Video Lectures

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Informally, uncertainty principle says that function and its Fourier transform can not be both concentrated. Uncertainty principle has a lot of applications in areas like compressed sensing, error correcting codes, number theory and many others. In...

We study some problems relating to polynomials evaluated either at random Gaussian or random Bernoulli inputs. We present some new work on a structure theorem for degree-d polynomials with Gaussian inputs. In particular, if p is a given degree-d...

We propose an “analytical” framework for studying parallel repetitions of one-round two-prover games. We define a new relaxation of the value of a game, val+, and prove that it is both multiplicative and a good approximation for the true value of...

Homotopy Theory in Type Theory

"Homotopy Group"- (1)Dan Licata, (2)Guillaume Brunerie, (3)Peter Lumsdaine

In this general survey talk, we will describe an approach to doing homotopy theory within Univalent Foundations. Whereas classical homotopy theory may be described as "analytic", our approach is synthetic in the sense that, in ``homotopy type theory...