Memories of Henri Epstein by Giovanni Gallavotti

I first met Henri in the early ’70s at IHES. His approachability quickly eased my hesitation about engaging with a scientist of his stature, and he almost immediately offered strong encouragement for my research on the renormalization group in quantum field theory. Since then, we met regularly, at least until the COVID-19 pandemic.

I often visited IHES and was always eager to spend time with Henri to seek his advice and ideas on a wide range of topics. I was particularly impressed by his formidable expertise in holomorphic functions. In the early ’80s, Henri, Pierre Collet, and I began working on SL(2,R), which eventually led us to develop a KAM theory of perturbations of geodesic flows on surfaces of constant negative curvature. This was a long project to which Henri contributed essential ideas and techniques. I remember those two years as an exciting time, filled with frequent new developments, as everyone working in non-Euclidean geometry would expect.

After that, we continued to meet in various places such as Les Houches, Zurich, and, of course, Paris. He helped me understand Mitchell Feigenbaum’s work on universality by patiently explaining it through the lens of his own contributions, often referring back to applications of holomorphic functions. He also explained his work with Jean-Pierre Eckmann, which allowed them to recover classical results in stability theory and normal form theorems for PDEs.

In the ’90s, Henri introduced me to the Linux operating system, demonstrating his remarkable open-mindedness. I owe him particular gratitude for the time he dedicated to this—though brief, it was very intense and effective. During this period, he also returned to quantum field theory, revisiting his early career interests with Jacques Bros and Vladimir Glaser in perturbation theory and scattering amplitudes—their early papers had impressed me even before we first met. He continued to work steadily on quantum fields in anti-de Sitter geometry, introducing new and original ideas and techniques.

I still have vivid memories of my last brief technical discussion with him during the daily tea break at IHES. He was determined to understand the details of a proof on the location of the roots of a class of self-inversive polynomials on the unit circle. I also remember our frequent gourmet meetings at Paris restaurants or at his home with mutual colleagues, often accompanied by his sister Evelyne. Together, we frequently discussed world affairs (particularly French politics), often in Italian—a language he mastered perfectly.

Kindness and availability characterized his personality and served as an example for many. Several young postdocs benefited from his teachings and were inspired by his conferences. The theoretical physics community will miss him. I miss you already, caro amico Henri.

Giovanni Gallavotti, Roma, August 2024