CANCELLED Department of Physics Colloquium CANCELLED
Monday, March 28, 2022 4pm to 5pm
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Central Campus
#physicsCANCELLED General Physics Colloquium, Professor Tara Holm, Math, Cornell University
Title: Understanding Symplectic Geometry through Polytopes and Lattice Points
Host: Itai Cohen
Abstract: Symplectic geometry is the natural geometry of classical and quantum mechanics, where coordinates come in pairs corresponding to position and momentum. Replacing phase spaces with more abstract symplectic manifolds, the laws of physics translate into a way to measure 2-dimensional areas. I will give a guided tour of this part of mathematics and the physics that inspires it. Along the way, we will revisit classical work of Archimedes, the Heisenberg uncertainty principle, and modern applications in low-energy lunar transfer. We will explore how the geometry and topology of symmetries in this context relate to properties of convex shapes called polytopes, motivated by many pictures and examples. I will conclude with how some recent work, of my own and many others, comes to feature continued fractions, counting lattice points, and the Philadelphia subway system.
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This talk will also be available via Zoom, and the link will be emailed to the Physics listserv the week of the talk. If you are not on the listserv, please contact Sue Sullivan at sfc1@cornell.edu by Monday at 3:00 pm to request the link.
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