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DTSTART;TZID=America/New_York:20260506T140000
DTEND;TZID=America/New_York:20260506T150000
DTSTAMP:20260506T045403
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UID:10003154-1778076000-1778079600@www.math.harvard.edu
SUMMARY:New directions in synthetic data
DESCRIPTION:Synthetic data has been an effective\, if boring set of techniques: prompt some language model to restructure your corpus to match some downstream task\, with occasionally some distillation. In this talk\, we will take a more expansive view of synthetic data as a general algorithmic tool for generative modeling\, arguing that the design space and possibilities of synthetic data are much bigger than it might seem. Through a few recent works\, we will show that synthetic data has major benefits beyond transforming the data – improving in-domain perplexities\, and enabling unique algorithmic primitives\, such as neighborhood smoothing and concatenated ‘mega’ documents. With this broader view\, we will point towards a nascent but interesting possibility of treating data itself as an algorithmic object to be engineered and optimized end-to-end. \nZoom: https://harvard.zoom.us/j/91864143060?pwd=liDbUVYXs47QsYhxdzXYowl8vpQGy1.1
URL:https://www.math.harvard.edu/event/new-directions-in-synthetic-data/
LOCATION:Virtually
CATEGORIES:CMSA NEW TECHNOLOGIES IN MATHEMATICS
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DTSTART;TZID=America/New_York:20260506T150000
DTEND;TZID=America/New_York:20260506T160000
DTSTAMP:20260506T045403
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LAST-MODIFIED:20260430T132252Z
UID:10003164-1778079600-1778083200@www.math.harvard.edu
SUMMARY:Formalization of QFT
DESCRIPTION:Interactive theorem proving with the Lean 4 theorem prover\, Mathlib and AI coding assistants has recently become a powerful method for checking and developing rigorous mathematical proofs. In this talk we introduce the technology and survey recent works using it in mathematical physics. These include the construction of the free massive bosonic field and verification of the Osterwalder-Schrader axioms\, and work in progress to formalize the OS reconstruction theorem\, the construction of P(\phi)_2 theory\, and the proof of the Yang-Mills mass gap at strong coupling. Joint work with Sarah Hoback\, Anna Mei\, Ron Nissim\, Matteo Cipollina and Xi Yin. \nIn-person only\, to be posted after the talk on https://www.youtube.com/@mathematicalpicturelanguag2715/videos
URL:https://www.math.harvard.edu/event/formalization-of-qft/
LOCATION:Jefferson Lab 368\, 17 Oxford St\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MATHEMATICAL PICTURE LANGUAGE
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DTSTART;TZID=America/New_York:20260506T161500
DTEND;TZID=America/New_York:20260506T171500
DTSTAMP:20260506T045403
CREATED:20260504T172120Z
LAST-MODIFIED:20260504T172120Z
UID:10003167-1778084100-1778087700@www.math.harvard.edu
SUMMARY:L-log-concavity and a proof of the conjecture of Lam\, Postnikov and Pylyavskyy
DESCRIPTION:Let lambda\, mu\, lambda’\, mu’ be partitions. The conjecture of Lam\, Postnikov and Pylyavskyy states that\, if (lambda\, mu\, lambda’\, mu’) obey certain natural inequalities\, then s_{lambda’} s_{mu’} – s_{lambda} s_{mu} is Schur nonnegative. We prove this conjecture. Our proof is based on two key ideas. First\, we introduce a new combinatorial model for Littlewood-Richardson coefficients which we name “skeps”\, which are similar to but distinct from Knutson and Tao’s hives. Second\, we use tools from Murota’s theory of L-convexity to prove an L-log-concavity theorem for skeps. \nFor information about the Richard P. Stanley Seminar in Combinatorics\, visit… https://math.mit.edu/combin/
URL:https://www.math.harvard.edu/event/l-log-concavity-and-a-proof-of-the-conjecture-of-lam-postnikov-and-pylyavskyy/
LOCATION:MIT\, Room 2-132
CATEGORIES:HARVARD-MIT COMBINATORICS
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