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DTSTART;TZID=America/New_York:20230202T123000
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DTSTAMP:20260618T102855
CREATED:20230817T175011Z
LAST-MODIFIED:20240121T174936Z
UID:10001272-1675341000-1675344600@cmsa.fas.harvard.edu
SUMMARY:Neural Optimal Stopping Boundary
DESCRIPTION:Speaker: Max Reppen (Boston University) \nTitle: Neural Optimal Stopping Boundary \nAbstract:  A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments\, some in high dimensions\, are analyzed through this method\, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.
URL:https://cmsa.fas.harvard.edu/event/colloquium_2223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-02.02.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221207T153000
DTEND;TZID=America/New_York:20221207T163000
DTSTAMP:20260618T102855
CREATED:20230807T165823Z
LAST-MODIFIED:20240110T091938Z
UID:10001187-1670427000-1670430600@cmsa.fas.harvard.edu
SUMMARY:Fourier quasicrystals and stable polynomials
DESCRIPTION:Probability Seminar \nNote location change: Science Center Room 300H \nSpeaker: Lior Alon (MIT) \nTitle: Fourier quasicrystals and stable polynomials \nAbstract: 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 non-periodic 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 Pavel Kurasov and Peter Sarnak provided a construction of crystalline measures with ‘good’ convergence (Fourier quasicrystals) using stable polynomials\, a family of multivariate polynomials that were previously used in proving the Lee-Yang circle theorem and the Kadison-Singer conjecture. After providing the needed background\, I will discuss a recent work in progress with Cynthia Vinzant on the classification of these Kurasov-Sarnak measures and their supporting sets. We prove that these sets have well-defined gap distributions. We show that each Kurasov-Sarnak measure decomposes according to the irreducible decomposition of its associated polynomial\, and the measures associated with each irreducible factor is either supported on an arithmetic progression\, or its support has a bounded intersection with any arithmetic progression. Finally\, we construct random Kurasov-Sarnak measures with gap distribution as close as we want to the eigenvalues spacing of a random unitary matrix. \nBased on joint work with Pravesh Kothari.
URL:https://cmsa.fas.harvard.edu/event/probability-12722/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-12.07.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221130T150000
DTEND;TZID=America/New_York:20221130T160000
DTSTAMP:20260618T102855
CREATED:20230807T165526Z
LAST-MODIFIED:20240110T091213Z
UID:10001186-1669820400-1669824000@cmsa.fas.harvard.edu
SUMMARY:Lipschitz properties of transport maps under a log-Lipschitz condition
DESCRIPTION:Probability Seminar \n\nLocation: Room 109\, Harvard Science Center\, 1 Oxford Street\, Cambridge MA 02138\nSpeaker: Dan Mikulincer (MIT) \n\n\nTitle: Lipschitz properties of transport maps under a log-Lipschitz condition \nAbstract: 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 log-Lipschitz condition. \nI will present a construction of a transport map\, constructed infinitesimally along the Langevin flow\, and explain how to analyze its Lipschitz constant. The analysis of this map leads to several new results which apply both to Euclidean spaces and manifolds\, and which\, at the moment\, seem to be out of reach of the classically studied optimal transport theory. \nJoint work with Max Fathi and Yair Shenfeld.
URL:https://cmsa.fas.harvard.edu/event/probability-113022/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.30.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221116T153000
DTEND;TZID=America/New_York:20221116T163000
DTSTAMP:20260618T102855
CREATED:20230802T172705Z
LAST-MODIFIED:20240110T084219Z
UID:10001185-1668612600-1668616200@cmsa.fas.harvard.edu
SUMMARY:Outlier-Robust Algorithms for Clustering Non-Spherical Mixtures
DESCRIPTION:Probability Seminar \n\nSpeaker: Ainesh Bakshi (MIT) \nTitle: Outlier-Robust Algorithms for Clustering Non-Spherical Mixtures \nAbstract: In this talk\, we describe the first polynomial time algorithm for robustly clustering a mixture of statistically-separated\, high-dimensional 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 hyper-contractivity of degree-two polynomials and anti-concentration of linear projections\, which are necessary and sufficient for clustering.
URL:https://cmsa.fas.harvard.edu/event/probability-111622/
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.16.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221109T153000
DTEND;TZID=America/New_York:20221109T163000
DTSTAMP:20260618T102855
CREATED:20230802T172421Z
LAST-MODIFIED:20240110T075312Z
UID:10001184-1668007800-1668011400@cmsa.fas.harvard.edu
SUMMARY:Liouville quantum gravity from random matrix dynamics
DESCRIPTION:Probability Seminar \nSpeaker: Hugo Falconet (Courant Institute\, NYU) \nTitle: Liouville quantum gravity from random matrix dynamics \nAbstract: 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 Fisher-Hartwig asymptotics of Toeplitz determinants with real symbols\, which extends to multi-time settings. I will explain this method and how to obtain multi-time loop equations by stochastic analysis on Lie groups. \nBased on a joint work with Paul Bourgade. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-11922/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.09.22-1.png
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