*讲座内容简介：
Various compatibility conditions among replicated copies of operations in a given algebraic structure have appeared in broad contexts in recent years. Taking an uniform approach, this paper gives an operadic study of compatibility conditions for nonsymmetric operads with unary and binary operations, and homogeneous quadratic and cubic rela...
摘要：We would describe various vanishing theorems involving multiplier ideals and give various applications to linear systems, birational geometry and commutative algebra.
*讲座内容简介：
A relation between the finite W-superalgebras and finite W-algebras was found in one of my work joint with Bin Shu. This relation turns out to be very useful in the representation theory of finite W-superalgebras. In this talk I first introduce this rel...
*讲座内容简介：
In this talk, we establish the cohomology of the relative Rota-Baxter operators on Lie-Yamaguti algebras using the Yamaguti cohomology. Then we use this type of cohomology to characterize the deformations of the relative Rota-Baxter operators on Lie-Yamaguti algebras. We show that if two linear or formal deformations of a relative Rota-Bax...
*讲座内容简介：
Derived Algebraic Geometry (DAG) allows us to extend Grothendieck's theory of projectivizations and Grassmannians from sheaves to complexes. This extension proves valuable for constructing and studying moduli spaces, especially in the presence of singularities. In this talk, we discuss the construction and properties of derived projectivizat...
Witten deformation is a versatile tool with numerous applications in mathematical physics and geometry. In this talk, we will focus on the analysis of Witten deformation for a family of non-Morse functions, leading to a new proof of the gluing formula for analytic torsions. Then we could see that the gluing formula can be reformulate...
主持人：邹燕清
报告时间：2020年6月6日 14:00-15:00
报告平台：ZOOM会议 ID: 274 175 4144 ，密码：930643
https://cernet.zoom.com.cn/j/2741754144?pwd=TzRiV0gwT2l0NU1CRWtmODlpRUdrZz09
报告人简介：王家军 国家杰出青年获得者
报告内容摘要：
The geometrization theorem implies that the fundamental group of a 3-manifold determines the 3-manifold, except the lens spac...
摘要： We say that a rational map f is regularly ramified if there exists a group G of confromal automorphisms of complex sphere, so that two points p and q of the complex sphere have the same image if and only if there is a group element g in G with g(p)=q. In this talk, we survey some of our recent results on the dynamics of regularly ramified rational maps. These are joint works with Jun Hu ...
摘要：It is shown that the boundary $\partial B$ of any immediate root basin $B$ of $f$ is locally connected. Moreover, $\partial B$ is a Jordan curve if and only if ${\rm deg}(f|_B)=2$. This implies that the boundaries of all components of root basins, for all polynomials' Newton maps, from the viewpoint of topology, are tame. This generalizes Roesch's groundbreaking work (Annals of Math. 2008...
Symplectic property is preserved along the mean curvature ow in Kahler-Einstein surface, which is called Symplectic mean curvature ow . It was proved that there is no nite time Type I singularities for the symplectic mean curva ture ow. In this talk, I will rst review known results and then I will talk about an important Type II sing...
*讲座内容简介：
In this talk, we first introduce geometric quantities for capillary hypersurfaces, and then establish isoperimetric type inequalities, Alexandrov-Fenchel inequalities, by studying corresponding geometric flows. We will also talk about a related Minkowski type problem and other related problems. The talk is based on a joint work with Chao Xia...
While the hexagonal lattice is ubiquitous in two dimensions, the body centered cubic lattice and the face centered cubic lattice are both commonly observed in three dimensions. A geometric variational problem motivated by the diblock copolymer theory consists of a short range interaction energy and a long range interaction energy. In...
We prove that for $n=4$ and $6$, axially symmetric solution to the $\mathbb{Q}$-curvature type problem
$$
\alpha P_n u + c_n \left(1 - \frac{e^{nu}}{\int_{S^n}e^{nu}} \right) = 0
$$
on $S^n$ must be constants, provided that $\frac{1}{2} \le \alpha \le 1$. This result is sharp. The proof is based on two ty...
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