The number theory and modular forms behind 8- and 24-dimensional sphere packing

Abstract: Although the solution to the sphere packing and "universal optimality" energy minimization problems in dimensions 8 and 24 have a very analytic flavor, number theory is pervasive behind the scenes. I'll describe the rationality conjectures with Cohn which first pointed to the appearance of modular forms, as well as Viazovska's interpolation ansatz which more directly linked with modular forms, especially for energy minimization. (Joint work with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska.)

algebraic geometrynumber theory

Audience: researchers in the topic

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MIT number theory seminar

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