In this video, I present a very classical example of a duality argument: Namely, I show that T^T is one-to-one if and only if T is onto and use that to show that T is one-to-one if and only if T^T is onto. This illustrates the beautiful interplay between a vector space and its dual space,
From playlist Dual Spaces
In this video, I show a very neat result about dual spaces: Namely, any basis of V* is automatically a dual basis of some basis of V. Even though this result is very interesting, it's the proof that makes this very exciting, by simply using the fact that V and V** are 'very' isomorphic. En
From playlist Dual Spaces
Dual basis definition and proof that it's a basis In this video, given a basis beta of a vector space V, I define the dual basis beta* of V*, and show that it's indeed a basis. We'll see many more applications of this concept later on, but this video already shows that it's straightforwar
From playlist Dual Spaces
Definition of the transpose Have you ever wondered where the transpose comes from? In this video, I show that the transpose arises naturally in the setting of dual spaces. This should also illustrate why dual spaces are so important. Enjoy! Transpose Example (Sequel): https://youtu.be/x2
From playlist Dual Spaces
Duality and emergent gauge symmetry - Nathan Seiberg
Nathan Seiberg Institute for Advanced Study; Faculty, School of Natural Science February 20, 2014 For more videos, visit http://video.ias.edu
From playlist Mathematics
Higher Algebra 12: The Tate construction
In this video we introduce the Tate construction and especially Tate spectra. This is defined as the cofibre of a certain norm map, which we introduced for completely general group objects and stable infinity categories. We then also explain what it has to do with Poncaré duality and that
From playlist Higher Algebra
Jeremy Hahn : Prismatic and syntomic cohomology of ring spectra
CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR
From playlist Topology
Selmer groups and a Cassels-Tate pairing for finite Galois modules - Alexander Smith
Joint IAS/Princeton University Number Theory Seminar Topic: Selmer groups and a Cassels-Tate pairing for finite Galois modules Speraker: Alexander Smith Affiliation: Massachusetts Institute of Technology Date: February 25, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Cyril Demarche: Cohomological obstructions to local-global principles - lecture 3
Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these
From playlist Algebraic and Complex Geometry
Types of Colloids and Their Properties
Earlier we learned that as far as mixtures go, we can have homogeneous solutions, or totally heterogeneous mixtures, where components don't mix. But there are actually intermediary mixtures, where substances mix to some limited degree. Let's learn about colloids as well as suspensions! Wa
From playlist General Chemistry
Moduli of p-divisible groups (Lecture 4) by Ehud De Shalit
PROGRAM 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
From playlist Perfectoid Spaces 2019
In this video, I show how to explicitly calculate dual bases. More specifically, I find the dual basis corresponding to the basis (2,1) and (3,1) of R^2. Hopefully this will give you a better idea of how dual bases work. Subscribe to my channel: https://www.youtube.com/c/drpeyam What is
From playlist Dual Spaces
Complexes of tori and rational points on homogeneous (...) - Harari - Workshop 1 - CEB T2 2019
David Harari (Université Paris Sud) / 20.05.2019 Complexes of tori and rational points on homogeneous spaces over a function field We explain new arithmetic duality theorems for finite group schemes and 2-term complexes of tori defined over a global field of positive characteristic. We
From playlist 2019 - T2 - Reinventing rational points
Gonçalo Tabuada - 3/3 Noncommutative Counterparts of Celebrated Conjectures
Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
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
Serre Duality on Character Varieties and Explicit Reciprocity Laws by Otmar Venjakob
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
What is the difference between convex and concave
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
David Morrison - WHAT IS … F-theory? [2014]
Dave Morrison Event: SCGP Weekly Talk Title: WHAT IS … F-theory? Date: 2014-09-09 @1:00 PM Location: 102 Abstract: In the spirit of the “WHAT IS …” series of articles in the Notices of the American Mathematical Society, I will give a description of F-theory from first priniciples. On the
From playlist Mathematics
This video introduces similarity and explains how to determine if two figures are similar or not. http://mathispower4u.com
From playlist Number Sense - Decimals, Percents, and Ratios