廣州數(shù)學(xué)大講壇第二期
第十一講——英國巴斯大學(xué)Manuel del Pino教授學(xué)術(shù)報告
題目：Compact Equilibria in the Liquid Drop Model
時間：2026年1月18 日（周日）16:30-18:00
地點：行政西前座334會議室
報告人：Manuel del Pino 教授
摘要：This work addresses the liquid drop model, introduced by Gamow in 1930 and Bohr–Wheeler in 1939, to describe the structure of atomic nuclei in nuclear physics. The problem involves finding a surface in three-dimensional space that is critical for a specific energy functional, balancing surface tension and nonlocal repulsion, subject to a volume constraint. Spherical solutions always exist and minimize the energy for sufficiently small volumes. However, for larger volumes, constructing non-minimizing critical points becomes more challenging. In this study, we present a new class of large-volume solutions, resembling “pearl collars” arranged along an axis in the shape of a large circle, with geometry close to Delaunay's unduloids—surfaces of constant mean curvature. We also construct non-minimizing solutions with small mass that resemble two nearly identical spheres connected by a narrow neck.
This is collaboration with Mónica Musso, Andrés Zú?iga, and Rupert Frank.
報告人簡介：
Manuel del Pino, 英國University of Bath數(shù)學(xué)系教授，國際知名數(shù)學(xué)家，主要從事Analysis of nonlinear partial differential equations, Blow-up patterns in nonlinear evolution problems, Singular limits in variational problems with loss of compactness. Manuel del Pino與合作者在 asymptotic patterns insingular perturbation problems and singularity formation in time dependent settings做出一系列開創(chuàng)新的結(jié)果，開辟了parabolic gluing 方法。 Manuel del Pino已經(jīng)發(fā)表了超過170余篇論文，其中包括了著名的De Giorgi猜想的反例,? 開創(chuàng)新地引進parabolic gluing方法在臨界熱方程， 平面harmonic map flow奇性解的構(gòu)造，在Mathscinet上引用已達7000多次。Manuel的學(xué)術(shù)成果發(fā)表在Ann. of Math., Invent. Math., J. Eur. Math. Soc., CPAM, Duke Math. J. 等國際頂級期刊。 Manuel del Pino獲得過很多榮譽，其中包括2010 ICM 45分鐘報告，2013成為Chilean Academy of Sciences院士，the Chilean National Award in 2013，the recipient of a Research Professorship from the UK Royal Society (2018-2023).
