时间：2025年12月12日（星期五）上午8：50-12：10，下午15:00-17:30。
地点：数统院245教室
报告信息（Titles and Abstracts）
Curvature of Complex Bundles and Invariant Subspaces Operators
Chunlan Jiang
Hebei Normal University
Abstract:In this report, we prove that every operator with a spectral rad-ius strictly less than 1 can induces a complex Hermitian holomorphic bu-ndle. Furthmore,by using techniques of complex geometry and curvature of bundles, we show that a class of operators with ideal propert have non-trivial invariant subspaces, thereby providing a partial affirmative answer to von Neumann's problem.
On Klee's convex body problem
Lixin Cheng
Xiamen University
Abstract:(This is a joint work with Prof. Chunlan Jiang and Prof.Liping Yuan) It is well known that every convex body in a finite dime-nsional normed space can be uniformly approximated by strictly convex and smooth convex bodies. However, in the case of infinite dimensions, little progress has been made since Klee asked how it is in the case of infinite dimensions in 1959. In this talk,we show that for an infinite di-mensional Banach space $X$, (1) every convex body can be uniformly approximated by strictly convex bodies if and only if $X$ admits an equivalent strictly convex norm; (2) every convex body can be uniformly approximated by G\^{a}teaux smooth convex bodies if the dual $X^*$ of $X$ admits an equivalent strictly convex dual norm; (3) If $X$ admits an equivalent strictly convex norm such that its dual is also strictly conv-ex on $X^*$, then every convex body can be uniformly approximated by strictly convex and G\^{a}teaux smooth convex bodies; in particular, (4) if $X$ is either separable, or reflexive, then every convex body in $X$ can be uniformly approximated by strictly convex and smooth con-vex bodies. They are done by showing that some correspondences among the sets of all convex bodies endowed with the Hausdorff metric, all continu-ous coercive Minkowski functionals and Fenchel's transform defined on all quadratic homogenous continuous convex functions equipped with the metric induced by the sup-norm of all bounded continuous functions defi-ned on the closed unit ball $B_X$ are actually locally Lipschitzisomorp-hisms.
“学数学最需要勇气，老师给足了学生底气”
—谈研究生培养及数学研究
杨大春教授（北京师范大学）
摘要：在此报告中，杨大春教授将结合自己从事基础数学“调和分析及其应用”三十余年的经历，和大家分享在研究生培养和数学研究方面的心得与体会。
Some recent progress on noncommutative martingales
Lian Wu
Central South University
Abstract:In this talk, some important martingale inequalities and their noncommutative counterparts will be introduced. Some recent advances on noncommutative martingale inequalities will be also presented.
Distributional estimates for Marcinkiewicz multipliers
Dmitriy Zanin
UNSW
Abstract:Marcinkiewicz multipliers do not (usually) send $L_1$ to $L_{1,\infty}.$ For operators acting from $L_1$ to $L_{1,\infty},$ a distributional estimate of the shape $$\mu(Tx)\leq c_TS\mu(x)$$ is available (here, $S$ is the Calderon operator). Based on the work of Bakas et al. we found a suitable endpoint estimate replacing the weak $(1,1)$-estimate and proved a general extrapolation result which yields
$$\mu(m(D)f)\leq c_mS^{\frac32}\mu(f)$$ for every Marcinkiewicz multiplier $m$ on $\mathbb{R}.$ We prove similar estimates for comm- utators and for square functions with sharp ends.
Regularity Theory for the Non-Cutoff Boltzmann Equation
Nguyen Quoc Hung(阮国兴)
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Abstract:I will discuss recent progress in understanding the regularity properties of solutions to the non-cutoff Boltzmann equation. The talk will cover new estimates, structural insights, and analytical tools that reveal how the non-cutoff kernel influences smoothing effects and solution behavior.
