34 citations · 260 across the 72 of their papers we have counts for
8 papers · 1 filter
Linear stable range for homology of congruence subgroups via FI-modules
Wee Liang Gan, Liping Li
We answer positively a question of Church, Miller, Nagpal and Reinhold on existence of a linear bound on the presentation degree of the homology of a complex of FI-modules. This im…
Local cohomology and the multi-graded regularity of FI-modules
Liping Li, Eric Ramos
We develop a local cohomology theory for FI-modules, and show that it in many ways mimics the classical theory for multi-graded modules over a polynomial ring. In particular, w…
An application of Nakayama functor in representation stability theory
Wee Liang Gan, Liping Li, Changchang Xi
Using the Nakayama functor, we construct an equivalence from a Serre quotient category of a category of finitely generated modules to a category of finite-dimensional modules. We t…
Bounds on homological invariants of VI-modules
Wee Liang Gan, Liping Li
We give bounds for various homological invariants (including Castelnuovo-Mumford regularity, degrees of local cohomology, and injective dimension) of finitely generated VI-modules…
On the Dirichlet form of three-dimensional Brownian motion conditioned to hit the origin
Patrick J. Fitzsimmons, Liping Li
Our concern in this paper is the energy form induced by an eigenfunction of a self-adjoint extension of the restriction of the Laplace operator to $C_c^\infty(\mathbf{R}^3\setminus…
FI-modules over Noetherian rings
Liping Li, Nina Yu
In this paper we study representation theory of the category FI introduced by Gadish which is a product of copies of the category FI, and show that quite a few interesting repr…
Asymptotic behaviors of representations of graded categories with inductive functors
Wee Liang Gan, Liping Li
In this paper we describe an inductive machinery to investigate asymptotic behaviors of homology groups and related invariants of representations of certain graded combinatorial ca…
On symmetric one-dimensional diffusions
Liping Li, Jiangang Ying
The main purpose of this paper is to explore the structure of local and regular Dirichlet forms associated with symmetric linear diffusions. Let be a re…