Schemes 5: Definition of a scheme
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We give some historical background, then give the definition of a scheme and some simple examples, and finish by explaining the origin of the word "spectrum".
From playlist Algebraic geometry II: Schemes
Quantum Mechanics -- a Primer for Mathematicians
Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w
From playlist Mathematics
Formal Definition of a Function using the Cartesian Product
Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
Visual Group Theory, Lecture 1.6: The formal definition of a group
Visual Group Theory, Lecture 1.6: The formal definition of a group At last, after five lectures of building up our intuition of groups and numerous examples, we are ready to present the formal definition of a group. We conclude by proving several basic properties that are not built into t
From playlist Visual Group Theory
There is a great deal of confusion about the term 'grammar'. Most people associate with it a book written about a language. In fact, there are various manifestations of this traditional term: presecriptive, descriptive and reference grammar. In theoretical linguistics, grammars are theory
From playlist VLC107 - Syntax: Part II
A (proper) introduction to derived CATegories
While there are introductions to derived categories that are more sensible for practical aspects, in this video I give the audience of taste of what's involved in the proper, formal definition of derived categories. Special thanks to Geoff Vooys, whose notes (below) inspired this video: ht
From playlist Miscellaneous Questions
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
How to use the rule of a sequence to evaluate for any term in the sequence
👉 Learn how to write the rule of a sequence given a sequence of numbers. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. To write the explicit formula of a sequence of numbers, we first determine whether e
From playlist Sequences
C. Gasbarri - Techniques d’algébrisation en géométrie analytique... (Part 3)
Dans ce cours, nous nous proposons d’expliquer comment des théorèmes d’algébrisation classiques, concernant des variétés ou des faisceux cohérents analytiques, possèdent des avatars en géométrie formelle et en géométrie diophantienne. Nous mettrons l’accent sur les points communs entre les
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
C. Gasbarri - Techniques d’algébrisation en géométrie analytique... (Part 4)
Dans ce cours, nous nous proposons d’expliquer comment des théorèmes d’algébrisation classiques, concernant des variétés ou des faisceux cohérents analytiques, possèdent des avatars en géométrie formelle et en géométrie diophantienne. Nous mettrons l’accent sur les points communs entre les
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
A stacky approach to crystalline (and prismatic) cohomology - Vladimir Drinfeld
Joint IAS/Princeton University Number Theory Seminar Topic: A stacky approach to crystalline (and prismatic) cohomology Speaker: Vladimir Drinfeld Affiliation: The University of Chicago; Visiting Professor, School of Mathematics Date: October 3, 2019 For more video please visit http://vi
From playlist Mathematics
Bertrand Toën - Deformation quantization and derived algebraic geometry
Bertrand TOĂ‹N (CNRS - Univ. de Montpellier 2, France)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
Moduli of p-divisible groups (Lecture 1) by Ehud De Shalit
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
Matthew Morrow: Relative integral p-adic Hodge theory
Abstract: Given a smooth scheme X over the ring of integers of a p-adic field, we introduce the notion of a relative Breuil-Kisin-Fargues module M on X. Each such M simultaneously encodes the data of a lisse Ă©tale sheaf, a module with flat connection, and a crystal, whose cohomologies are
From playlist Algebraic and Complex Geometry
Arithmetic D-modules and locally analytic representations
T. Schmidt (Université de Münster) Arithmetic D-modules and locally analytic representations Conférence de mi-parcours du programme ANR Théorie de Hodge p-adique et Développements (ThéHopaD) 25-27 septembre 2013 Centre de conférences Marilyn et James Simons IHÉS Bures / Yvette France
From playlist ConfĂ©rence de mi-parcours du programme ANRThĂ©orie de Hodge p-adique et DĂ©veloppements (ThĂ©HopaD)Â25-27 septembre 2013
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define open and closed immersion, and give some basic properties and some examples.
From playlist Algebraic geometry II: Schemes
Vladimir Berkovich - Hodge theory for non-Archimedean analytic spaces
Correction: The affiliation of Lei Fu is Tsinghua University. In a work in progress, I defined integral “etale” cohomology and de Rham cohomology for so called bounded non-Archimedean analytic spaces over the field of formal Laurent power series with complex coefficients. The former are l
From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021