Related papers: Direct Splitting Method for the Baum-Connes Conjec…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
We introduce the notion of crystallographic T-duality, inspired by the appearance of $K$-theory with graded equivariant twists in the study of topological crystalline materials. Besides giving a range of new topological T-dualities, it also…
Splitting methods constitute a well-established class of numerical schemes for solving convection-diffusion-reaction problems. They have been shown to be effective in solving problems with periodic boundary conditions. However, in the case…
Let $G$ and $H$ be finitely generated groups. In this paper, we prove the quantitative coarse Baum--Connes conjecture for the free product $G* H$ under the assumption that the conjecture holds for both $G$ and $H$.
An exotic crossed product is a way of associating a C*-algebra to each C*-dynamical system that generalizes the well-known universal and reduced crossed products. Exotic crossed products provide natural generalizations of, and tools to…
Direct search is one of the most popular derivative-free optimization paradigms, that relies on exploring the variable space using polling directions. To analyze and implement direct search, one typically relies on positive spanning sets.…
We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…
In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…
Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC…
A new simple way to prove the Frobenius conjecture on the dimensions of real algebras without zero divisors is given.
We give a systematic method of providing numerical evidence for higher order Stark-type conjectures such as (in chronological order) Stark's conjecture over $\mathbb{Q}$, Rubin's conjecture, Popescu's conjecture, and a conjecture due to…
We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of…
We introduce a new overlapping Domain Decomposition Method (DDM) to solve the fully nonlinear Monge-Amp\`ere equation. While DDMs have been extensively studied for linear problems, their application to fully nonlinear partial differential…
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…
Bourbaki seminar 1062, October 2012.
The separation of two sets (or more specific of two cones) plays an important role in different fields of mathematics such as variational analysis, convex analysis, convex geometry, optimization. In the paper, we derive some new results for…
We use homological ideals in triangulated categories to get a sufficient criterion for a pair of subcategories in a triangulated category to be complementary. We apply this criterion to construct the Baum-Connes assembly map for locally…
The classical convex feasibility problem in a finite dimensional Euclidean space is studied in the present paper. We are interested in two cases. First, we assume to know how to compute an exact project onto one of the sets involved and the…
We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…