In mathematics, specifically enumerative geometry, the virtual fundamental class of a space is a replacement of the classical fundamental class in its chow ring which has better behavior with respect to the enumerative problems being considered. In this way, there exists a cycle with can be used for answering specific enumerative problems, such as the number of degree rational curves on a quintic threefold. For example, in Gromov–Witten theory, the for a scheme and a class in , their behavior can be wild at the boundary, such aspg 503 having higher-dimensional components at the boundary than on the main space. One such example is in the moduli space for the class of a line in . The non-compact "smooth" component is empty, but the boundary contains maps of curves whose components consist of one degree 3 curve which contracts to a point. There is a virtual fundamental class which can then be used to count the number of curves in this family. (Wikipedia).
Fundamentals of Mathematics - Lecture 25: Quotient Maps (Real Projective Line, Modular Arithmetic)
course page - https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton, UVM
From playlist Fundamentals of Mathematics
The Fundamental Theorem of Calculus - Full Tutorial
This is a full tutorial on the Fundamental Theorem of Calculus and related topics. Here are the three main topics covered. Note several examples of computing definite integrals are given. - The Fundamental Theorem of Calculus - Computing Definite Integrals - The Second Fundamental Theorem
From playlist Math Tutorials
First Fundamental Theorem of Calculus Calculus 1 AB
I introduce and define the First Fundamental Theorem of Calculus. I finish by working through 4 examples involving Polynomials, Quotients, Radicals, Absolute Value Function, and Trigonometric Functions. Check out http://www.ProfRobBob.com, there you will find my lessons organized by clas
From playlist Calculus
What is the Fundamental theorem of Algebra, really? | Abstract Algebra Math Foundations 217
Here we give restatements of the Fundamental theorems of Algebra (I) and (II) that we critiqued in our last video, so that they are now at least meaningful and correct statements, at least to the best of our knowledge. The key is to abstain from any prior assumptions about our understandin
From playlist Math Foundations
Abstract Algebra - 11.1 Fundamental Theorem of Finite Abelian Groups
We complete our study of Abstract Algebra in the topic of groups by studying the Fundamental Theorem of Finite Abelian Groups. This tells us that every finite abelian group is a direct product of cyclic groups of prime-power order. Video Chapters: Intro 0:00 Before the Fundamental Theorem
From playlist Abstract Algebra - Entire Course
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Calculus 1 (Stewart) Ep 34, Fundamental Theorem of Calculus (Dec 3, 2021)
This is a recording of a live class for Math 1171, Calculus 1, an undergraduate course for math majors (and others) at Fairfield University, Fall 2021. The textbook is Stewart. PDF of the written notes, and a list of all episodes is at the class website. Class website: http://cstaecker.f
From playlist Math 1171 (Calculus 1) Fall 2021
Markus Banagl : The L-Homology fundamental class for singular spaces and the stratified Novikov
Abstract : An oriented manifold possesses an L-homology fundamental class which is an integral refinement of its Hirzebruch L-class and assembles to the symmetric signature. In joint work with Gerd Laures and James McClure, we give a construction of such an L-homology fundamental class for
From playlist Topology
Legendary Physics Book for Self-Study
You can learn physics with this classic textbook by Halliday, Resnick, and Walker. The book is called Fundamentals of Physics and this is Volume 1. There are various editions out there a few are below. Here is one version: https://amzn.to/3Stg6BY Newer Edition: https://amzn.to/3IvNaEX Ano
From playlist Book Reviews
Gromov–Witten Invariants and the Virasoro Conjecture - II (Remote Talk) by Ezra Getzler
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Thomas Koberda - "Residual properties of 3-manifold groups"
Koberda delivers a research level talk at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Sheagan John: Secondary higher invariants, and cyclic cohomology for groups of polynomial growth
Talk by Sheagan John in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on December 2, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Lothar Gottsche - SU(r) Vafa-Witten Invariants and Continued Fractions
This is joint work with Martijn Kool and Thies Laarakker. We conjecture a formula for the structure of SU(r) Vafa-Witten invariants of surfaces with a canonical curve, generalizing a similar formula proven by Laarakker for the monopole contribution. This expresses the Vafa-Witten invariant
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
When invariants are equivalent - Jean Pierre Mutanguha
Short Talks by Postdoctoral Members Topic: When invariants are equivalent Speaker: Jean Pierre Mutanguha Affiliation: Member, School of Mathematics Date: September 28, 2021
From playlist Mathematics
Monika Kudlinska: Quasi-isometries of Free-by-cyclic Groups
Monika Kudlinska, University of Oxford Title: Quasi-isometries of Free-by-cyclic Groups A group is free-by-cyclic if it admits an epimorphism onto the infinite cyclic group with kernel a free group of finite rank. The study of free-by-cyclic groups is largely motivated by the case of 3-man
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Integer-valued Gromov-Witten type invariants - Guangbo Xu
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Integer-valued Gromov-Witten type invariants Speaker: Guangbo Xu Affiliation: Texas A&M University Date: June 03, 2022 Gromov-Witten invariants for a general target are rational-valued but not necessarily int
From playlist Mathematics
Emily Stark: Action rigidity for free products of hyperbolic manifold groups
CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 22, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Virtual Conference
John Pardon: Virtual fundamental cycles and contact homology
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 Jean-Morlet Chair - Lalonde/Teleman
Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 3/5
The main topics will be the intersection theory of tautological classes on moduli space of curves, the enumeration of stable maps via Gromov-Witten theory, and the enumeration of sheaves via Donaldson-Thomas theory. I will cover a mix of classical and modern results. My goal will be, by th
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Fundamental Counting Principle | AND OR Rule | PERMUTATION SERIES | CREATA CLASSES
This is the first video under the PERMUTATION series. This video covers the Fundamental Principle of Counting. And also the concept of AND and OR is discussed in detail. All these with help of Animation & Visual tools. Visit our website: https://creataclasses.com/ For a full-length co
From playlist PERMUTATION