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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Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Lagrangian Relations, HalfDensities and BV Fiber Integrals
Jan Pulmann University of Edinburgh

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Quantum Field Theory for Cosmology  Lecture 20240404
Achim Kempf University of Waterloo

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

SAGBI bases and mirror constructions for Kronecker moduli spaces
Elana Kalashnikov University of Waterloo