- Series
- School of Mathematics Colloquium
- Time
- Thursday, September 1, 2016 - 11:05am for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Gérard Ben Arous – Courant Institute, NYU
- Organizer
- Christian Houdré

**Please Note:** Link to the Stelson Lecture announcement http://www.math.gatech.edu/news/stelson-lecture-dr-g-rard-ben-arous

This Colloquium will be Part II of the Stelson Lecture. A function of many variables, when chosen at random, is typically
very complex. It has an exponentially large number of local minima or
maxima, or critical points. It defines a very complex landscape, the
topology of its level lines (for instance their Euler characteristic) is
surprisingly complex. This complex picture is valid even in very simple
cases, for random homogeneous polynomials of degree p larger than 2.
This has important consequences. For instance trying to find the minimum
value of such a function may thus be very difficult. The
mathematical tool suited to understand this complexity is the spectral
theory of large random matrices. The classification of the different
types of complexity has been understood for a few decades in the
statistical physics of disordered media, and in particular spin-glasses,
where the random functions may define the energy landscapes. It is also
relevant in many other fields, including computer science and Machine
learning. I will review recent work with collaborators in mathematics
(A. Auffinger, J. Cerny) , statistical physics (C. Cammarota, G. Biroli,
Y. Fyodorov, B. Khoruzenko), and computer science (Y. LeCun and his
team at Facebook, A. Choromanska, L. Sagun among others), as well as
recent work of E. Subag and E.Subag and O.Zeitouni.