Related papers: ACC for log canonical thresholds for complex analy…
In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an (information-theoretically secure) streaming proof with a…
In this paper, we study transcendental aspects of the cohomology groups of adjoint bundles of log canonical pairs, aiming to establish an analytic theory for log canonical singularities. As a result, in the case of purely log terminal…
In this paper, we prove a `cut-by-curves criterion' for an overconvergent isocrystal on a smooth variety over a field of characteristic $p>0$ to extend logarithmically to its smooth compactification whose complement is a strict normal…
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…
We show that every structurally submodular separation system admits a canonical tree set which distinguishes its tangles.
This paper is about the logarithmic limit sets of real semi-algebraic sets, and, more generally, about the logarithmic limit sets of sets definable in an o-minimal, polynomially bounded structure. We prove that most of the properties of the…
We prove that a projective semistable morphism of fs log analytic spaces yields polarized log Hodge structures in the canonical way.
We characterize the ideals $I$ of $\mathcal O_n$ of finite colength whose integral closure is equal to the integral closure of an ideal generated by pure monomials. This characterization, which is motivated by an inequality proven by…
We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic…
We prove that the linear syzygy spaces of a general canonical curve are spanned by syzygies of minimal rank.
We show that any directed colimit of acessible categories and accessible full embeddings is accessible and, assuming the existence of arbitrarily large strongly compact cardinals, any directed colimit of acessible categories and accessible…
In this paper, we prove a `cut-by-curves criterion' for the overconvergence of integrable connections on certain rigid analytic spaces and certain varieties over $p$-adic fields.
The ACC conjecture for local volumes predicts that the set of local volumes of klt singularities $x\in (X,\Delta)$ satisfies the ACC if the coefficients of $\Delta$ belong to a DCC set. In this paper, we prove the ACC conjecture for local…
We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.
It is well known that every solution of an elliptic equation is analytic if its coefficients are analytic. However, less is known about the ultra-analyticity of such solutions. This work addresses the problem of elliptic equations with…
We develop a theory of log adic spaces by combining the theories of adic spaces and log schemes, and study the Kummer \'etale and pro-Kummer \'etale topology for such spaces. We also establish the primitive comparison theorem in this…
We present the complex analytic and principal complex analytic realizability of a link in a 3-manifold $M$ as a tool for understanding the complex structures on the cone $C(M)$.
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
Our concern is the data complexity of answering linear monadic datalog queries whose atoms in the rule bodies can be prefixed by operators of linear temporal logic LTL. We first observe that, for data complexity, answering any connected…
In this paper, we initiate our investigation of log canonical models for the moduli space of curves with the boundary divisor $\a \d$ as we decrease $\a$ from 1 to 0. We prove that for the first critical value $\a = 9/11$, the log canonical…