In mathematics, and especially differential geometry and mathematical physics, gauge theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics should not be confused with the closely related concept of a gauge theory in physics, which is a field theory which admits gauge symmetry. In mathematics theory means a mathematical theory, encapsulating the general study of a collection of concepts or phenomena, whereas in the physical sense a gauge theory is a mathematical model of some natural phenomenon. Gauge theory in mathematics is typically concerned with the study of gauge-theoretic equations. These are differential equations involving connections on vector bundles or principal bundles, or involving sections of vector bundles, and so there are strong links between gauge theory and geometric analysis. These equations are often physically meaningful, corresponding to important concepts in quantum field theory or string theory, but also have important mathematical significance. For example, the Yang–Mills equations are a system of partial differential equations for a connection on a principal bundle, and in physics solutions to these equations correspond to vacuum solutions to the equations of motion for a classical field theory, particles known as instantons. Gauge theory has found uses in constructing new invariants of smooth manifolds, the construction of exotic geometric structures such as hyperkähler manifolds, as well as giving alternative descriptions of important structures in algebraic geometry such as moduli spaces of vector bundles and coherent sheaves. (Wikipedia).
Representation Theory as Gauge Theory - David Ben-Zvi [2016]
Slides for this talk: https://drive.google.com/file/d/1FHl_tIOjp26vuULi0gkSgoIN7PMnKLXK/view?usp=sharing Notes for this talk: https://drive.google.com/file/d/1BpP2Sz_zHWa_SQLM6DC6T8b4v_VKZs1A/view?usp=sharing David Ben-Zvi (University of Texas, Austin) Title: Representation Theory as G
From playlist Number Theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than
From playlist Physics
This is a second lecture on "Stochastic Yang-Mills" by Professor Martin Hairer. For more materials and slides visit: https://sites.google.com/view/oneworld-pderandom/home
From playlist Summer School on PDE & Randomness
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From playlist Science Unplugged: General Relativity
Lecture 6 | String Theory and M-Theory
(October 25, 2010) Leonard Susskind focuses on the different dimensions of string theory and the effect it has on the theory. String theory (with its close relative, M-theory) is the basis for the most ambitious theories of the physical world. It has profoundly influenced our understanding
From playlist Lecture Collection | String Theory and M-Theory
Lecture 5 | New Revolutions in Particle Physics: Standard Model
(February 8, 2010) Professor Leonard Susskind discusses gauge theories. This course is a continuation of the Fall quarter on particle physics. The material will focus on the Standard Model of particle physics, especially quantum chromodynamics (the theory of quarks) and the electroweak th
From playlist Lecture Collection | Particle Physics: Standard Model
Lecture 7 | String Theory and M-Theory
(November 1, 2010) Leonard Susskind discusses the specifics of strings including Feynman diagrams and mapping particles. String theory (with its close relative, M-theory) is the basis for the most ambitious theories of the physical world. It has profoundly influenced our understanding of
From playlist Lecture Collection | String Theory and M-Theory
Particle Physics is Founded on This Principle!
Take your first steps toward understanding gauge field theory, which underlies everything we know about particle physics! Sponsored by Blinkist: Start your free trial and get 25% off! https://www.blinkist.com/elliot Get the notes for free here: https://courses.physicswithelliot.com/notes-
From playlist Field Theory Sequence
Lecture 2 | String Theory and M-Theory
(September 27, 2010) Professor Leonard Susskind discusses how the forces that act upon strings can affect the quantum mechanics. He also reviews many of the theories of relativity that contributed to string theory today. String theory (with its close relative, M-theory) is the basis for t
From playlist Lecture Collection | String Theory and M-Theory
Yang-Mills for mathematicians (Lecture - 01) by Sourav Chatterjee
INFOSYS-ICTS RAMANUJAN LECTURES SOME OPEN QUESTIONS ABOUT SCALING LIMITS IN PROBABILITY THEORY SPEAKER Sourav Chatterjee (Stanford University, California, USA) DATE & TIME 14 January 2019 to 18 January 2019 VENUE Madhava Lecture Hall, ICTS campus GALLERY Lecture 1: Yang-Mills for mathemat
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AMMI Course "Geometric Deep Learning" - Lecture 10 (Gauges) - Taco Cohen
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 10: Gauges • Gauge transformat
From playlist AMMI Geometric Deep Learning Course - First Edition (2021)
The Abel Prize announcement 2019 - Karen Uhlenbeck
0:48 Introduction by Jim Al-Khalili, British physicist and science communicator 2:38 The Abel Prize announced by Hans Petter Graver, President of The Norwegian Academy of Science and Letters 3:44 Citation by Hans Munthe-Kaas, Chair of the Abel committee 12:06 Popular presentation of the pr
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Instantons and Monopoles (Lecture 1) by Sergey Cherkis
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
A Mathematical Introduction to 3d N = 4 Gauge Theories (Lecture 1) by Mathew Bullimore
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Quantum Invariance & The Origin of The Standard Model
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/DonateSPACE In simple terms a gauge theory is one that has mathematical parameters, or “degrees of freedom” that can be changed without affecting the predictions of the theory. Y
From playlist The Map of Quantum Physics Expanded
Line operators and geometry in 3d N=4 gauge theory by Tudor Dimofte
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
Edward Witten - What One Can Hope To Prove About Three-Dimensional Gauge Theory [2012]
Slides for this talk: https://drive.google.com/file/d/1nElawiw308_IYUQlJpTanscZIXqfRY_-/view?usp=sharing Name: Edward Witten Event: Mathematical Foundations of Quantum Field Theory Workshop Event URL: view webpage Title: What One Can Hope To Prove About Three-Dimensional Gauge Theory Date
From playlist Mathematics
Gauge-string duality in lattice gauge theories (Lecture - 02) by Sourav Chatterjee
INFOSYS-ICTS RAMANUJAN LECTURES SOME OPEN QUESTIONS ABOUT SCALING LIMITS IN PROBABILITY THEORY SPEAKER Sourav Chatterjee (Stanford University, California, USA) DATE & TIME 14 January 2019 to 18 January 2019 VENUE Madhava Lecture Hall, ICTS campus GALLERY Lecture 1: Yang-Mills for mathemat
From playlist Infosys-ICTS Ramanujan Lectures
What is the goal of string theory?
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From playlist Science Unplugged: String Theory