主講人：王克磊 武漢大學(xué)教授

時(shí)間：2026年1月6日16：00

地點(diǎn)：徐匯校區(qū)三號(hào)樓301室

舉辦單位：數(shù)理學(xué)院

主講人介紹：王克磊，武漢大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授， ICCM 數(shù)學(xué)銀獎(jiǎng)、ICCM 若琳獎(jiǎng)、中國(guó)數(shù)學(xué)會(huì)鐘家慶獎(jiǎng)。
研究方向?yàn)榉蔷€(xiàn)性偏微分方程、變分法和幾何測(cè)度論，在 Allen-Cahn 方程、超臨界集中現(xiàn)象、DeGiorgi 猜想以及非線(xiàn)性橢圓方程的穩(wěn)定解和有限 Morse 指標(biāo)解的分類(lèi)等問(wèn)題上做出一系列突出貢獻(xiàn)。
在 Bubbling/blow up (Crelle、Poincare、JFA) ；反應(yīng)擴(kuò)散方程與行波解 (ARMA、MA.、JMPA)；Allen-Cahn 方程 (CPAM、JEMS、Crelle、Poincare、CPDE、ARMA、AiM、JMPA、TAMS)；有限 Morse 指標(biāo) (AiM、MA、CVPDE)；競(jìng)爭(zhēng)系統(tǒng) (CPDE、Poincare、AiM、MA、TAMS、JFA) 等高水平期刊發(fā)表論文 50 篇。

內(nèi)容介紹：It is known that the singular limits of Allen-Cahn equations with fractional Laplacian $(-\Delta)^s$ ($0 ＜ s ＜ 1/2$) are nonlocal minimal hypersurfaces (introduced by Caffarelli-Roquejoffre-Savin in [Comm. Pure Appl. Math. 2010]). For energy minimizers, this correspondence was established by Savin and Valdinochi via the $\Gamma$-convergence method.
In this talk, we discuss the case of general critical points. By using the quantitative stratification theory developed by Cheeger-Naber and Naber-Valtorta, we derive precise estimates for transition layers in fractional Allen-Cahn equations. These estimates imply that general critical points converge to nonlocal minimal hypersurfaces, which is substantially better than the convergence behavior observed in classical Allen-Cahn equations.
The talk is based on two joint works with Vincent Millot and Yannick Sire, Juncheng Wei and Ke Wu.