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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Cotangent complexes of moduli spaces and Ginzburg dg algebras
Sarah Scherotzke University of Luxembourg
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Z-algebras from Coulomb branches
Oscar Kivinen California Institute of Technology
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Fundamental local equivalences in quantum geometric Langlands
Gurbir Dhillon Stanford University
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Tate's thesis in the de Rham setting
Sam Raskin The University of Texas at Austin
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Yangians and cohomological Hall algebras of Higgs sheaves on curves
Olivier Schiffmann University of Paris-Saclay
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Singularities of Schubert varieties within a right cell
Martina Lanini University of Rome Tor Vergata
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On the classification of topological phases
Theo Johnson-Freyd Dalhousie University
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Conformal blocks in genus zero, and Elliptic cohomology
Nitu Kitchloo Johns Hopkins University
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Quasi-elliptic cohomology theory and the twisted, twisted Real theories
Zhen Huan Huazhong University of Science and Technology
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Sigma-VOA correspondence
Miranda Cheng Universiteit van Amsterdam