矩映射与等变体积

An intertwining relation for equivariant Seidel maps

The Seidel maps are two maps associated to a Hamiltonian circle action on a convex symplectic manifold, one on Floer cohomology and one on quantum cohomology. We extend their definitions to $S^1$-equivariant Floer cohomology and $S^1$-equivariant quantum cohomology based on a construction of Maulik and Okounkov. The $S^1$-action used to construct $S^1$-equivariant Floer cohomology changes after applying the equivariant Seidel map (a similar phenomenon occurs for $S^1$-equivariant quantum cohomology). We show the equivariant Seidel map on $S^1$-equivariant quantum cohomology does not commute wi…

矩映射与等变Szego核

Moment maps and equivariant Szego kernels

设给定极化复射影流形$(M,L)$上紧致半单李群的一个Hamilton作用.本文利用微局部技巧研究了由$G$的作用和不可约表示定义的$M$上线性级数的局部和整体渐近行为。

Burnside groups and orbifold invariants of birational maps

We construct new invariants of equivariant birational isomorphisms taking values in equivariant Burnside groups.

An Introduction to Higgs Bundles via Harmonic Maps

This survey studies equivariant harmonic maps arising from Higgs bundles. We explain the non-abelian Hodge correspondence and focus on the role of equivariant harmonic maps in the correspondence. With the preparation, we review current progress towards some open problems in the study of equivariant harmonic maps.

Chow groups and equivariant geometry

Observations on rational Chow groups and cycle class maps in equivariant contexts.

等变映射的 Gromov Oka 原理

Gromov's Oka principle for equivariant maps

本文建立 Gromov 式 Oka 理论的等变框架，定义 G-Oka 等性质，并证明有限群作用下连续等变映射可形变为全纯等变映射，同时支持逼近与 jet 插值。