birch and Swinnerton-Dyer conjecture | Diophantine equation | Elliptic curve | Congruent number | Number theory