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UID:20250718T034912EDT-1576BEZ0z8@132.216.98.100
DTSTAMP:20250718T074912Z
DESCRIPTION:CRM-ISM Probability Seminar\n\nTitle: Number of saddles of the 
 pure spherical p-spin model\n\nAbstract:\n\nThe pure spherical p-spin mode
 l is a Gaussian random polynomial H of degree p on an N-dimensional sphere
 \, with N large. The sphere is the state space of a physical system with m
 any degrees of freedom\, and the random function H is an energy landscape.
 \n\nUsing the Kac-Rice formula\, Auffinger\, Ben Arous and Cerny computed 
 the average number of critical points of H with a given index\, and with e
 nergy below a given value. This average is exponentially large in N for p 
 > 2\; the rate of growth\, called the complexity\, is a function of the in
 dex chosen and of the energy cutoff. The complexity describes the topology
  of H: below an energy threshold marking the bottom of the landscape\, all
  critical points are local minima or saddles with an index not diverging i
 n N\, and the complexity reveals a nested structure in these finite-index 
 saddles.\n\nSubag’s remarkable 2017 paper used a second moment approach to
  show the total number of critical points concentrates around its mean. At
  the bottom of the landscape\, the average number of critical points is do
 minated by minima at the exponential scale\, demonstrating that typical be
 havior of the minima reflects their average behavior. We show the number o
 f critical points of any finite\, positive index concentrates around its m
 ean. This is a step towards understanding dynamics in the landscape\, thou
 ght to be related to protein folding and training neural nets. Joint work 
 with Antonio Auffinger at Northwestern.\n\nLink: https://mcgill.zoom.us/j/
 87596694672?pwd=VG5WZjllUFdQVWxjN29rV2RMZDFlUT09\n\nMeeting ID: 875 9669 4
 672\n\nPasscode: problab\n\n \n
DTSTART:20210224T180000Z
DTEND:20210224T190000Z
SUMMARY:Julian Gold (Northwestern)
URL:/mathstat/channels/event/julian-gold-northwestern-
 327894
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