Related papers: Remarks on logarithmic K-stability
We investigate stability properties of the reductive Borel-Serre categories; these were introduced as a model for unstable algebraic K-theory in previous work. We see that they exhibit better homological stability properties than the…
We study the existence of extremal K\"ahler metrics on K\"ahler manifolds. After introducing a notion of relative K-stability for K\"ahler manifolds, we prove that K\"ahler manifolds admitting extremal K\"ahler metrics are relatively…
In this note, we use recent advances concerning the K-stability of $\mathbb{Q}$-Fano varieties to provide settings for which Vojta's conjecture holds.
In this follow up work to [45, 33, 32, 46] we introduce and study a notion of geodesic stability restricted to rays with prescribed singularity types. A number of notions of interest fit into this framework, in particular algebraic- and…
This note adds some critical remarks on the discussion presented in the McDonald's paper ([1]) on stability of steady motion of the well known problem of a disk rolling on a rough horizontal plane.
We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.
We give a brief account of the interplay between spectral morphisms, K-theory, and stable ranks in the context of Banach algebras.
We extend the algebraic K-stability theory to projective klt pairs with a big anticanonical class. While in general such a pair could behave pathologically, it is observed in this note that K-semistability condition will force them to have…
We give another proof, using tools from Geometric Invariant Theory, of a result due to S. Sam and A. Snowden in 2014, concerning the stability of Kro-necker coefficients. This result states that some sequences of Kronecker coefficients…
We give a simple necessary and sufficient condition for uniform K-stability of $\mathbb{Q}$-Fano varieties.
In this paper, we will give estimates for the logarithmic derivative $ \left\vert \frac{f^{\left( k\right) }\left( z\right) }{f\left( z\right) } \right\vert $ where $f$ is a meromorphic function in a region of the form $ D\left( 0,R\right)…
We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.
We give a stability version of of the Blaschke-Santal\'{o} inequality in the plane.
This expository article is based on the author's talk at the Kinosaki Algebraic Geometry Symposium 2025. We discuss some recent progress surrounding stable degeneration in algebraic K-stability theory.
Assume that a projective variety together with a polarization is uniformly K-stable. If the polarization is canonical or anti-canonical, then the projective variety is uniformly K-stable with respects to any polarization sufficiently close…
We show cocycle stability for linear maps with a weak irreducibility condition and their jointly integrable perturbations.
In this paper, we study an inverse coefficients problem for two coupled Schr\"{o}dinger equations with an observation of one component of the solution. The observation is done in a nonempty open subset of the domain where the equations…
We present a simple analysis of k-means|| (Bahmani et al., PVLDB 2012) -- a distributed variant of the k-means++ algorithm (Arthur and Vassilvitskii, SODA 2007). Moreover, the bound on the number of rounds is improved from $O(\log n)$ to…
Algebraic K-theory is the stable homotopy theory of homotopy theories, and it interacts with algebraic structures accordingly. In particular, we prove the Deligne Conjecture for algebraic K-theory.
We introduce a new compactification of the space of relative stable maps. This new method uses logarithmic geoemtry in the sense of Kato-Fontaine-Illusie rather than the expanded degeneration. The underlying structure of our log stable maps…