Intersection theory | Algebraic geometry
In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory. (Wikipedia).
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Trigonometry 8 The Tangent and Cotangent of the Sum and Difference of Two Angles.mov
Derive the tangent and cotangent trigonometric identities.
From playlist Trigonometry
AlgTopReview: An informal introduction to abstract algebra
This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is
From playlist Algebraic Topology
In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
Injective, Surjective and Bijective Functions (continued)
This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.
From playlist Foundational Math
First steps of non-archimedean enumerative geometry - Tony Yue Yu
Short talks by postdoctoral members Topic: First steps of non-archimedean enumerative geometry Speaker: Tony Yue Yu Affiliation: Member, School of Mathematics Date: January 30, 2017 For more video, visit http://video.ias.edu
From playlist Mathematics
Set Theory (Part 18): The Rational Numbers are Countably Infinite
Please feel free to leave comments/questions on the video and practice problems below! In this video, we will show that the rational numbers are equinumerous to the the natural numbers and integers. First, we will go over the standard argument listing out the rational numbers in a table a
From playlist Set Theory by Mathoma
Isabel Vogt - An enriched count of the bitangents to a smooth plane quartic curve - AGONIZE
Recent work of Kass–Wickelgren gives an enriched count of the 27 lines on a smooth cubic surface over arbitrary fields, generalizing Segre’s signed count count of elliptic and hyperbolic lines. Their approach using 𝔸1-enumerative geometry suggests that other classical enumerative problems
From playlist Arithmetic Geometry is ONline In Zoom, Everyone (AGONIZE)
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Game Programming Patterns 6.1 - (Reading) Flyweight Pattern
We read through the Flyweight pattern chapter of the Game Programming Patterns book. Links code - https://github.com/brooks-builds/learning_game_design_patterns twitter - https://twitter.com/brooks_patton book - http://gameprogrammingpatterns.ocm/ -- Watch live at https://www.twitch.tv/
From playlist Game Programming Patterns Book
Weyl groups, and their generalizations in, enumerative geometry II - Okounkov
Hermann Weyl Lectures Topic: Weyl groups, and their generalizations in, enumerative geometry II Speaker: Andrei Okounkov Date: Wednesday, March 16 These lectures will be about enumerative K-theory of curves (and more general 1-dimensional sheaves) in algebraic threefolds. In the firs
From playlist Hermann Weyl Lectures
Weyl groups, and their generalizations, in enumerative geometry I - Andrei Okounkov
Hermann Weyl Lectures Topic: Weyl groups, and their generalizations, in enumerative geometry I Speaker: Andrei Okounkov Date: Tuesday, March 15 These lectures will be about enumerative K-theory of curves (and more general 1-dimensional sheaves) in algebraic threefolds. In the first lec
From playlist Hermann Weyl Lectures
Bertrand Eynard - 3/4 Topological Recursion, from Enumerative Geometry to Integrability
https://indico.math.cnrs.fr/event/3191/ Topological recursion (TR) is a remarkable universal recursive structure that has been found in many enumerative geometry problems, from combinatorics of maps (discrete surfaces), to random matrices, Gromov-Witten invariants, knot polynomials, confor
From playlist Bertrand Eynard - Topological Recursion, from Enumerative Geometry to Integrability
Bertrand Eynard - 2/4 Topological Recursion, from Enumerative Geometry to Integrability
https://indico.math.cnrs.fr/event/3191/ Topological recursion (TR) is a remarkable universal recursive structure that has been found in many enumerative geometry problems, from combinatorics of maps (discrete surfaces), to random matrices, Gromov-Witten invariants, knot polynomials, confor
From playlist Bertrand Eynard - Topological Recursion, from Enumerative Geometry to Integrability
Counting planar (genus 0) degree d curves in P^3 by Ritwik Mukherjee
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Topological Strings and String Dualities (Lecture - 02) by Rajesh Gopakumar
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
Panorama of Mathematics: Andrei Okounkov
Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Andrei Okounkov: "Enumerati
From playlist Panorama of Mathematics
Classification of Real Numbers, Inequalities, and Number Line
I define and discuss Real Numbers their subsets of Rational Numbers, Integers, Whole Numbers, Natural Numbers, and finally Irrational Numbers. I finish with Inequalities and the Number line at 23:53 Find free review test, useful notes and more at http://www.mathplane.com If you'd like to
From playlist Algebra 1