[Ml-stat-talks] Gérard Ben Arous in tomorrow's colloquium at ORFE

Philippe Rigollet rigollet at Princeton.EDU
Mon Nov 19 09:42:27 EST 2012

=== ORFE Colloquium Announcement ===

DATE:   Tuesday, November 20, 2012

TIME:   4:30pm

LOCATION:   Room 101, Sherrerd Hall

SPEAKER:   Gérard Ben Arous. Courant Institute of Mathematical Sciences, NYU

TITLE:   Complexity of Random Smooth Functions of Many Variables 

ABSTRACT:  Can one count the number of critical points for random smooth functions of many variables? 
How complex is a typical random smooth function? 
How complex is the topology of its level sets? 
We study here the simplest case of smooth Gaussian random functions defined on the sphere 
in high dimensions. We show that such a randomly chosen smooth function is very complex, 
i.e. that it’s number of critical points of given index is exponentially large. We also study the 
topology of the level sets of these functions, and give sharp estimates of their Euler 
characteristic. This study, which is a joint work with Tuca Auffinger (Chicago) and partly 
with Jiri Cerny (Vienna), relies rather surprisingly on Large deviations results in Random 
Matrix Theory. 
The main motivation comes from the study of energy landscapes for general spherical spinglasses. Time-permitting, I will detail the interesting picture we get for the complexity of 
these random Hamiltonians.

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