37 citations · 362 across the 39 of their papers we have counts for
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Stability conditions on cyclic categories I: basic definitions and examples
Yucheng Liu
A triangulated category with a canonical Bott's isomorphism is called a cyclic category in this paper. We give a new notion of stability con…
Continuous-time weakly self-avoiding walk on has strictly monotone escape speed
Yucheng Liu
Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On , Greven and den Hollander proved in 1993 that the discret…
Convexity of multiplicities of filtrations on local rings
Harold Blum, Yuchen Liu, Lu Qi
We prove that the multiplicity of a filtration of a local ring satisfies various convexity properties. In particular, we show the multiplicity is convex along geodesics. As a conse…
Filtrations and torsion pairs in Abramovich Polishchuk's heart
Yucheng Liu
We study some abelian subcategories and torsion pairs in Abramovich Polishchuk's heart. And we construct stability conditions on a full triangulated subcategory $\mathcal{D}^{\leq…
On the boundedness of singularities via normalized volume
Yuchen Liu, Joaquín Moraga, Hendrik Süß
In this article we study conjectures regarding normalized volume and boundedness of singularities. We focus on singularities with a torus action of complexity 1, threefold singular…
K-stability of Fano threefolds of rank 2 and degree 14 as double covers
Yuchen Liu
We prove that every smooth Fano threefold from the family No 2.8 is K-stable. Such a Fano threefold is a double cover of the blow-up of at one point branched along a…
Infinitely many families of Sasaki-Einstein metrics on spheres
Yuchen Liu, Taro Sano, Luca Tasin
We show that there exist infinitely many families of Sasaki-Einstein metrics on every odd-dimensional standard sphere of dimension at least . We also show that the same result i…