Eric DeGiuli joined the IPM in April 2017. He obtained his Ph.D at the University of British Columbia in 2013 and did a first postdoc split between NYU (2013-2015) and Ecole Polytechnique Federale de Lausanne (2015-2017). One thread of his work is on the rheological and vibrational properties of amorphous matter near rigidity transitions. With Matthieu Wyart (EPFL), Edan Lerner (Amsterdam) and Gustavo Düring (Santiago, Chile) he worked on the mean-field theory of amorphous solids from the elementary-excitation perspective. In particular, he used the coherent potential approximation to derive the phase diagram of amorphous solids near their solid-fluid transition and compute the anomalous vibrational properties of colloidal glasses near the jamming point. With Wyart, Lerner, and Düring, he also worked on the rheology of dense flows of hard particles. With the ansatz that configurations of particles in flow are similar to marginal packings that have been forced, they proposed a theory for the exponents characterizing flow of hard frictionless particles. These exponents inherit anomalous behavior from the singular distribution of forces and particle gaps at the jamming point. The theory is in quantitative agreement with precise numerical simulations, both for viscous flows, modelling dense suspensions, and inertial flows, modelling emulsions and foams.

This work continued with the characterization of dense flow of frictional particles. He discovered that such flow is characterized by a new exponent, which states that steady flows have a large population of particle-particle contacts just on the verge of slipping. With Wyart he showed that an instability mechanism due to mechanical noise, acting on this population, can explain the hysteretic behavior of granular media, believed to be the root cause of dynamic triggering of earthquakes [37].

Together with an approach, using the replica method, by G Parisi, J Kurchan, F Zamponi, and others, the mean-field theory of amorphous matter is now well developed. Since joining the IPM, Eric has been pursuing a field-theoretical formalism that promises to go beyond mean-field. Retaining the basic insight that disorder is defined by mechanical constraints, the field theory is restricted to metastable states, generalizing what has been called an Edwards ensemble, after SF Edwards. In a first series of works, he showed that this formalism parsimoniously explains long-range correlations of stress in amorphous matter [38,39]. Moreover he extracted equations of state and field equations, and showed that for packings of repulsive particles, new terms are needed, which bring the theory close to Liouville gravity [39]. He is currently using this formalism to probe anomalous vibrational properties induced by long-range stress correlations.

A second thread of work concerns the generative, or linguistic, aspect of complex systems. Life is written in the language of DNA ; protein structure is written in a language of amino acids, and human endeavour is often written in text. Are there universal aspects of the relationship between sequence and structure ? In an attempt to answer this question, Eric is initiating the statistical mechanics of language, using the framework of generative grammar. In a first work, he showed that a simple model of random languages has a nontrivial transition marking the emergence of information-propagation in language [40]. He is currently working on theory to explain the observations in [40].