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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Quantum groups from character varieties
Gus Schrader University of California, Berkeley
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Supersymmetric Field Theories for Mathematicians
Kevin Costello Perimeter Institute for Theoretical Physics
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Supersymmetric Field Theories for Mathematicians
Kevin Costello Perimeter Institute for Theoretical Physics
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Mathematical Physics Seminar
Davide Gaiotto Perimeter Institute for Theoretical Physics
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Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group
Giuseppe Sellaroli Perimeter Institute for Theoretical Physics
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Supersymmetric Field Theories for Mathematicians
Kevin Costello Perimeter Institute for Theoretical Physics
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On the mathematics of étale gerbes inspired by physics
Hsian-Hua Tseng Ohio State University
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Supersymmetric Field Theories for Mathematicians
Kevin Costello Perimeter Institute for Theoretical Physics
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Shifted Yangians, loop groups, and (co)products
Alex Weekes University of Saskatchewan
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Supersymmetric Field Theories for Mathematicians
Kevin Costello Perimeter Institute for Theoretical Physics