Related papers: Counterexamples to the pseudo-Riemannian Lichnerow…
As recently pointed out by Gabe, a fundamental paper by Elliott and Kucerovsky concerning the absorption theory for C*-algebras contains an error, and as a consequence we must report that Lemma 4.5 in "Classifying C*-algebras with both…
The title is self-explanatory. We aim to give an easy to read and self-contained introduction to the field of harmonic manifolds. Only basic knowledge of Riemannian geometry is required. After we gave the definition of harmonicity and…
In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.
We describe Greenberg's pseudo-null conjecture, and prove a result describing conditions under which the pseudo-null conjecture for a number field $K$ implies the conjecture for finite extensions of $K$. We then apply the result to the…
Signatures of quadratic forms have been generalized to hermitian forms over algebras with involution. In the literature this is done via Morita theory, which causes sign ambiguities in certain cases. In this paper, a hermitian version of…
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We continue to discuss the example presented in \cite{JarPfl2015}. In particular, we clarify some gaps and complete the description of the Shilov boundary.
The Heisenberg groups are examples of sub-Riemannian manifolds homeomorphic, but not diffeomorphic to the Euclidean space. Their metric is derived from curves which are only allowed to move in so-called horizontal directions. We report on…
In this paper I present a comparison theorem for the waist of Riemannian manifolds with positive sectional curvature. The main theorem of this paper gives a partial positive answer to a conjecture formulated by M.Gromov in [8]. The content…
We give a counterexample to a conjecture of Wang and Hou related with the sum of the $k$ largest Laplacian eigenvalues of signed graphs.
In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.
Let $G$ be a split semisimple linear algebraic group and let $X$ denote the generically twisted variety of Borel subgroups in $G$. Nikita Karpenko conjectured that the map from the Chow ring of $X$ to the associated graded ring of the…
A correction is brought to the opinion expressed in a previous note published in this journal that the off critical line points indicated by some authors as being non trivial zeros of the Davenport and Heilbronn function are affected of…
Problems in two axiomatizations of Ja\'skowski's discussive (or discursive) logic D2 are considered. A recent axiomatization of D2 and completeness proof relative to D2's intended semantics seems to be mistaken because some formulas valid…
We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
This paper has been withdrawn by the author due to a crucial error.
We generalise the work of Sarnak-Tsimerman to twisted sums of Kloosterman sums and thus give evidence towards the twisted Linnik-Selberg Conjecture.
We show that the Gromov-Lawson-Rosenberg conjecture for the Semi-Dihedral group of order 16 is true.
Certain solvable extensions of $H$-type groups provide noncompact counterexamples to the so-called Lichnerowicz conjecture, which asserted that ``harmonic'' Riemannian spaces must be rank 1 symmetric spaces.