Related papers: Log-decay $F$-isocrystals on higher dimensional va…

We study the mechanical response of a dislocation-free 2D crystal under homogenous shear using a new mesoscopic approach to crystal plasticity, a Landau-type theory, accounting for the global invariance of the energy in the space of strain…

We show that there exists a positive real number $\delta>0$ such that for any normal quasi-projective $\mathbb{Q}$-Gorenstein $3$-fold $X$, if $X$ has worse than canonical singularities, that is, the minimal log discrepancy of $X$ is less…

We generalize Nakamaye's description, via intersection theory, of the augmented base locus of a big and nef divisor on a normal pair with log-canonical singularities or, more generally, on a normal variety with non-lc locus of dimension at…

Recent DFT (density functional theory) simulations showed that metals have a hitherto overlooked symmetry termed "hidden scale invariance" [Hummel {\em et al.}, Phys. Rev. B {\bf{92}}, 174116 (2015)]. According to isomorph theory, this…

Let $S$ be an fs log scheme, and let $F$ be a group scheme over the underlying scheme which is \'etale locally representable by (1) a finite dimensional $\mathbb{Q}$-vector space, or (2) a finite rank free abelian group, or (3) a finite…

We study irreducible subvarieties of the universal hypersurface $\mathcal{X}/B$ of degree $d$ and dimension $n$. We prove that when $d$ is sufficiently large, a degree $kd$ subvariety $Z$ which dominates $B$ comes from intersection with a…

Let X be an algebraic variety over a field k, and L(X) be the scheme of formal arcs in X. Let f be an arc whose image is not contained in the singularities of X. Grinberg and Kazhdan proved that if k has characteristic 0 then the formal…

In this paper, by combining techniques from Ricci flow and algebraic geometry, we prove the following generalization of the classical uniformization theorem of Riemann surfaces. Given a complete noncompact complex two dimensional K\"ahler…

Given a log canonical pair $(X, \Delta)$, we show that $K_X+\Delta$ is nef assuming there is no non-constant map from the affine line with values in the open strata of the stratification induced by the non-klt locus of $(X, \Delta)$. This…

Let $G$ be a graph and $f: G\rightarrow G$ be a continuous map. We establish a structure theorem which describes the structures of the set $R(f)-\overline{P(f)}$, where $R(f)$ and $P(f)$ are the recurrent point set and the periodic point…

We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to…

The Riemann hierarchy is the simplest example of rank one, ($1$+$1$)-dimensional integrable system of nonlinear evolutionary PDEs. It corresponds to the dispersionless limit of the Korteweg-de Vries hierarchy. In the language of formal…

The deck of a graph $X$, $D(X)$, is defined as the multiset of all vertex-deleted subgraphs of $X$. Two graphs are said to be hypomorphic, if they have the same deck. Kelly-Ulam conjecture states that any two hypomorphic graphs on at least…

As part of his work on special Lagrangian (sLag) submanifolds with isolated conical singularities, Joyce proved a criterion for the existence of sLag smoothings, along a small variation of complex structure, for the union of two connected,…

For a $p$-divisible group $G$ over a smooth projective variety $X$ over $k$, where $k$ is a field finitely generated over a perfect field of characteristic $p$, we show that the formal group $R^i f_{\fppf*} G$ is isogenous to a…

Given a smooth projective variety $X$ with a simple normal crossing divisor $D:=D_1+D_2+...+D_n$, where $D_i\subset X$ are smooth, irreducible and nef. We prove a mirror theorem for multi-root stacks $X_{D,\vec r}$ by constructing an…

Given a map $\phi:X\rightarrow Y$ between $F$-analytic manifolds over a local field $F$ of characteristic $0$, we introduce an invariant $\epsilon_{\star}(\phi)$ which quantifies the integrability of pushforwards of smooth compactly…

Using the de Rham stack of Bhatt-Lurie and Drinfeld, we prove that de Rham complex of a smooth quasi-F-split variety over a perfect field of positive characteristic decomposes in all degrees. In particular, smooth proper quasi-F-split…

This article records multiple results coming from interplay between de-completed topological periodic cyclic homology, Segal conjecture, and F-smoothness. We establish completeness of motivic filtration on de-completed topological periodic…

We show that if $f$ is a nonzero, noninvertible function on a smooth complex variety $X$ and $J_f$ is the Jacobian ideal of $f$, then ${\rm lct}(f,J_f^2)>1$ if and only if the hypersurface defined by $f$ has rational singularities.…