The award recognizes his remarkable work on the long-time behaviour of solutions to fundamental equations of mathematical physics, in particular on the asymptotic stability of soliton solutions and the dynamics of multi-solitons.
The 2025 ICTP-IMU Ramanujan Prize Ceremony will take place in the Budinich Lecture Hall at 15:00 hrs on Tuesday 9 December 2025, and will include a lecture titled ‘The asymptotic stability of kinks in scalar field models' by Prof. Claudio Muñoz.
Abstract: In this talk, we will review the asymptotic stability problem of the 1+1 dimensional kinks in one dimensional scalar field models, concentrating efforts in the phi4 model. This is an old well-known problem in mathematical physics. The first ingredient is the kink, a special static solution present in many models. The second ingredient is the long-time behaviour of perturbations of this simple solution. Since Segur and Kruskal in the early 1980s, many researchers have studied this problem, arguing that the convergence of perturbations of the kink solution as time t tends to infinity is of order O(t^{-1/2}). Mathematically speaking, proving this fact is still an open problem in the case of general perturbations in the energy space (and any other general subspace). Recent results are promising: working with odd data only, one can effectively prove convergence. We will discuss the main difficulties appearing in this problem, new insights and the most recent results in this direction.
Light refreshments will be served after the ceremony.
The event will be livestreamed.
ICTP administers the ICTP-IMU Ramanujan Prize jointly with the International Mathematical Union (IMU). The prize is awarded annually to a researcher from a developing country who is less than 45 years of age on 31 December of the year of the award, and who has conducted outstanding research in a developing country. Researchers working in any branch of the mathematical sciences are eligible.
* Claudio Muñoz studied mathematical engineering and astronomy at the University of Chile, under the supervision of Prof. Manuel del Pino. He obtained a PhD in mathematics in 2010 at the University of Versailles Saint-Quentin, France, under the supervision of professors Yvan Martel and Frank Merle. Between 2011 and 2013 he was appointed L.E. Dickson instructor at the University of Chicago, United States, where Carlos Kenig was his postdoctoral mentor. Muñoz has been Chargé de Recherche CNRS (on leave) since 2013, and he has been Full Professor at the University of Chile and a principal investigator at the Center for Mathematical Modelling (CMM) since 2020. Between 2022 and 2024 he was head of the Mathematical Engineering Department. His main research interests are in nonlinear dispersive equations. In particular, he has been studying the asymptotic stability of the phi4 kink, in collaboration with M. Kowalczyk and Y. Martel. More recently, he has addressed new synergies between partial differential equations (PEDs) and number theory problems, and the mathematics of deep neural networks in PDEs.