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DTSTART;TZID=America/New_York:20211203T093000
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SUMMARY:Black Holes\, 2D Gravity\, and Random Matrices
DESCRIPTION:Member Seminar \nSpeaker: Dan Kapec \nTitle: Black Holes\, 2D Gravity\, and Random Matrices \nAbstract: I will discuss old and new connections between black hole physics\, 2D quantum gravity\, and random matrix theory. Black holes are believed to be very complicated\, strongly interacting quantum mechanical systems\, and certain aspects of their Hamiltonians should be well approximated by random matrix theory. The near-horizon effective dynamics of near-extremal black holes is two-dimensional\, and many theories of 2D quantum gravity are known to have random matrix descriptions. All of these expectations were recently borne out in surprising detail with the solution of the Jackiw-Teitelboim (JT) model\, but this result raises more questions than it answers. If time permits\, I will discuss some extensions of these results and possible future directions.
URL:https://cmsa.fas.harvard.edu/event/12-3-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
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DTSTART;TZID=America/New_York:20211210T093000
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CREATED:20240214T072023Z
LAST-MODIFIED:20240301T110742Z
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SUMMARY:On the solution space of the Ising perceptron model
DESCRIPTION:Member Seminar  \nSpeaker: Changji Xu \nTitle: On the solution space of the Ising perceptron model \nAbstract:  Consider the discrete cube $\{-1\,1\}^N$ and a random collection of half spaces which includes each half space $H(x) := \{y \in \{-1\,1\}^N: x \cdot y \geq \kappa \sqrt{N}\}$ for $x \in \{-1\,1\}^N$ independently with probability $p$. The solution space is the intersection of these half spaces. In this talk\, we will talk about its sharp threshold phenomenon\, the frozen structure of the solution space\, and the Gardner formula.
URL:https://cmsa.fas.harvard.edu/event/12-10-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
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