Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory
Category Theory 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category Theory
Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
What is the goal of string theory?
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From playlist Science Unplugged: String Theory
There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determ
From playlist Philosophy of Science
Christian Sattler: Do cubical models of type theory also model homotopy types
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: I will give an alternative exposition of Kapulkin and Voevodsky's result about simplicial sets forming a subtopos of certain cubical sets: https://arxiv.org/abs/1805.0412
From playlist Workshop: "Types, Homotopy, Type theory, and Verification"
Is string theory a unified theory?
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From playlist Science Unplugged: String Theory
This video contains the origins of group theory, the formal definition, and theoretical and real-world examples for those beginning in group theory or wanting a refresher :)
From playlist Summer of Math Exposition Youtube Videos
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
Geometry of the moduli space of curves – Rahul Pandharipande – ICM2018
Plenary Lecture 3 Geometry of the moduli space of curves Rahul Pandharipande Abstract: The moduli space of curves, first appearing in the work of Riemann in the 19th century, plays an important role in geometry. After an introduction to the moduli space, I will discuss recent directions
From playlist Plenary Lectures
Anne TAORMINA - Mathieu Moonshine: Symmetry Surfing and Quarter BPS States at the Kummer Point
The elliptic genus of K3 surfaces encrypts an intriguing connection between the sporadic group Mathieu 24 and non-linear sigma models on K3, dubbed “Mathieu Moonshine”. By restricting to Kummer K3 surfaces, which may be constructed as Z2 orbifolds of complex 2-tori with blown up singularit
From playlist Integrability, Anomalies and Quantum Field Theory
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
Federico Zerbini - Amplitudes de cordes et équations de type Knizhnik–Zamolodchikov
Les amplitudes de diffusion nous donnent la probabilité d'interaction des particules élémentaires. L'approche perturbative nous amène à considérer une série dont les coefficients sont calculés par les intégrales de Feynman. En théorie des cordes, un tel développement perturbatif est indexé
From playlist 10e séminaire ITZYKSON – Valeurs zêta multiples et fonctions modulaires de graphes en théorie des cordes
Counting embedded curves in symplectic 6-manifolds - Aleksander Doan
Symplectic Dynamics/Geometry Seminar Topic: Counting embedded curves in symplectic 6-manifolds Speaker: Aleksander Doan Affiliation: Columbia University Date: February 03, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Holomorphic Curves and the ADHM Vortex Equations by Aleksander Doan
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Siegel modular forms: Classical and adelic aspects by Ameya Pitale
PROGRAM : ALGEBRAIC AND ANALYTIC ASPECTS OF AUTOMORPHIC FORMS ORGANIZERS : Anilatmaja Aryasomayajula, Venketasubramanian C G, Jurg Kramer, Dipendra Prasad, Anandavardhanan U. K. and Anna von Pippich DATE & TIME : 25 February 2019 to 07 March 2019 VENUE : Madhava Lecture Hall, ICTS Banga
From playlist Algebraic and Analytic Aspects of Automorphic Forms 2019
Elliptic Curves - Lecture 1 - Introduction to diophantine equations
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Thorsten Altenkirch - 1/2 Towards a Syntax for Cubical Type Theory
One of the key problems of Homotopy Type Theory is that it introduces axioms such as extensionality and univalence for which there is no known computational interpretation. We propose to overcome this by introducing a Type Theory where a heterogenous equality is defined recursively and equ
From playlist T2-2014 : Semantics of proofs and certified mathematics
Charles Rezk: Elliptic cohomology and elliptic curves (Part 1)
The lecture was held within the framework of the Felix Klein Lectures at Hausdorff Center for Mathematics on the 1. June 2015
From playlist HIM Lectures 2015