Related papers: A note on a recent attempt to prove Sendov's conje…

We prove Stanley's plethysm conjecture for the $2 \times n$ case, which composed with the work of Black and List provides another proof of Foulkes conjecture for the $2 \times n$ case. We also show that the way Stanley formulated his…

Our paper arXiv:2101.11629 contains a technical error which changes some of the conclusions. We thank Streltsov, Pedernales, and Plenio for bringing the essence of this error to our attention. Here we explain the error, examine its…

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

We prove the Effective Bogomolov Conjecture, and so the Bogomolov Conjecture, over a function field of characteristic 0 by proving Zhang's Conjecture about certain invariants of metrized graphs. In the function field case, these conjectures…

A recent paper (arXiv:1404.5619) claimed the presence of a loophole in the current-algebra proof of Goldstone Theorem. The enforcing of manifest covariance would lead to contradictory results also in scalar theory. We show that the argument…

In this note, we show that a "Toy Conjecture" made by (Boyle, Ishai, Pass, Wootters, 2017) is false, and propose a new one. Our attack does not falsify the full ("non-toy") conjecture in that work, and it is our hope that this note will…

The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…

We give an explicit counterexample to an entanglement inequality suggested in a recent paper [quant-ph/0005126] by Benatti and Narnhofer. The inequality would have had far-reaching consequences, including the additivity of the entanglement…

Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.

Two conjectures recently proposed by one of the authors are disproved

This survey article is the written version of a talk given at the Bourbaki seminar in April 2021. We give an introduction to Zagier's conjecture on special values of Dedekind zeta functions, and its relation to $K$-theory of fields and the…

I give an example showing that the recent claimed solution by Feder, Kinne and Rafiey to the CSP Dichotomy Conjecture is not correct.

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.

A conjecture regarding the structure of expander graphs is discussed.

This paper has been withdrawn by author due to an error in the proof.

On [3, p. 199] one says "We mention parenthetically that the proof of [99, Lemma 41.3] is incorrect, and we do not know whether it, [99, Theorem 41.5] and [99, Theorem 41.6] are true". The previously cited reference [99] is our reference…

This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.

The paper has been withdrawn due to a crucial error in section 3.

In this article, we discuss and survey the recent progress towards the Schottky problem, and make some comments on the relations between the Andr{\'e}-Oort conjecture, Okounkov convex bodies, Coleman's conjecture, stable modular forms,…