Related papers: Mitschke's Theorem is sharp

We explore the notion of m-intermediate Ricci curvature assumption introduced by Brendle-Hirsch-Johne further. If a manifold has non-negative m-intermediate Ricci curvature and stable weighted slicing of order m-1, then the last slice has…

We prove limit relations between the sharp constants in the multivariate Bernstein-Nikolskii type inequalities for trigonometric polynomials and entire functions of exponential type with the spectrum in a centrally symmetric convex body.

We prove a new sharp correlation inequality for sums of i.i.d. square integrable lattice distributed random variables. We also apply it to establish an almost sure local limit theorem for iid square integrable random variables taking values…

Stable infiniteness, strong finite witnessability, and smoothness are model-theoretic properties relevant to theory combination in satisfiability modulo theories. Theories that are strongly finitely witnessable and smooth are called…

We show that a variety with J\'onsson terms $t_1, \dots, t_{n-1}$ has directed J\'onsson terms $d_1, \dots, d_{n-1}$, for the same value of the indices, solving a problem raised by Kazda et al.. Refined results are obtained for locally…

We determine when a quasi-isometry between discrete spaces is at bounded distance from a bilipschitz map. From this we prove a geometric version of the Von Neumann conjecture on amenability. We also get some examples in geometric groups…

The homomorphic image of a congruence is always a tolerance (relation) but, within a given variety, a tolerance is not necessarily obtained this way. By a Maltsev-like condition, we characterize varieties whose tolerances are homomorphic…

Using quantization techniques, we show that the $\delta$-invariant of Fujita-Odaka coincides with the optimal exponent in certain Moser-Trudinger type inequality. Consequently we obtain a uniform Yau-Tian-Donaldson theorem for the existence…

In this note we prove the optimality of a family of known coincidence theorems for absolutely summing multilinear operators. We connect our results with the theory of multiple summing multilinear operators and prove the sharpness of similar…

Similar to a tree grammar, a Horn theory can be used to describe an infinite set of terms. In this paper, we present a class of Horn theories such that the set of definable predicates is closed wrt. conjunction and such that the…

We show that the maximum likelihood degree of a smooth very affine variety is equal to the signed topological Euler characteristic. This generalizes Orlik and Terao's solution to Varchenko's conjecture on complements of hyperplane…

We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then…

This paper uses previous results of the authors on vector-valued modular forms to study certain non-congruence modular forms. We prove that these forms have unbounded denominators, and in certain cases we verify congruences of…

We study the strength of axioms needed to prove various results related to automata on infinite words and B\"uchi's theorem on the decidability of the MSO theory of $(N, {\le})$. We prove that the following are equivalent over the weak…

Let $n, m$ be positive integers, $n\geq m$. We make several remarks on the relationship between approximate differentiability of higher order and Morse-Sard properties. For instance, among other things we show that if a function…

Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.

Let $\alpha$, $\beta$, $\gamma, \dots$ $\Theta$, $\Psi, \dots$ $R$, $S$, $T, \dots$ be variables for, respectively, congruences, tolerances and reflexive admissible relations. Let juxtaposition denote intersection. We show that if the…

We extend the validity of Kiss's characterization of the commutator from congruence modular varieties to varieties with a difference term. This fixes a recently discovered gap in our paper [A finite basis theorem for difference-term…

We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between…

The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…