The computation of observables in general interacting theories, be them quantum
mechanical, field, gauge or string theories, is a non-trivial problem which in many cases can …

We present a concise review of the recent development of relativistic hydrodynamics and its
applications to heavy-ion collisions. Theoretical progress on the extended formulation of …

In these lectures I present a review of non‐perturbative instanton effects in quantum
theories, with a focus on large N gauge theories and matrix models. I first consider the …

We illustrate the physical significance and mathematical origin of resurgent trans-series
expansions for energy eigenvalues in quantum mechanical problems with degenerate …

This highly pedagogical textbook for graduate students in particle, theoretical and
mathematical physics, explores advanced topics of quantum field theory. Clearly divided into …

A bstract A general quantum mechanical or quantum field theoretical system in the path
integral formulation has both real and complex saddles (instantons and ghost-instantons) …

In a large variety of quantum mechanical systems, we show that the full nonperturbative
expression for energy eigenvalues, containing all orders of perturbative, nonperturbative …

In a wide range of quantum theoretical settings—from quantum mechanics to quantum field
theory, from gauge theory to string theory—singularities in the complex Borel plane, usually …

A bstract We derive a system of TBA equations governing the exact WKB periods in one-
dimensional Quantum Mechanics with arbitrary polynomial potentials. These equations …

Expansions of physical functions are controlled by their singularities, which have special
structure because they themselves are physical, corresponding to instantons, caustics or …