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DTSTART;TZID=America/New_York:20240913T120000
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DTSTAMP:20260622T021747
CREATED:20240907T183113Z
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UID:10003414-1726228800-1726232400@cmsa.fas.harvard.edu
SUMMARY:Abundance for mixed characteristic threefolds
DESCRIPTION:Member Seminar \nSpeaker: Iacopo Brivio (CMSA) \nTitle: Abundance for mixed characteristic threefolds \nAbstract: The Minimal Model Program (MMP) predicts that every algebraic variety X is birational to either a fibration in Fano varieties\, or it admits a “minimal model” X’\, that is a birational model with nef canonical bundle K_X’. The Abundance conjecture predicts then that K_X’ is actually semiample\, in particular it endows X’ with the structure of a Calabi-Yau fibration. These conjectures were initially phrased for complex varieties\, but more recently there has been a lot of interest in working over positive characteristic fields\, or even mixed characteristic rings. In this talk I will give a broad overview of the subject\, starting from the case of complex surfaces. In the last part I will outline a proof of the Abundance conjecture for mixed characteristic threefolds (based on joint work with F. Bernasconi and L. Stigant).
URL:https://cmsa.fas.harvard.edu/event/member-seminar_91324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-09.13.24.png
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DTSTART;TZID=America/New_York:20240913T143000
DTEND;TZID=America/New_York:20240913T170000
DTSTAMP:20260622T021747
CREATED:20240723T202450Z
LAST-MODIFIED:20240911T134726Z
UID:10003401-1726237800-1726246800@cmsa.fas.harvard.edu
SUMMARY:Freedman CMSA Seminar
DESCRIPTION:Freedman CMSA Seminar \n  \n2:00-3:30 pm ET \nSpeaker: Mike Freedman\, Harvard CMSA \nTitle: Detecting hidden structures in linear maps \nAbstract: I’ll consider the problem of detecting spectral features and tensor structures within linear maps both in a quantum and classical contexts. In the quantum context there is the question of whether a Hamiltonian is local\, and if so\, local in distinct coordinate systems (a “duality”). Also\, in the case of a unitary described by a quantum circuit\, does it possess unusual spectral features or tensor structure? In ML one optimizes many linear maps. How would we know – and would we care – if the resulting maps (approximately) tensor factored? \n  \n3:30-4:00 pm ET \nBreak/Discussion \n  \n4:00-5:30 pm ET \nSpeaker: Ryan O’Donnell\, Carnegie Mellon University \nTitle: Quartic quantum speedups for planted inference \nAbstract: Consider the following task (“noisy 4XOR”)\, arising in CSPs\, optimization\, and cryptography. There is a ‘secret’ Boolean vector x in {-1\,+1}^n. One gets m randomly chosen pairs (S\, b)\, where S is a set of 4 coordinates from [n] and b is x^S := prod_{i in S} x_i with probability 1-eps\, and -x^S with probability eps. Can you tell the difference between the cases eps = 0.1 and eps = 0.5? \nIt depends on m. The best known algorithms use the “Kikuchi method” and run in time ~n^L when m ~ n^2/L. We will review this method\, and also show that the running time can be improved to roughly n^{L/4} with a quantum algorithm. \nJoint work with Alexander Schmidhuber (MIT)\, Robin Kothari (Google)\, and Ryan Babbush (Google).
URL:https://cmsa.fas.harvard.edu/event/freedman_91324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-09.13.2024.png
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