Mathematical physics, including mathematics, is a research area where novel mathematical techniques are invented to tackle problems in physics, and where novel mathematical ideas find an elegant physical realization. Historically, it would have been impossible to distinguish between theoretical physics and pure mathematics. Often spectacular advances were seen with the concurrent development of new ideas and fields in both mathematics and physics. Here one might note Newton's invention of modern calculus to advance the understanding of mechanics and gravitation. In the twentieth century, quantum theory was developed almost simultaneously with a variety of mathematical fields, including linear algebra, the spectral theory of operators and functional analysis. This fruitful partnership continues today with, for example, the discovery of remarkable connections between gauge theories and string theories from physics and geometry and topology in mathematics.
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PSI 13/14 - Complex Analysis - Lecture 1
Perimeter Institute for Theoretical Physics -
The closest cousins of quantum theory from three simple principles
Government of the United Kingdom -
Quantum Tasks in Minkowski Space
University of Cambridge -
Relaxation in Driven Integer Quantum Hall Edge States
University of Oxford -
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Curvature Flows in Complex Geometry
Princeton University -
A Theorem of Existence for Asymptotically Conical Calabi-Yau Manifolds
McMaster University -
A Geometric Framework for Integrable Systems
University of California, Irvine -
Flat Bundles and Grassmann Framings
McGill University