Abstract: The TAP variational formula was orginally proposed by Thouless, Anderson, and Palmer as a method to solve the Sherrington-Kirpatrick model in spin glass theory, but the approach was not quite successful at that time. The critical points of the variational formula are the so called TAP equations which are supposed to be equations satisfied by the random Gibbs means. They are similar to standard equations in means-field theory, but were thought to be less useful due to inherent instability properties. Iterations which are bypassing these instabilities have been found recently, and are presently used in quite a number of applications, also outside spin glass theory, for instance in statistics and artificial intelligence, where they usually are called AMP-algorithms (for "approximate message passing). One application, still essentially inside spin glass theory, was a recent new proof of the Gardner formula in perceptron models. This is based on a joint paper with Shuta Nakajima, Nike Sun, and Changji Xu. If time allows, we also discuss open problems around the perceptron: For instance the possibility of a Sanov type large deviation theorem.

Bio-Sketch: Dr. Erwin Bolthausen received his Ph.D. in 1973 at ETH Zurich under the supervision of Prof. Beno Ekman, specializing in topology. Afterwards, Erwin turned to statistics, where he made fruitful contributions to martingale convergence theorems, combinatorial limit theorems, and large deviations theory. Later, he delved into stochastic models, such as random media, phenomena related to random interfaces, spin glasses and polymers in random media, and made substantial contributions in these areas. In 1990, he became a full professor at the University of Zurich.