Unsolved problems in number theory | Algebraic number theory

Hilbert's ninth problem

Hilbert's ninth problem, from the list of 23 Hilbert's problems (1900), asked to find the most general reciprocity law for the norm residues of k-th order in a general algebraic number field, where k is a power of a prime. (Wikipedia).

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M. Kisin - Hilbert's thirteenth problem and the moduli space of abelian varieties

The (multi-valued) solution of a general polynomial of degree n is a priori a function of n-1 variables. Hilbert's thirteenth problem and its variants ask when such functions can be written as a composite of functions in a smaller number of variables. I will explain some progress on this q

From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday

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Turing Machines & The Halting Problem (Part 1)

In the year 1900, David Hilbert gave a list of 23 mathematics problems for the mathematicians of the new generation. His tenth problem proved to be an enigma for many years until Alan Turing solved it while simultaneously creating the modern computer. Watch the video to see how Alan Turi

From playlist Math

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Yuri Matiyasevich - On Hilbert's 10th Problem [2000]

On Hilbert's 10th Problem - Part 1 of 4 Speaker: Yuri Matiyasevich Date: Wed, Mar 1, 2000 Location: PIMS, University of Calgary Abstract: A Diophantine equation is an equation of the form $ D(x_1,...,x_m) $ = 0, where D is a polynomial with integer coefficients. These equations were n

From playlist Number Theory

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A Maths Puzzle: Find the nine digit number solution

Solution to the nine digit number puzzle. Sorry for the bad audio. Thanks to Mismag822 or the problem, which kept me awake when I had a presentation in the morning. Swine.

From playlist My Maths Videos

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Galois theory: Hilbert's theorem 90

This lecture is part of an online graduate course on Galois theory. We discuss two forms of Hilbert's theorem 90: the original version for cyclic extensions, and Noether's more general version for arbitrary finite Galois extensions. The proofs use a lemma of Artin about the linear indepen

From playlist Galois theory

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Panorama of Mathematics: Andrei Okounkov

Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Andrei Okounkov: "Enumerati

From playlist Panorama of Mathematics

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Why was Connes' embedding conjecture refuted and there are still no known... -Michael Chapman

Stability and Testability Topic: Why was Connes' embedding conjecture refuted and there are still no known non-hyperlinear groups? Speaker: Michael Chapman Affiliation: Hebrew University Date: March 24, 2021 For more video please visit http://video.ias.edu

From playlist Stability and Testability

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Algebraic geometry 49: Hilbert polynomials

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a review of the Hilbert polynomial of a graded module over a graded ring, and classifies integer-valued polynomials.

From playlist Algebraic geometry I: Varieties

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Matrix Entanglement by Vaibhav Gautam

PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II

From playlist NUMSTRING 2022

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Line operators and geometry in 3d N=4 gauge theory by Tudor Dimofte

Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries

From playlist Quantum Fields, Geometry and Representation Theory

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Fractal Snowflakes, Symmetries, and Beautiful Math Decorations

Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free, and hurry—the first 200 people get 20% off an annual premium subscription. Today is MATH CRAFTS day! We're going to make some holiday decorations and then also chat about the cool math behind them. We'll learn a

From playlist Cool Math Series

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Quadratisch Praktisch Gut - Zur Quadratischen Gleichung | Bernd Sturmfels

Mathematische Weihnachtsvorlesung 2020 gehalten von Prof. Dr. Bernd Sturmfels Direktor am Max-Planck-Institut für Mathematik in den Naturwissenschaften und Leiter der Nonlinear Algebra Arbeitsgruppe. Für Schüler:innen ab Klassenstufe 10

From playlist Schulvorträge

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The Geometry of Hilbert's 13th problem - Jesse Wolfson

Special Seminar on Hilbert's 13th Problem I Topic: The Geometry of Hilbert's 13th problem Speaker: Jesse Wolfson Affiliation: University of California, Irvine Date: December 5, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

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Joshua Ciappara: Hilbert Schemes Lecture 10

SMRI Seminar Series: 'Hilbert Schemes' Lecture 10 Representations of Heisenberg algebras on homology of Hilbert schemes Joshua Ciappara (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way tha

From playlist SMRI Course: Hilbert Schemes

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Rodrigo Bañuelos: "Events of Small Probabilities Do Happen"

Latinx in the Mathematical Sciences Conference 2018 "Events of Small Probabilities Do Happen" Rodrigo Bañuelos, Purdue University Institute for Pure and Applied Mathematics, UCLA March 9, 2018 For more information: http://www.ipam.ucla.edu/programs/special-events-and-conferences/latinx-

From playlist Latinx in the Mathematical Sciences 2018

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From currents to oriented varifolds for data fidelity (...) - Kaltenmark - Workshop 2 - CEB T1 2019

Irène Kaltenmark (Univ. Bordeaux) / 14.03.2019 From currents to oriented varifolds for data fidelity metrics; growth models for computational anatomy. In this talk, I present a general setting that extends the previous frameworks of currents and varifolds for the construction of data fi

From playlist 2019 - T1 - The Mathematics of Imaging

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Turing Centennial Conference: Turing, Church, Gödel, Computability, Complexity and Randomization

Turing, Church, Gödel, Computability, Complexity and Randomization Presented by Prof. Michael Rabin, Turing Award laureate, Hebrew University & Harvard University Alan M. Turing Centennial Conference - Israel April 4, 2012 The Wohl Centre Bar-Ilan University Ramat-Gan, Israel For more in

From playlist Alan M. Turing Centennial Conference - Israel

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What is the Riemann Hypothesis?

This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation

From playlist Mathematics

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Anthony Licata: Hilbert Schemes Lecture 7

SMRI Seminar Series: 'Hilbert Schemes' Lecture 7 Kleinian singularities 2 Anthony Licata (Australian National University) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students inter

From playlist SMRI Course: Hilbert Schemes

Related pages

Non-abelian class field theory | Algebraic number field | Helmut Hasse | Hilbert symbol | Prime number | Emil Artin | Class field theory | Igor Shafarevich | Teiji Takagi | List of unsolved problems in mathematics | Abelian extension | Hilbert's twelfth problem | Artin reciprocity law