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.
Format results
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Symplectic duality and a presentation of the cohomology of Nakajima quiver varieties
Alex Weekes University of Saskatchewan
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2-associahedra and functoriality for the Fukaya category
Nathaniel Bottman Northeastern University
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Geometric Langlands and symplectic duality
Davide Gaiotto Perimeter Institute for Theoretical Physics
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Holomorphic Floer Quantization
Yan Soibelman Kansas State University
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Representations of truncated shifted Yangians and symplectic duality
Joel Kamnitzer University of Toronto
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Basic aspects of 3d N=4 theories and symplectic duality
Kevin Costello Perimeter Institute for Theoretical Physics
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Half-BPS boundary conditions in 3d N=4 theories
Davide Gaiotto Perimeter Institute for Theoretical Physics
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Boundaries and D-modules in 3d N=4 theories
Tudor Dimofte University of Edinburgh
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Introduction to symplectic duality
Davide Gaiotto Perimeter Institute for Theoretical Physics