Nonstandard analysis | Ordered algebraic structures | Real algebraic geometry

Non-Archimedean ordered field

In mathematics, a non-Archimedean ordered field is an ordered field that does not satisfy the Archimedean property. Examples are the Levi-Civita field, the hyperreal numbers, the surreal numbers, the Dehn field, and the field of rational functions with real coefficients with a suitable order. (Wikipedia).

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Geometry Of Frobenioids - part 6 - Archimedean Frobenioids

This is contained in Mochizuki's Geometry of Frobenioids 2.

From playlist Geometry of Frobenioids

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Archimedean Theory - Alex Kontorovich

Speaker: Alex Kontorovich (Rutgers/IAS) Title: Archimedean Theorem More videos on http://video.ias.edu

From playlist Mathematics

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GT10. Examples of Non-Isomorphic Groups

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From playlist Abstract Algebra

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Non-archimedean geometry for symplectic geometers - Mohammed Abouzaid

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From playlist Mathematics

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Non-archimedean geometry for symplectic geometers - Mohammed Abouzaid

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From playlist Mathematics

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GT13. Groups of Order 8

Abstract Algebra: We classify all groups of order 8 up to isomorphism. There are 3 abelian isomorphism classes and two non-abelian classes, the symmetry group of the square D8 and the quaternion group Q. We define and describe Q and compute Inn(Q) and Out(Q). U.Reddit course materials

From playlist Abstract Algebra

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What is a field ?

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From playlist Real Numbers

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Field Definition (expanded) - Abstract Algebra

The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They

From playlist Abstract Algebra

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Analytic Geometry Over F_1 - Vladimir Berkovich

Vladimir Berkovich Weizmann Institute of Science March 10, 2011 I'll talk on work in progress on algebraic and analytic geometry over the field of one element F_1. This work originates in non-Archimedean analytic geometry as a result of a search for appropriate framework for so called skel

From playlist Mathematics

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Perfectoid spaces (Lecture 1) by Kiran Kedlaya

PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath

From playlist Perfectoid Spaces 2019

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CTNT 2018 - "Function Field Arithmetic" (Lecture 1) by Christelle Vincent

This is lecture 1 of a mini-course on "Function Field Arithmetic", taught by Christelle Vincent (UVM), during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2018 - "Function Field Arithmetic" by Christelle Vincent

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Function Field Arithmetic - Lecture 1/4 by Christelle Vincent [CTNT 2018]

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From playlist Number Theory

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Yifeng Liu - Derivative of L-functions for unitary groups (3/3)

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From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)

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Salma Kuhlmann: Real closed fields and models of Peano arithmetic

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.

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Johannes Nicaise: The non-archimedean SYZ fibration and Igusa zeta functions - part 2/3

Abstract : The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its

From playlist Algebraic and Complex Geometry

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Tony Yue Yu - 1/4 The Frobenius Structure Conjecture for Log Calabi-Yau Varieties

Notes: https://nextcloud.ihes.fr/index.php/s/GwJbsQ8xMW2ifb8 1/4 - Motivation and ideas from mirror symmetry, main results. --- We show that the naive counts of rational curves in an affine log Calabi-Yau variety U, containing an open algebraic torus, determine in a surprisingly simple wa

From playlist Tony Yue Yu - The Frobenius Structure Conjecture for Log Calabi-Yau Varieties

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Maxim Kontsevich - 4/4 Bridgeland Stability over Non-Archimedean Fields

Bridgeland stability structure/condition on a triangulated category is a vast generalization of the notion of an ample line bunlde (or polarization) in algebraic geometry. The origin of the notion lies in string theory, and is applicable to derived categories of coherent sheaves, quiver re

From playlist Maxim Kontsevitch - Bridgeland Stability over Non-Archimedean Fields

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Johannes Nicaise: The non-archimedean SYZ fibration and Igusa zeta functions - part 1/3

Abstract: The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its

From playlist Algebraic and Complex Geometry

Related pages

Surreal number | Infinitesimal | Parallel postulate | Rational function | Least-upper-bound property | Formal power series | Rational number | Levi-Civita field | Nonstandard analysis | Hyperreal number | Ordered field | Real number | Non-Euclidean geometry | Unit fraction | Archimedean property