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
From playlist Abstract Algebra 2
Dugald Macpherson: Pseudofinite groups I
The lecture was held within the framework of the Hausdorff Trimester Program: Logic and Algorithms in Group Theory. Abstract: An infinite group is pseudofinite if it has the 'finite model property' – that is, if every sentence of first order logic which is true of it is also true of some
From playlist HIM Lectures: Trimester Program "Logic and Algorithms in Group Theory"
Dugald Macpherson: Pseudofinite groups III
The lecture was held within the framework of the Hausdorff Trimester Program: Logic and Algorithms in Group Theory. Abstract: An infinite group is pseudofinite if it has the 'finite model property' – that is, if every sentence of first order logic which is true of it is also true of some
From playlist HIM Lectures: Trimester Program "Logic and Algorithms in Group Theory"
Dugald Macpherson: Pseudofinite groups II
The lecture was held within the framework of the Hausdorff Trimester Program: Logic and Algorithms in Group Theory. Abstract: An infinite group is pseudofinite if it has the 'finite model property' – that is, if every sentence of first order logic which is true of it is also true of some
From playlist HIM Lectures: Trimester Program "Logic and Algorithms in Group Theory"
Field Theory: Definition/ Axioms
This video is about the basics axioms of fields.
From playlist Basics: Field Theory
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
This video is about extensions of fields.
From playlist Basics: Field Theory
Algebraic and Transcendental Elements; Finite Extensions - Field Theory - Lecture 01
In this video we introduce the notion of algebraic and transcendental. We then introduce a notion of "finite extension" which will help us prove every element in an extension is algebraic. See @MatthewSalomone's Abstract Algebra 2 videos. They complement this presentation with better exa
From playlist Field Theory
Moduli of Representations and Pseudorepresentations - Carl Wang Erickson
Carl Wang Erickson Harvard University May 2, 2013 A continuous representation of a profinite group induces a continuous pseudorepresentation, where a pseudorepresentation is the data of the characteristic polynomial coefficients. We discuss the geometry of the resulting map from the moduli
From playlist Mathematics
John s. Wilson - Metric ultraproducts of finite simple groups
John S. Wilson (University of Oxford, England) Metric ultraproducts of structures have arisen in a variety of contexts. The study of the case when the structures are finite groups is recent and motivated partly by the connection with sofic groups. We report on current joint work with An
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
Tamagawa Numbers of Linear Algebraic Groups over (...) - Rosengarten - Workshop 2 - CEB T2 2019
Zev Rosengarten (Hebrew University of Jerusalem) / 26.06.2019 Tamagawa Numbers of Linear Algebraic Groups over Function Fields In 1981, Sansuc obtained a formula for Tamagawa numbers of reductive groups over number fields, modulo some then unknown results on the arithmetic of simply con
From playlist 2019 - T2 - Reinventing rational points
Ariyan Javanpeykar: Arithmetic and algebraic hyperbolicity
Abstract: The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have onl
From playlist Algebraic and Complex Geometry
Local (\ell = p) Galois Deformation Rings - Ashwin Iyengar
Joint IAS/Princeton University Number Theory Seminar Topic: Local (\ell = p) Galois Deformation Rings Speaker: Ashwin Iyengar Affiliation: Johns Hopkins University Date: February 10, 2022 I will present joint work with V. Paškūnas and G. Böckle concerning deformation rings for mod p Galo
From playlist Mathematics
Iwasawa theory of the fine Selmer groups of Galois representations by Sujatha Ramdorai
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
Bjorn Poonen, Heuristics for the arithmetic of elliptic curves
VaNTAGe seminar on Sep 1, 2020. License: CC-BY-NC-SA. Closed captions provided by Brian Reinhart.
From playlist Rational points on elliptic curves
Moduli Stacks of Galois Representations by Mathew Emerton
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
Pseudo-reductive groups by Brian Conrad
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)
Bjorn Poonen: Heuristics for boundedness of ranks of elliptic curves
Abstract: We present heuristics that suggest that there is a uniform bound on the rank of E(ℚ) as E varies over all elliptic curves over ℚ. This is joint work with Jennifer Park, John Voight, and Melanie Matchett Wood. Recording during the thematic meeting : "Rational Points and Algebraic
From playlist Algebraic and Complex Geometry
Field Theory - Algebraically Closed Fields - Lecture 9
In this video we define what an algebraically closed field and assert without proof that they exist. We also explain why if you can find a single root for any polynomial, then you can find them all.
From playlist Field Theory