FST Distinguished Talk – Recent Progress on Hamilton–Ivey-Type Curvature Pinching for Ricci SolitonsSpeaker: Dr. Huai-Dong CAO from Lehigh UniversityHosted by: Prof. Chang Feng GUI

Dr. Huai-Dong Cao delivered a compelling seminar at the Faculty of Science and Technology of the University of Macau on 8 January 2026, titled “Recent Progress on Hamilton-Ivey-Type Curvature Pinching for Ricci Solitons.” He began with a clear overview of the classical Hamilton-Ivey estimate—central to 3D Ricci flow—which asserts that positive curvature dominates negative curvature near singularities, ensuring non-negative sectional curvature in blow-up limits like steady or shrinking solitons.

He then presented recent joint work with Junming Xie, extending these pinching estimates to higher dimensions and, notably, to asymptotically conical expanding solitons. These advances deepen our understanding of singularity formation and long-time behavior in Ricci flow and offer new tools for classifying soliton geometries.

Dr. Cao’s seminar balanced technical precision with intuitive insight, engaging an audience of students, postdocs, and faculty. The lively Q&A touched on applications to other flows and links to major results like the Poincaré conjecture. His distinguished background—Ph.D. under Shing-Tung Yau, faculty positions at top institutions, and prestigious fellowships—underscored his authority in geometric analysis.

曹懷東博士於2026年1月8日在澳門大學科技學院發表了一場引人入勝的研討會，題為《里奇孤子中哈密頓–艾維型曲率壓縮的最新進展》。他首先清晰地概述了經典的哈密頓–艾維估計——此為三維里奇流理論的核心結果——該估計指出，在奇點附近，正曲率的增長速度超過負曲率的絕對值，從而保證了作為流爆破極限出現的穩態或收縮梯度里奇孤子必具有非負截面曲率。

隨後，他介紹了與謝俊明近期的合作成果，將這類曲率壓縮估計推廣至更高維度，特別是應用於漸近錐形的擴張孤子。這些進展深化了我們對里奇流中奇點形成機制及長時間行為的理解，並為里奇孤子幾何結構的分類提供了新工具。

曹博士的研討會兼具技術嚴謹性與直觀洞見，吸引了眾多學生、博士後研究員及教職員參與。在熱烈的問答環節中，聽眾探討了該理論在其他幾何流（如平均曲率流）中的潛在應用，以及與龐加萊猜想等重大成果的關聯。他卓越的學術背景——師從丘成桐教授取得博士學位，曾任教於哥倫比亞大學、德州農工大學、IPAM等頂尖機構，並榮獲斯隆獎、古根海姆獎及西蒙斯獎等殊榮——充分彰顯了他在幾何分析領域的權威地位。