8 citations · 27 across the 15 of their papers we have counts for
17 papers
Ergodicity for eventually continuous Markov--Feller semigroups on Polish spaces
Fuzhou Gong, Yong Liu, Yuan Liu +1
This paper investigates the ergodicity of Markov--Feller semigroups on Polish spaces, focusing on very weak regularity conditions, particularly the Cesàro eventual continuity. Firs…
On the -rank of class groups of -extensions
Yuan Liu
We prove a local-global principle for the embedding problems of global fields with restricted ramification. By this local-global principle, for a global field , we use only the…
Cartan's method and its applications in sheaf cohomology
Yuan Liu
This paper aims to use Cartan's original method in proving Theorem A and B on closed cubes to provide a different proof of the vanishing of sheaf cohomology over a closed cube if e…
Non-abelian Cohen--Lenstra Heuristics in the presence of roots of unity
Yuan Liu
For a Galois extension of Galois group with , we define an invariant , and show that it determines the Weil pairing of the curve corresp…
On the holomorphic convexity of reductive Galois coverings over compact Kähler surfaces
Yuan Liu
This article generalizes the result of Katzarkov and Ramachandran from algebraic surfaces to Kähler surfaces. We follow their argument to prove the holomorphic convexity of a reduc…
Tamely Ramified Covers of the Projective Line with Alternating and Symmetric Monodromy
Renee Bell, Jeremy Booher, William Y. Chen +1
Let be an algebraically closed field of characteristic and let the projective line over with three points removed. We investigate which finite groups can arise…
Presentations of Galois groups of maximal extensions with restricted ramification
Yuan Liu
Motivated by the work of Lubotzky, we use Galois cohomology to study the difference between the number of generators and the minimal number of relations in a presentation of the Ga…
Generalized Bockstein maps and Massey products
Yeuk Hay Joshua Lam, Yuan Liu, Romyar Sharifi +2
Given a profinite group G of finite p-cohomological dimension and a pro-p quotient H of G by a closed normal subgroup N, we study the filtration on the Iwasawa cohomology of N by p…
A predicted distribution for Galois groups of maximal unramified extensions
Yuan Liu, Melanie Matchett Wood, David Zureick-Brown
We consider the distribution of the Galois groups of maximal unramified extensions as ranges over -extensions of o…
The Poincaré inequality and quadratic transportation-variance inequalities
Yuan Liu
It is known that the Poincaré inequality is equivalent to the quadratic transportation-variance inequality (namely ), see Jourdain \cit…
On the level of modular curves that give rise to isolated -invariants
Abbey Bourdon, Ozlem Ejder, Yuan Liu +2
We say a closed point on a curve is sporadic if has only finitely many closed points of degree at most and that is isolated if it is not in…
The free group on n generators modulo n+u random relations as n goes to infinity
Yuan Liu, Melanie Matchett Wood
We show that, as n goes to infinity, the free group on n generators, modulo n+u random relations, converges to a random group that we give explicitly. This random group is a non-ab…
The Realizability Problem with Inertia Conditions
Yuan Liu
In this paper, we consider the inverse Galois problem with described inertia behavior. For a finite group , one of its subgroups and a prime integer , we ask whether or n…
A new characterization of quadratic transportation-information inequalities
Yuan Liu
It is known that a quadratic transportation-information inequality interpolates between the Talagrand's inequality and the log-Sobolev inequality (L…
A link between the log-Sobolev inequality and Lyapunov condition
Yuan Liu
We give an alternative look at the log-Sobolev inequality (LSI in short) for log-concave measures by semigroup tools. The similar idea yields a heat flow proof of LSI under some qu…
Gaussian integrability of distance function under the Lyapunov condition
Yuan Liu
In this note we give a direct proof of the Gaussian integrability of distance function as for some provided the Lyapunov condition holds for symme…
Ergodicity and asymptotic stability of Feller semigroups on Polish metric spaces
Fu-Zhou Gong, Yuan Liu
We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As application, the 2D Navier-Stokes equat…