
Speaker: Lior AlonTitle: Fourier quasicrystals and stable polynomialsVenue: Harvard Science CenterProbability Seminar Note location change: Science Center Room 300H Speaker: Lior Alon (MIT) Title: Fourier quasicrystals and stable polynomials Abstract: The Poisson summation formula says that the countable sum of exp(int), over all integers n, vanishes as long as t is not an integer multiple of 2 pi. Can we find a nonperiodic discrete set A, such that the sum of exp(iat), over a in A, vanishes for all t outside of a discrete set? The surprising answer is yes. Yves Meyer called the atomic measure supported on such a set a crystalline measure. Crystalline measures provide another surprising connection between physics (quasicrystals) and number theory (the zeros of the Zeta and L functions under GRH). A recent work of… 

Speaker: Dan MikulincerTitle: Lipschitz properties of transport maps under a logLipschitz conditionVenue: Harvard Science CenterProbability Seminar Location: Room 109, Harvard Science Center, 1 Oxford Street, Cambridge MA 02138 Speaker: Dan Mikulincer (MIT) Title: Lipschitz properties of transport maps under a logLipschitz condition Abstract: Consider the problem of realizing a target probability measure as a push forward, by a transport map, of a given source measure. Typically one thinks about the target measure as being ‘complicated’ while the source is simpler and often more structured. In such a setting, for applications, it is desirable to find Lipschitz transport maps which afford the transfer of analytic properties from the source to the target. The talk will focus on Lipschitz regularity when the target measure satisfies a logLipschitz condition. I will present a construction of… 

Speaker: Ainesh BakshiTitle: OutlierRobust Algorithms for Clustering NonSpherical MixturesVenue: CMSA, 20 Garden St, G10Probability Seminar Speaker: Ainesh Bakshi (MIT) Title: OutlierRobust Algorithms for Clustering NonSpherical Mixtures Abstract: In this talk, we describe the first polynomial time algorithm for robustly clustering a mixture of statisticallyseparated, highdimensional Gaussians. Prior to our work this question was open even in the special case of 2 components in the mixture. Our main conceptual contribution is distilling analytic properties of distributions, namely hypercontractivity of degreetwo polynomials and anticoncentration of linear projections, which are necessary and sufficient for clustering. 

Speaker: Hugo FalconetTitle: Liouville quantum gravity from random matrix dynamicsVenue: CMSA Room G10Probability Seminar Speaker: Hugo Falconet (Courant Institute, NYU) Title: Liouville quantum gravity from random matrix dynamics Abstract: The Liouville quantum gravity measure is a properly renormalized exponential of the 2d GFF. In this talk, I will explain how it appears as a limit of natural random matrix dynamics: if (U_t) is a Brownian motion on the unitary group at equilibrium, then the measures $det(U_t – e^{i theta}^gamma dt dtheta$ converge to the 2d LQG measure with parameter $gamma$, in the limit of large dimension. This extends results from Webb, Nikula and Saksman for fixed time. The proof relies on a new method for FisherHartwig asymptotics of Toeplitz determinants with real symbols, which extends to multitime settings. I will explain this… 