Related papers: A counterexample of two Romanov type conjectures
We found a counterexample to the conjecture of Karvatskyi and Pratsiovytyi concerning the topological type of the achievement set of an intermediate series (Proceedings of the International Geometry Center, 2023.…
I prove Zamolodchikov's periodicity conjecture for type A with both ranks arbitrary.
Let $\mathbb{Q}$ denote the poset which adds a Cohen real then shoots a club through the complement of $\big( [\omega_2]^\omega \big)^V$ with countable conditions. We prove that the version of Strong Chang's Conjecture from \cite{MR2965421}…
We provide various counter-examples to the long-standing so-called "Omnibus Conjecture" in Rational Homotopy Theory. That is, we show that a space with finite dimensional even-degree rational cohomology and finite dimensional spherical…
In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.
We verify Katzarkov-Kontsevich-Pantev conjecture for Landau-Ginzburg models of smooth Fano threefolds.
This paper has been withdrawn by the author, due to a crucial error in page 5.
We prove Chern conjecture, which states that the Euler characteristic vanishes for closed flat affine manifolds. Our key innovation is a deformation argument for the Euler form.
This article demonstrates that the recent proof of the invariant subspace problem, as presented by Khalil et al., is incorrect.
We provide new sufficient conditions under which Ryser's conjecture holds.
We show that the $\theta=\infty$ conjecture implies the Riemann hypothesis.
We build here several counterexamples for two weight bi-parameter Carleson embedding theorem.
We provide a counter-example to Proposition 3.2 of "A note on the Fundamental Group of a Triangular Algebra", by F.Xu.
Addressing a question of Shioya, we show that two-step iterations of the Laver collapse can force saturated ideals and Chang conjectures.
We discuss various recent advances on weak forms of the Twin Prime Conjecture.
In this paper, we study some vanishing identities for Gromov-Witten invariants conjectured by K. Liu and H. Xu. We will prove these conjectures in the case that the summation range is large compare to genus. In fact, in such cases, we can…
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…
We survey recent developments on the Restriction conjecture.
We prove vanishing results for unramified stable cohomology of finite groups of Lie type.
We prove a characterization of Fano type varieties.