Abstract: The liquid drop model for atomic nuclei goes back to Gamow in the 1930s and it is widely used in the physics literature to explain qualitatively the critical mass in nuclear fission reactions. However, from the mathematical point of view, many of its fundamental properties remains unknown. I will discuss some rigorous results on the existence and nonexistence of minimizers, as well as the connection of these results to the ionization conjecture for atoms. The talk is based on recent joint work with Rupert L. Frank.

Bio-Sketch: Phan Thanh Nam received his PhD in Mathematics from the University of Copenhagen in 2011. He is currently a Professor at LMU Munich, where his research is centered on analysis and mathematical physics. He was awarded the EMS Prize in 2020 and an ERC grant in 2024 for his contributions to the rigorous analysis of quantum many-body systems.