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DTSTART;TZID=America/New_York:20240506T163000
DTEND;TZID=America/New_York:20240506T173000
DTSTAMP:20260524T015244
CREATED:20240319T201629Z
LAST-MODIFIED:20240507T201738Z
UID:10000819-1715013000-1715016600@cmsa.fas.harvard.edu
SUMMARY:Liouville Theory and Weil-Petersson Geometry
DESCRIPTION:Colloquium \nSpeaker: Sarah Harrison (Northeastern University) \nTitle: Liouville Theory and Weil-Petersson Geometry \nAbstract: Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Liouville conformal field theory in the classical (large central charge) limit encodes the geometry of the moduli space of Riemann surfaces. I describe an efficient algorithm to compute the Weil–Petersson metric to arbitrary accuracy using Zamolodchikov’s recursion relation for conformal blocks\, focusing on examples of a sphere with four punctures and generalizations to other one-complex-dimensional moduli spaces. Comparison with analytic results for volumes and geodesic lengths finds excellent agreement. In the case of M_{0\,4}\, I discuss numerical results for eigenvalues of the Weil-Petersson Laplacian and connections with random matrix theory. \nBased on work with K. Coleville\, A. Maloney\, K. Namjou\, and T. Numasawa.
URL:https://cmsa.fas.harvard.edu/event/colloquium-5624/
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/CMSA-Colloquium-05.06.2024.docx-1.png
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DTSTART;TZID=America/New_York:20240513T163000
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DTSTAMP:20260524T015244
CREATED:20240130T151206Z
LAST-MODIFIED:20240508T203329Z
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SUMMARY:Errors and Correction in Cumulative Knowledge
DESCRIPTION:Colloquium \nSpeaker: Madhu Sudan\, Harvard University \nTitle: Errors and Correction in Cumulative Knowledge \nAbstract: Societal accumulation of knowledge is a complex\, and arguably error-prone\, process. The correctness of new units of knowledge depends not only on the correctness of the new reasoning\, but also on the correctness of old units that the new one builds on. If left unchecked\, errors could completely ruin the validity of most of this knowledge so there must some error-correcting going on. What are the error-corrections processes employed in nature and how effective are they? In this talk\, we describe our attempts to model such phenomena using probablistic models – we describe models for growth of cumulative knowledge\, emergence of errors and methods to check for errors and eliminate them. We then analyze in this compound model\, when effects of errors may survive\, and when they are totally eliminated. \nThe central discovery in our work is the following optimistic statement: If we do checking correctly (most of the time) investing just a constant factor (<1) of our effort in checking (and saving the remaining constant factor towards deriving new units of knowledge)\, then effects of errors can be kept in check. Notably the amount of effort expended on checking does not scale with the volume of total knowledge or the depth of dependencies in the new units of knowledge\, either of which would be overwhelming. \nBased on the papers: \nIs this correct? Let’s check!\nOmri Ben-Eliezer\, Dan Mikulincer\, Elchanan Mossel\, Madhu Sudan\narXiv:2211.12301 \nErrors are Robustly Tamed in Cumulative Knowledge Processes\nAnna Brandenberger\, Cassandra Marcussen\, Elchanan Mossel\, Madhu Sudan\narXiv:2309.05638
URL:https://cmsa.fas.harvard.edu/event/colloquium-4124/
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/CMSA-Colloquium-05.13.2024.png
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