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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G-equivariant factorization algebras
Laura Wells University of Notre Dame
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Homotopy types and geometries below Spec(Z)
Matilde Marcolli University of Toronto
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Higher operations in supersymmetric field theory
Andrew Neitzke The University of Texas at Austin
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Vertex models and En-algebras
Damien Calaque University of Montpellier
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The Duistermaat–Heckman distribution for the based loop group
Lisa Jeffrey University of Toronto
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Moduli of connexions on open varieties
Bertrand Toen Paul Sabatier University
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The low-energy TQFT of the generalized double semion model
Arun Debray University of Texas - Austin
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Cutting and gluing branes
David Nadler University of California, Berkeley
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Geometric Langlands: Comparing the views from CFT and TQFT
Joerg Teschner Deutsches Elektronen-Synchrotron DESY