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X-WR-CALNAME:IAS Special Program
BEGIN:VEVENT
UID:d2cfce41-f5cb-42f9-a8e6-bc898cb157f3
DTSTAMP:20210623T002231Z
CREATED:20201123T163627Z
DESCRIPTION:Topic: Statistical physics of random CSPs\n\nSpeakers: Nike Sun
\n\nAffiliation: Massachusetts Institute of Technology\n\nI will describe
recent progress in determination of asymptotic\nbehavior in random constra
int satisfaction problems\, including the\nindependent set problem on rand
om graphs\, random regular NAE-SAT\, and\nrandom SAT. The results include
sharp phase transitions and some\nunderstanding of solution geometry\, par
ticularly in the setting of the\nrandom regular NAE-SAT problem. In this l
ecture I will survey the\nphysics heuristics\, and explain how they lead t
o combinatorial models\nfor the solution geometry\, which form a basis of
mathematical\napproaches to these problems.\n\nThis lecture is based in pa
rt on joint works with Zsolt Bartha\, Jian\nDing\, Allan Sly\, and Yumeng
Zhang.\n\n \n
DTSTART:20210419T190000Z
DTEND:20210419T200000Z
LAST-MODIFIED:20210419T121207Z
LOCATION:Remote Access via Zoom videoconferencing (link below)
SUMMARY:Marston Morse Lectures
URL:https://www.ias.edu/math/events/marston-morse-lectures
END:VEVENT
BEGIN:VEVENT
UID:98924e9e-b9b4-4693-a11e-671b8416f13c
DTSTAMP:20210623T002231Z
CREATED:20210302T194233Z
DESCRIPTION:Topic: Probabilistic analysis of random CSPs\n\nSpeakers: Nike
Sun\n\nAffiliation: Massachusetts Institute of Technology\n\n(This lecture
is related to the preceding lecture\, but I will try to\nmake it self-con
tained as much as possible.) In this lecture I will\nelaborate on some of
the existing mathematical approaches to the study\nof random CSPs\, partic
ularly involving the (first and second) moment\nmethod. We will see that i
mplementing the moment method often reduces\nto the solution of difficult
(non-convex) optimization problems. I\nwill discuss one basic strategy tha
t has been used to solve some of\nthese problems\, which is to (1) use a p
riori estimates to localize the\noptimization to a small neighborhood\, an
d (2) use the contractivity of\ntree recursions and a 'local update' proce
dure to solve the\noptimization within the small neighborhood.\n\nThis lec
ture is based in part on joint works with Zsolt Bartha\, Jian\nDing\, Alla
n Sly\, and Yumeng Zhang.\n \n
DTSTART:20210421T190000Z
DTEND:20210421T200000Z
LAST-MODIFIED:20210421T121039Z
LOCATION:Remote Access via Zoom videoconferencing (link below)
SUMMARY:Marston Morse Lectures
URL:https://www.ias.edu/math/events/marston-morse-lectures-98
END:VEVENT
BEGIN:VEVENT
UID:6e5adfec-3922-4ad2-b796-1c23bf5cfb2e
DTSTAMP:20210623T002231Z
CREATED:20210302T194306Z
DESCRIPTION:Topic: On the Ising perceptron model\n\nSpeakers: Nike Sun\n\nA
ffiliation: Massachusetts Institute of Technology\n\n(This lecture will be
self-contained.) In high dimensions\, what does\nit look like when we tak
e the intersection of a set of random\nhalf-spaces with either the sphere
or the Hamming cube? This is one\nphrasing of the so-called perceptron pro
blem\, whose study originated\nwith a toy model of a very simple neural ne
twork. A non-rigorous\nsolution was given in the 1980s (Gardner\, Derrida\
, Krauth\, Mézard)\nusing methods of statistical physics. Shcherbina and T
irozzi gave a\nrigorous solution to the positive spherical perceptron\, ma
king crucial\nuse of the convexity of this problem. The other cases of the
model are\nnon-convex and remain open problems. I will survey the physics
\nsolution and describe some results for the perceptron on the Hamming\ncu
be.\n\nThis lecture is based on joint work with Jian Ding.\n
DTSTART:20210423T190000Z
DTEND:20210423T200000Z
LAST-MODIFIED:20210423T124103Z
LOCATION:Remote Access via Zoom videoconferencing (link below)
SUMMARY:Marston Morse Lectures
URL:https://www.ias.edu/math/events/marston-morse-lectures-99
END:VEVENT
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