Related papers: The Rost invariant has zero kernel for quasi-split…
This paper provides answers to questions regarding the almost sure limiting behavior of rooted, binary tree-structured rules for regression. Examples show that questions raised by Gordon and Olshen in 1984 have negative answers. For these…
Gromov-Witten invariants have been constructed to be deformation invariant, but their behavior under other transformations is subtle. In this note we show that logarithmic Gromov-Witten invariants are also invariant under appropriately…
We generalise the Kreck-Stolz invariants s_2 and s_3 by defining a new invariant, the t-invariant, for quaternionic line bundles E over closed spin-manifolds M of dimension 4k-1 with H^3(M; \Q) = 0 such that c_2(E)\in H^4(M) is torsion. The…
We propose a kernel-based nonparametric test of relative goodness of fit, where the goal is to compare two models, both of which may have unobserved latent variables, such that the marginal distribution of the observed variables is…
Flag kernels are tempered distributions which generalize these of Calderon-Zygmund type. For any homogeneous group $\mathbb{G}$ the class of operators which acts on $L^{2}(\mathbb{G})$ by convolution with a flag kernel is closed under…
We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…
A basic question concerning indecomposable Soergel bimodules is to understand their endomorphism rings. In characteristic zero all degree-zero endomorphisms are isomorphisms (a fact proved by Elias and the second author) which implies the…
We prove that homological filling functions over a ring $R$ equipped with the discrete norm are quasi-isometry invariants for all groups of type $\mathrm{FP}_n$. This confirms a conjecture of Bader-Kropholler-Vankov in the case of discrete…
In a digraph, a quasi-kernel is a subset of vertices that is independent and such that the shortest path from every vertex to this subset is of length at most two. The ``small quasi-kernel conjecture,'' proposed by Erd\H{o}s and Sz\'ekely…
In the presence of crystalline symmetry, topologically ordered states can acquire a host of symmetry-protected invariants. These determine the patterns of crystalline symmetry fractionalization of the anyons in addition to fractionally…
We prove a conjecture of Artur Elezi in a generalized form suggested by Givental. Namely, our main result relates genus-0 Gromov--Witten invariants of a bundle space with such invariants of the base, provided that the fiber is a toric…
This work aims to prove that the classical Gaussian kernel, when defined on a non-Euclidean symmetric space, is never positive-definite for any choice of parameter. To achieve this goal, the paper develops new geometric and analytical…
Twisted Gromov-Witten invariants are intersection numbers in moduli spaces of stable maps to a manifold or orbifold X which depend in addition on a vector bundle over X and an invertible multiplicative characteristic class. Special cases…
In this note we show that if $G$ is a solvable group acting on the line, and if there is $T\in G$ having no fixed points, then there is a Radon measure $\mu$ on the line quasi-invariant under $G$. In fact, our method allows for the same…
Let G be a group of type E8 of compact type over the field of rational numbers, let K be a field of characteristic 0, and q the 5-fold Pfister form which is the sum of 32 squares. J-P. Serre posed in a letter to M. Rost written on June 23,…
We study a spatial asymptotic behaviour at infinity of kernels $p_t(x)$ for convolution semigroups of nonlocal pseudo-differential operators. We give general and sharp sufficient conditions under which the limits $$ \lim_{r \to \infty}…
We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in…
Heat kernels are used in this paper to express the analytic index of projectively invariant Dirac type operators on G-covering spaces of compact manifolds, as elements in the K-theory of certain unconditional completions of the twisted…
A short proof of a conjecture of Kropholler is given. This gives a relative version of Stallings' Theorem on the structure of groups with more than one end. A generalisation of the Almost Stability Theorem is also obtained, that gives…
We construct examples of groups showing that virtual solvability and the property of being virtually torsion-free are not preserved by bi-Lipschitz maps and hence by quasi-isometries.