Hamiltonian group actions on symplectic Deligne-Mumford stacks and toric orbifolds

A homotopical description of Deligne-Mumford compactifications

We give a description of the Deligne-Mumford properad expressing it as the result of homotopically trivializing S1 families of annuli (with appropriate compatibility conditions) in the properad of smooth Riemann surfaces with parameterized boundaries. This gives an analog of the results of Drummond-Cole and Oancea--Vaintrob in the setting of properads. We also discuss a variation of this trivialization which gives rise to a new partial compactification of Riemann surfaces relevant to the study of operations on symplectic cohomology.

Deligne-Mumford 算元作为圆周作用的平凡化

The Deligne-Mumford operad as a trivialization of the circle action

本文证明树状 Deligne-Mumford 算元是高亏格带标架小圆盘算元中圆周平凡化的同伦模型，通过节点环带的几何论证和拓扑模问题形式化框架实现。

实有理曲线Deligne-Mumford空间的爆破

Blowdowns of the Deligne-Mumford Spaces of Real Rational Curves

本文构造了实有理曲线Deligne-Mumford模空间的一列光滑商爆破，给出Keel爆破构造的实类比，并显式描述了中间空间及三类爆破，为后续完全确定实模空间的有理（上）同调环奠定基础。

带$1+p$个标记点的亏格零Deligne-Mumford空间的$\mathbb Z/p$-等变上同调

The $\mathbb Z/p$-equivariant cohomology of genus zero Deligne-Mumford space with $1+p$ marked points

本文证明了带$1+p$个标记点的亏格零Deligne-Mumford空间相关纤维化的Serre谱序列在$E_2$页坍塌，并据此得出其$\mathbb Z/p$-等变上同调中的挠元均为非等变元，从而确定唯一的有趣等变运算是量子Steenrod幂运算。

与 Lagrangian 子流形相关的开闭 Deligne–Mumford 场论

An open-closed Deligne-Mumford field theory associated to a Lagrangian submanifold

本文构造任意亏格、边界在 Lagrangian 子流形上的全纯映射全局 Kuranishi 图，并据此建立统一 Fukaya 代数与 Gromov–Witten 理论的开闭 Deligne–Mumford 场论。

Hodge-Theoretic Mirror Symmetry for Toric Stacks

Using the mirror theorem [CCIT15], we give a Landau-Ginzburg mirror description for the big equivariant quantum cohomology of toric Deligne-Mumford stacks. More precisely, we prove that the big equivariant quantum D-module of a toric Deligne-Mumford stack is isomorphic to the Saito structure associated to the mirror Landau-Ginzburg potential. We give a GKZ-style presentation of the quantum D-module, and a combinatorial description of quantum cohomology as a quantum Stanley-Reisner ring. We establish the convergence of the mirror isomorphism and of quantum cohomology in the big and equivariant …

Logarithmic trace and orbifold products

We give a purely equivariant construction of orbifold products for quotient Deligne-Mumford stacks [X/G] where G is an arbitrary linear algebraic group (not necessarily finite). The key to our construction is the definition of the "logarithmic trace" of an equivariant vector bundle. We also prove that there is an orbifold Chern character homomorphism which induces an isomorphism of a canonical summand in the orbifold Grothendieck ring with the orbifold Chow ring. As an application we obtain an associative orbifold product on the Grothendieck ring of [X/G] (as opposed to its inerita stack) take…