Related papers: Weak positivity via mixed Hodge modules

A simple formula to read out the weak value from the wave function of the measuring device after the postselection with the initial Gaussian profile is proposed. We apply this formula for the weak value to the classical experiment of the…

Duality results connecting persistence modules for absolute and relative homology provides a fundamental understanding into persistence theory. In this paper, we study similar associations in the context of zigzag persistence. Our main…

After making correct, and then improving, our definition of the category of irregular mixed Hodge modules thanks to Mochizuki's recent results arXiv:2108.03843, we show how these results allow us to obtain Kodaira-Saito-type vanishing…

If X is a complex projective variety with klt singularities, then the mixed Hodge structures on the first two singular cohomology groups are pure. We describe the pieces of the Hodge decomposition in terms of reflexive differential forms.…

Let $T$ be a Noetherian ring and $f$ a nonzerodivisor on $T$. We study concrete necessary and sufficient conditions for a module over $R=T/(f)$ to be weakly liftable to $T$, in the sense of Auslander, Ding and Solberg. We focus on cyclic…

Let G be a semisimple, simply-connected algebraic group over an algebraically closed field of characteristic p > 0. We observe that the tensor product of the Steinberg module with a minuscule module is always indecomposable tilting.…

The real part of the weak value is identified as the conditional Bayes probability through the quantum analog of the Bayes relation. We present an explicit protocol to get the the weak values in a simple Mach-Zehnder interferometer model…

We construct a hermitian metric on the classifying spaces of graded-polarized mixed Hodge structures and prove analogs of the strong distance estimate between an admissible period map and the approximating nilpotent orbit. We also consider…

In this paper we study mixed Hodge structures on the cohomology of locally symmetric varieties and give an application to modular forms. After proving vanishing of some Hodge numbers, we focus on the weight filtration on the last Hodge…

We study generalized $V$-filtrations, defined by Sabbah, on $\mathcal D$-modules underlying mixed Hodge modules on $X\times \mathbf A^r$. Using cyclic covers, we compare these filtrations to the usual $V$-filtration, which is better…

We show that using only weak hyperbolicity (no smoothness, compactness or exponential rates) the Hopf argument produces multiple mixing in an elementary way. While this recovers classical results with far simpler proofs, the point is the…

We prove that a class of infinite measure preserving transformations, satisfying a "strong" weak mixing condition, generates all rigidity sequences of all conservative ergodic invertible measure preserving transformations defined on a…

This is a survey of vanishing and positivity theorems for Hodge modules, and their recent applications to birational and complex geometry, expanding on my lecture at the 2015 AMS Summer Institute.

Building on the nonabelian Hodge theory in positive characteristic developed by Ogus, Vologodsky, and Schepler, we propose a generalization of the decomposition theorem of Deligne and Illusie from the perspective of mixed Hodge modules.…

A general formalism for joint weak measurements of a pair of complementary observables is given. The standard process of optical three-wave mixing in a nonlinear crystal (such as in parametric down-conversion) is suitable for such tasks. To…

We present the universal theory of weak crossed biproducts, and we prove that every weak projection of weak bialgebras induces an example of this crossed structure. As an example, we give the construction of a weak projection of a weak…

Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak supersolutions become lower semicontinuous after redefinition on a set of measure zero.…

I provide additional arguments for refuting Vaidmans weak value analysis of the path of a particle in a nested Mach-Zehnder interferometer. The argument uses sequential weak values to supplement my previous analysis according to which even…

We present a sufficient condition that a pseudointegrable system has weak mixing property. The result is derived from Veech's weak mixing theorem for interval exhange [Veech, W.A. Amer.J.Math. {\bf 106}, 1331 (1984)]. We also present an…

Let $\mathfrak{g}$ be a complex simple Lie algebra. A simple $\mathfrak{g}$-module is called minimal if the associated variety of its annihilator ideal coincides with the closure of the minimal nilpotent coadjoint orbit. The main result of…