**李玉祥**（教授，东南大学数学学院）

**Title**: **Critical mass for supercritical Keller-Segel systems**

**Abstract:** This talk is concerned with a radially symmetric Keller-Segel systems with supercritical sensitivity subjected to homogeneous Neumann boundary conditions. We prove that there exists a critical mass m*, for arbitrary decreasing nonnegative initial data with mass large than m*, the corresponding solution blows up in finite time; for some decreasing nonnegative initial data with mass less than m*, the corresponding solutions are globally bounded. Our results extend that of Winkler's paper [Winkler, Math. Ann., 373 (2019), 1237-1282], where he proved similar results for the system with linear sensitivity.

**何薇 **（副教授，东南大学数学学院）

**Title：Spectrum of compression of the coordinate multiplier**

**Abstract: **Let $\mathcal{H}$ be a reproducing kernel Hilbert space of analytic functions over the unit disk $\mathbb{D}$. Let $T_z:~f\mapsto zf$ be the coordinate multiplier on $\mathcal{H}$. Suppose that $A$ is a zero set for $\mathcal{H}$ and $I_A$ is the invariant subspace for $T_z$ determined by $A$. Under some mild conditions, we prove that the spectrum of the compression of $T_z$ on $\mathcal{H}\ominus I_A$ is the closure of $A$. Since the reproducing kernel Hilbert spaces considered in this paper cover many classical spaces of analytic functions, such as Hardy space, Bergman space, some weighted Bergman spaces and etc., our approach is a uniform one, mainly based on operator theory, which covers the specific result in specific space.

**徐新冬**（副教授，东南大学数学学院）

**Title：KAM Type Theorem with Liouvillean frequncy for PDEs**

**Abstract:** We study the 1D Schrodinger equation forced by Liouvillean frequency. Quasi periodic solutions with Liouvillean frequency are constructed.