报告题目：Quantitative Stability and Geometric Rigidity: Onofri and Heisenberg–Pauli–Weyl

报告摘要：Stability questions ask whether a small deficit in a functional inequality implies that a function is close to an optimizer. This perspective also leads naturally to geometric stability: when an inequality characterizes a model space through the existence of extremizers, does a nearly vanishing deficit force the underlying manifold to be close to that model space? In the first half of the talk, we discuss the quantitative stability of the Trudinger–Moser–Onofri inequality and some of its variants on the two-sphere. In the second half, we turn to a geometric stability problem arising from the Heisenberg–Pauli–Weyl uncertainty principle. We show that a sequence of manifolds with vanishing deficits converges, in the Gromov–Hausdorff sense, to the corresponding model space.

报告人简介：Debabrata Karmakar，印度塔塔基础研究所（TIFR）应用数学中心研究员，博士毕业于塔塔基础研究所。主要研究方向为偏微分方程、非线性椭圆方程、双曲空间上的函数不等式及其定量稳定性。在 JFA、JDE、Adv. Math.、CVPDE 等国际期刊发表论文。代表性成果包括双曲空间上的 Adams 不等式、Poincaré–Sobolev 不等式的定量稳定性，以及具有奇异源项的 Toda 系统解的总质量研究。

报告时间：2026年11月7日 8:30-9:30 Talk 

                2026年11月7日 9:40-10:40 Research Discussion

报告地点：同析4号楼412会议室