Related papers: A counterexample to Lagrangian Poincar\'e recurren…

Counterexamples to Lagrangian Poincar\'e recurrence were recently found in dimensions greater than six by Bro\'ci\'c and Shelukhin. We construct counterexamples in dimension four using almost toric fibrations.

We present a simple dyadic construction that yields a new counterexample to Zygmund's conjecture. Our result recovers Soria's classical result in dimension three, through a different construction, and gives new ones in all other dimensions…

We give a counterexample to a conjecture posed by S. Ding regarding the index of a Gorenstein local ring by exhibiting several examples of one dimensional local complete intersections of embedding dimension three with index 5 and…

A high dimensional dynamical system is often studied by experimentalists through the measurement of a relatively low number of different quantities, called an observation. Following this idea and in the continuity of Boshernitzan's work,…

We present a counterexample to Viterbo's volume-capacity conjecture. This implies, in particular, that in contrast with a well-known conjecture, symplectic capacities do not coincide on the class of convex domains in the classical phase…

We use the generalized Minkowski billiard characterization of the EHZ-capacity of Lagrangian products in order to reprove that the $4$-dimensional Viterbo conjecture holds for the Lagrangian products (any triangle/parallelogram in…

In this paper, we give a simple counter example to the famous Hodge conjecture.

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

The paper presents a counterexample to the Hodge conjecture.

In this note, we show that the strong Viterbo conjecture holds true on any convex toric domain, and that the Viterbo's volume-capacity conjecture holds for the product of a $1$-unconditional convex body $A\subset\mathbb{R}^{n}$ and its…

A tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

We prove that the intersection of a Hirsch polytope and a cube may be a non-Hirsch polytope.

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

We improve the algebraic methods of Abhyankar for the Jacobian Conjecture in dimension two and describe the shape of possible counterexamples. We give an elementary proof of the result of Heitmann, which states that gcd(deg(P),deg(Q)) is…

We show that the Poincar\'e return time of a typical cylinder is at least its length. For one dimensional maps we express the Lyapunov exponent and dimension via return times.

A strong version of a conjecture of Viterbo asserts that all normalized symplectic capacities agree on convex domains. We review known results showing that certain specific normalized symplectic capacities agree on convex domains. We also…

In this note we give a counterexample to a conjecture proposed by Ciliberto about special linear systems of P^n through multiple base points.