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# Satellite Seminar of Tsukuba Workshop for Young Mathematicians

Satellite Seminar of Tsukuba Workshop for Young Mathematicians

ZHANG Qing and LU Jinpeng

1/31 (Thu) 10:20--12:30

10:20--11:20   ZHANG Qing
Title  On Torsionfree simple $\mathfrak{A}_1$-modules

The problems of determining the irreducible representations of the Lie algebra $\mathfrak{sl}_2$ and of the Weyl algebra $\mathfrak{A}_1$ has been solved by Richard E. Block in 1981. Let$\mathfrak{A} = \mathfrak{A}_1(\mathbb{Q})$ be the associative algebra $\mathbb{Q}[q; p]$ with two generators p, qsubject to the relation pq - qp = 1 and $\mathfrak{B} = \mathfrak{B}(\mathbb{Q}) = \mathbb{Q}(q)[p]$.In this talk,I will explain how to determine the socle of $\mathfrak{B}/\mathfrak{B}b$ ($b\in \mathfrak{B}$ is irreduclible) as $\mathfrak{A}$-module which gives all of the $S = \mathbb{Q}[q]-\{0\}$-torsion free simple$\mathfrak{A}$-modules.

11:30--12:30   LU Jinpeng
Title  Curvature estimates on stable CMC hypersurfaces
We will discuss curvature estimates and Bernstain-type theorems on stable CMC hypersurfaces. We will also talk about techniques to derive local curvature estimates.