Related papers: The Baum-Connes conjecture: an extended survey
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
We make an exposition of the proof of the Baum-Connes conjecture for the infinite dihedral group following the ideas of Higson and Kasparov.
A number of exciting advances have been made in automated fact-checking thanks to increasingly larger datasets and more powerful systems, leading to improvements in the complexity of claims which can be accurately fact-checked. However,…
Mathematical aspects of contemporary classical and quantum gauge theory are sketched.
In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.
Although it has been almost 100 years since the beginnings of quantum mechanics, the discussions about its interpretation still do not cease. Therefore, a survey of opinions regarding this matter is of particular interest. This poll was…
This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.
We associate a non-commutative $C^*$-algebra with any locally finite simplicial complex. We determine the $K$-theory of these algebras and show that they can be used to obtain a conceptual explanation for the Baum-Connes conjecture.
We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…
We wish to contribute to the discussion of "Comparing Consensus Monte Carlo Strategies for Distributed Bayesian Computation" by offering our views on the current best methods for Bayesian computation, both at big-data scale and with smaller…
In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…
In this survey paper, I first review the history of Bernoulli numbers, then examine the modern definition of Bernoulli numbers and the appearance of Bernoulli numbers in expansion of functions. I revisit some properties of Bernoulli numbers…
Is tame open? No answer so far. One may pose the Tame-Open Conjecture: Tame is open. But how to support it? No effective way to date. In this note, the rank of a wild algebra is introduced. The Wild-Rank Conjecture, which implies the…
Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…
This is a survey on the Farrell-Jones Conjecture about the algebraic K- and L-theory of groups rings and its applications to algebra, geometry, group theory, and topology.
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.