This lecture gives an introductory overview of the Chow ring of a nonsingular variety. The idea is to define a ring structure related to subvarieties with the product corresponding to intersection. There are several complications that have to be solved, in particular how to define intersec
From playlist Algebraic geometry: extra topics
Math 060 101317C Linear Transformations: Isomorphisms
Lemma: Linear transformations that agree on a basis are identical. Definition: one-to-one (injective). Examples and non-examples. Lemma: T is one-to-one iff its kernel is {0}. Definition: onto (surjective). Examples and non-examples. Definition: isomorphism; isomorphic. Theorem: T
From playlist Course 4: Linear Algebra (Fall 2017)
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
This is a lazy introduction to the idea of a Chow Ring. I don't prove anything :-(. Maybe soon in another video.
From playlist Intersection Theory
Burt Totaro: Decomposition of the diagonal, and applications
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 Algebraic and Complex Geometry
Linear Algebra 6c: Second Definition of Linear Dependence Fixed!
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications
Burnside's Lemma (Part 2) - combining math, science and music
Part 1 (previous video): https://youtu.be/6kfbotHL0fs Orbit-stabilizer theorem: https://youtu.be/BfgMdi0OkPU Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be
From playlist Traditional topics, explained in a new way
On the Hitchin fibration for algebraic surfaces
Distinguished Visitor Lecture Series On the Hitchin fibration for algebraic surfaces Ngô Bảo Châu The University of Chicago, USA and Vietnam Institute for Advanced Study in Mathematics, Vietnam
From playlist Distinguished Visitors Lecture Series
Beauville's splitting principle for Chow rings of projective hyperkaehler manifolds - Lie Fu
Lie Fu Member, School of Mathematics November 4, 2014 Being the natural generalization of K3 surfaces, hyperkaehler varieties, also known as irreducible holomorphic symplectic varieties, are one of the building blocks of smooth projective varieties with trivial canonical bundle. One of th
From playlist Mathematics
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Problems, Paradoxes, and Sophisms
Moduli of degree 4 K3 surfaces revisited - Radu Laza
Radu Laza Stony Brook University; von Neumann Fellow, School of Mathematics February 3, 2015 For low degree K3 surfaces there are several way of constructing and compactifying the moduli space (via period maps, via GIT, or via KSBA). In the case of degree 2 K3 surface, the relationship be
From playlist Mathematics
Cohomological decomposition of the diagonal in small dimension (Lecture - 05) by Claire Voisin
Infosys-ICTS Ramanujan Lectures Some new results on rationality Speaker: Claire Voisin (College de France) Date: 01 October 2018, 16:00 Venue: Madhava Lecture Hall, ICTS campus Resources Lecture 1: Some new results on rationality Date & Time: Monday, 1 October 2018, 04:00 PM Abstra
From playlist Infosys-ICTS Ramanujan Lectures
José Ignacio Burgos Gil: Arithmetic intersection of Bloch higher cycles
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: We give a new definition of higher arithmetic Chow groups for smooth projective varieties defined over a number field, which is similar to Gill
From playlist Workshop: "Periods and Regulators"
Victoria Hoskins: On the motive of the stack of vector bundles on a curve
Abstract: Following Grothendieck’s vision that a motive of an algebraic variety should capture many of its cohomological invariants, Voevodsky introduced a triangulated category of motives which partially realises this idea. After describing some of the properties of this category, I expla
From playlist Algebraic and Complex Geometry
Can p-adic integrals be computed? - Thomas Hales
Automorphic Forms Thomas Hales April 6, 2001 Concepts, Techniques, Applications and Influence April 4, 2001 - April 7, 2001 Support for this conference was provided by the National Science Foundation Conference Page: https://www.math.ias.edu/conf-automorphicforms Conference Agena: ht
From playlist Mathematics
In this video we prove the Lefschetz fixed point theorem assuming some properties of our cohomology theory. These notes were really useful as a graduate student, some of them are down now, but I think these notes I had came from here: http://mathsci.kaist.ac.kr/~jinhyun/useful.html
From playlist Riemann Hypothesis
Linear Algebra 6z: Outtakes from Chapters 5 and 6
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications
The Schwarz Lemma -- Complex Analysis
Part 1 -- The Maximum Principle: https://youtu.be/T_Msrljdtm4 Part 3 -- Liouville's theorem: https://www.youtube.com/watch?v=fLnRDhhzWKQ In today's video, we want to take a look at the Schwarz lemma — this is a monumental result in the subject of one complex variable, and has lead to many
From playlist Complex Analysis
Andrei Negut: Hilbert schemes of K3 surfaces
Abstract: We give a geometric representation theory proof of a mild version of the Beauville-Voisin Conjecture for Hilbert schemes of K3 surfaces, namely the injectivity of the cycle map restricted to the subring of Chow generated by tautological classes. Although other geometric proofs o
From playlist Algebraic and Complex Geometry