In algebraic geometry, the problem of residual intersection asks the following: Given a subset Z in the intersection of varieties, understand the complement of Z in the intersection; i.e., the residual set to Z. The intersection determines a class , the intersection product, in the Chow group of an ambient space and, in this situation, the problem is to understand the class, the residual class to Z: where means the part supported on Z; classically the degree of the part supported on Z is called the equivalence of Z. The two principal applications are the solutions to problems in enumerative geometry (e.g., Steiner's conic problem) and the derivation of the , the formula allowing one to count or enumerate the points in a fiber even when they are . The problem of residual intersection goes back to the 19th century. The modern formulation of the problems and the solutions is due to Fulton and MacPherson. To be precise, they develop the intersection theory by a way of solving the problems of residual intersections (namely, by the use of the Segre class of a normal cone to an intersection.) A generalization to a situation where the assumption on regular embedding is weakened is due to . (Wikipedia).
From playlist Intersection Theory
What is the Alternate Exterior Angle Converse Theorem
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
What is the Corresponding Angle Converse Theorem
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Alternative Locus Definition of an Ellipse (1 of 2: Algebraically finding Locus of an Ellipse)
More resources available at www.misterwootube.com
From playlist Further Work with Functions (related content)
What are parallel lines and a transversal
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Proving Parallel Lines with Angle Relationships
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Determining Supplementary Angles from Parallel Lines and a Transversal
👉 Learn how to identify angles from a figure. This video explains how to solve problems using angle relationships between parallel lines and transversal. We'll determine the solution given, corresponding, alternate interior and exterior. All the angle formed by a transversal with two paral
From playlist Parallel Lines and a Transversal
What is the Consecutive Interior Angle Converse Theorem
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Residual Intersections in Geometry and Algebra by David Eisenbud
DISTINGUISHED LECTURES RESIDUAL INTERSECTIONS IN GEOMETRY AND ALGEBRA SPEAKER: David Eisenbud (Director, Mathematical Sciences Research Institute, and Professor of Mathematics, UC Berkeley) DATE: 13 December 2019, 16:00 to 17:00 VENUE: Madhava Lecture Hall, ICTS-TIFR, Bengaluru In thi
From playlist DISTINGUISHED LECTURES
How Newton's method solves multiple equations at once
This video explains how Newton's method (also called the Newton-Raphson method) can solve more than one equation simultaneously. MDO Lab: https://mdolab.engin.umich.edu/ Engineering Design Optimization: https://mdobook.github.io/ Animations done using Manim: https://docs.manim.community/e
From playlist Summer of Math Exposition 2 videos
Riccardo Ontani - Jeffrey-Kirwan Localization for Quiver Varieties
In this talk, I will present an ongoing project on Jeffrey-Kirwan localization in the theory of quiver moduli spaces. In order to motivate the interest in this topic, in the first part of the talk I will recall the content of a previous joint work with Jacopo Stoppa (SISSA). Given a comple
From playlist Workshop on Quantum Geometry
EstimatingRegressionCoefficients.1.EstimatingResidualVariance
This video is brought to you by the Quantitative Analysis Institute at Wellesley College. The material is best viewed as part of the online resources that organize the content and include questions for checking understanding: https://www.wellesley.edu/qai/onlineresources
From playlist Estimating Regression Coefficients
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
Minerva Lectures 2012 - Ian Agol Talk 2: The virtual Haken conjecture & geometric group theory
Talk two of the second Minerva lecture series, by Prof. Ian Agol on October 23rd, 2012 at the Mathematics Department, Princeton University. More information available at: http://www.math.princeton.edu/events/seminars/minerva-lectures/minerva-lecture-ii-virtual-haken-conjecture-what-geomet
From playlist Minerva Lectures - Ian Agol
Descent obstructions on constant curves over global (...) - Creutz - Workshop 2 - CEB T2 2019
Brendan Creutz (University of Canterbury) / 26.06.2019 Descent obstructions on constant curves over global function fields Let C and D be proper geometrically integral curves over a finite field and let K be the function field of D. I will discuss descent obstructions to the existence o
From playlist 2019 - T2 - Reinventing rational points
Sam Hughes (11/10/22): Torsion homology growth and related topics
Let X be compact CW complex with residually finite group fundamental group G. Given a residual chain G_n of finite index subgroups of G, what can be said about the growth of Betti numbers normalised by index in the homology of finite covers X_n corresponding to G_n? In this talk we will ex
From playlist Topological Complexity Seminar
János Kollár - What determines a variety? - WAGON
A scheme X is a topological space---which we denote by |X|---and a sheaf of rings on the open subsets of |X|. We study the following natural but seldom considered questions. How to read off properties of X from |X|? Does |X| alone determine X? Joint work with Max Lieblich, Martin Olsson, a
From playlist WAGON
CTNT 2020 - Semistable models of hyperelliptic curves over residue characteristic 2 - Jeffrey Yelton
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
Denis Osin: Acylindrically hyperbolic groups (part 3)
The lecture was held within the framework of Follow-up Workshop TP Rigidity. 1.5.2015
From playlist HIM Lectures 2015
What is an Intersection? (Set Theory)
What is the intersection of sets? This is another video on set theory in which we discuss the intersection of a set and another set, using the classic example of A intersect B. We do not quite go over a formal definition of intersection of a set in this video, but we come very close! Be su
From playlist Set Theory