Nonstandard analysis | Ordered algebraic structures | Real algebraic geometry
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).
Geometry Of Frobenioids - part 6 - Archimedean Frobenioids
This is contained in Mochizuki's Geometry of Frobenioids 2.
From playlist Geometry of Frobenioids
Archimedean Theory - Alex Kontorovich
Speaker: Alex Kontorovich (Rutgers/IAS) Title: Archimedean Theorem More videos on http://video.ias.edu
From playlist Mathematics
GT10. Examples of Non-Isomorphic Groups
EDIT: Fix for 14:10: "Here's a quick way to fix. If y has order 3, then the order of yH divides 3. By assumption, yH has order 2, a contradiction. Recall that yH=H means y is in H. I'm actually overthinking the entire proof. Once we have H, pick any y not in H. Then yxy^-1=x^2.
From playlist Abstract Algebra
Non-archimedean geometry for symplectic geometers - Mohammed Abouzaid
Topic: Non-archimedean geometry for symplectic geometers Speaker: Mohammed Abouzaid, Columbia University; Member, School of Mathematics Time/Room: 10:45am - 12:00pm/S-101 More videos on http://video.ias.edu
From playlist Mathematics
Non-archimedean geometry for symplectic geometers - Mohammed Abouzaid
Topic: Non-archimedean geometry for symplectic geometers Speaker: Mohammed Abouzaid, Columbia University; Member, School of Mathematics Time/Room: 10:45am - 12:00pm/S-101 More videos on http://video.ias.edu
From playlist Mathematics
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
Definition of a Field In this video, I define the concept of a field, which is basically any set where you can add, subtract, add, and divide things. Then I show some neat properties that have to be true in fields. Enjoy! What is an Ordered Field: https://youtu.be/6mc5E6x7FMQ Check out
From playlist Real Numbers
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
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
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
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
Function Field Arithmetic - Lecture 1/4 by Christelle Vincent [CTNT 2018]
Full playlist: https://www.youtube.com/playlist?list=PLJUSzeW191QyYO8dd6uYoDqs4IGFAiNd2 Slides: https://ctnt-summer.math.uconn.edu/wp-content/uploads/sites/1632/2018/05/VincentLecture1.pdf Mini-course C: “Function Field Arithmetic” by Christelle Vincent (University of Vermont). This wi
From playlist Number Theory
Yifeng Liu - Derivative of L-functions for unitary groups (3/3)
In this lecture series, we will focus on the recent advance on the Beilinson-Bloch conjecture for unitary Shimura varieties, more precisely, a Gross-Zagier type formula for automorphic forms on unitary groups of higher ranks. We will start from the general theory of height pairings between
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
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.
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
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
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
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
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics