Sphere Packing and the Conformal Bootstrap: December 14-18, 2020


Organized by Henry Cohn, Thomas Hartman, Dalimil Mazac, Leonardo Rastelli and Maryna Viazovska

This workshop will assemble a group of mathematicians and physicists with diverse expertise to explore a new intriguing connection between discrete geometry and quantum field theory. This connection arises from a recent realization that certain powerful linear programming bounds on sphere packings have a natural interpretation in the language of the conformal bootstrap, and thereby are closely related to novel constraints on theories of quantum gravity.

This workshop will be held via Zoom and streamed live on YouTube for the general public.

For mathematicians interested in learning more about the conformal bootstrap:
– https://arxiv.org/pdf/1602.07982.pdf : lecture notes covering the physical foundations, mathematical formulation and applications of the conformal bootstrap
– https://arxiv.org/pdf/2007.14315.pdf : review talk explaining the bootstrap axioms aimed at mathematicians- https://arxiv.org/pdf/1905.01319.pdf : Section 2 gives a review of the modular bootstrap and Section 4 explains its connection to sphere packing bounds

Talk Schedule

Time Title Speaker
10:00am Introduction to the Conformal Bootstrap for Mathematicians Dalimil Mazac
1:00pm Fast Conformal Bootstrap and High-dimensional Sphere Packing Amir Tajdini

Time Title Speaker
10:00am TBA Henry Cohn
1:00pm Introduction to the crossing equation in higher dimensional CFTs David Simmons-Duffin

Time Title Speaker
10:00am A Quick Introduction to Conic Programming Fernando Oliveira
1:00pm The Siegel-Weil Formula and Quantum Gravity as an Average Alex Maloney

Time Title Speaker
10:00am Microscopic description of Coulomb gases Sylvia Serfaty
1:00pm Sphere packings, universal optimality, and Fourier interpolation Maryna Viazovska

Time Title Speaker
10:00am Modular bootstrap at High energy and Beurling-Selberg Extremization Sridip Pal
1:00pm Sign Uncertainty Felipe Gonçalves