Quantum Codes and Systolic freedom

Abstract: In work with Hastings we find a two-way street between quantum error correcting codes and Riemannian manifolds. A recent advance in coding theory allows us to produce the first example of a manifolds with $Z_2$-power law-systolic freedom. Specifically we find, for any$e>0$, a sequence of appropriately scaled 11D Riemannian manifolds $M_i$, so that for any dual 4 and 7 dimensional $Z_2$-cycles, $X_i$ and $Y_i$, resp.

$ Vol_4(X_i)*Vol_7(Y_i) > (Vol_{11}(M_i))^{(5/4-e)} $.

differential geometrymetric geometry

Audience: researchers in the discipline

Western Hemisphere colloquium on geometry and physics

Series comments: Description: Biweekly colloquium of geometers and physicists

This weekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from the website) asap after the event.