Related papers: Multiple mixing, 75 years of Rokhlin's problem

We use equivariant surgery to classify all involutions on closed surfaces, up to isomorphism. Work on this problem is classical, dating back to the nineteenth century, but some questions seem to have been left unanswered. We give a modern…

We investigate invariants of compact hyperk{\"a}hler manifolds introduced by Rozansky and Witten: they associate an invariant to each graph homology class. It is obtained by using the graph to perform contractions on a power of the…

We give new positive results on the long-standing open problem of geometric covering decomposition for homothetic polygons. In particular, we prove that for any positive integer k, every finite set of points in R^3 can be colored with k…

To the families of geometric measures of convex bodies (the area measures of Aleksandrov-Fenchel-Jessen, the curvature measures of Federer, and the recently discovered dual curvature measures) a new family is added. The new family of…

This article is the first in the cycle from two parts. It develops the ideas of integral manifolds method of M. M. Bogolubov in the case of linear differential equations in $R^m$ with variable coefficients. We distinguish linear subspaces…

In 1972, Marcel Berger defined a metric invariant that captures the `size' of k-dimensional homology of a Riemannian manifold. This invariant came to be called the k-dimensional SYSTOLE. He asked if the systoles can be constrained by the…

We define a variant of k-of-n testing that we call conservative k-of-n testing. We present a polynomial-time, combinatorial algorithm for the problem of maximizing throughput of conservative k-of-n testing, in a parallel setting. This…

We provide sufficient conditions for the existence of invariant probability measures for generic stochastic differential equations with finite time delay. This is achieved by means of the Krylov-Bogoliubov method. Furthermore, we focus on…

We propose a novel Hybrid High-Order method for the Cahn-Hilliard problem with convection. The proposed method is valid in two and three space dimensions, and it supports arbitrary approximation orders on general meshes containing…

We generalize a map by S. Mason regarding two combinatorial models for key polynomials, in a way that accounts for the major index. We also define similar variants of this map, that regards alternative models for the modified Macdonald…

We construct a version of Beilinson's regulator as a map of sheaves of commutative ring spectra and use it to define a multiplicative variant of differential algebraic K-theory. We use this theory to give an interpretation of Bloch's…

For a triple $(G,A,\kappa)$ (where $G$ is a group, $A$ is a $G$-module and $\kappa:G^3\to A$ is a 3-cocycle) and a $G$-module $B$ we introduce a new cohomology theory $_2H^n(G,A,\kappa;B)$ which we call the secondary cohomology. We give a…

A version of the Hodge-Riemann relations for valuations was recently conjectured and proved in several special cases by the first-named author. The Lefschetz operator considered there arises as either the product or the convolution with the…

Several physical problems modeled by second-order elliptic equations can be efficiently solved using mixed finite elements of the Raviart-Thomas family RTk for N-simplexes, introduced in the seventies. In case Neumann conditions are…

We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kaehler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of Kaehler-Einstein and constant scalar…

In 1974, D. Rolfsen asked: If two PL links in $S^3$ are isotopic (=homotopic through embeddings), then are they PL isotopic? We prove that they are PL isotopic to another pair of links which are indistinguishable from each other by finite…

We generalize overpartitions to (k,j)-colored partitions: k-colored partitions in which each part size may have at most j colors. We find numerous congruences and other symmetries. We use a wide array of tools to prove our theorems:…

We give a complete list, for $n \leq 6$, of non-isometric $\mathbb{T}^n$-invariant Kaehler-Einstein manifolds immersed in a finite dimensional complex projective space endowed with the Fubini-Study metric. This solves, in the aforementioned…

The present paper is the first in a series devoted to the study of asymptotic geometry of Riemann surfaces and their moduli spaces. We introduce the moduli space of hybrid curves as a new compactification of the moduli space of curves,…

K-area is an invariant for Riemannian manifolds introduced by Gromov as an obstruction to the existence of positive scalar curvature. However in general it is difficult to determine whether K-area is finite or not. though the definition of…