Related papers: Odd-dimensional Charney-Davis conjecture

We prove the McKay conjecture on characters of odd degree. A major step in the proof is the verification of the inductive McKay condition for groups of Lie type and primes $\ell$ such that a Sylow $\ell$-subgroup or its maximal normal…

A conjecture for higher order separation on generic rational surfaces with some new results about standard divisors.

We show that the Fr\"oberg conjecture holds in the second non-trivial degree for an ideal generated by generic forms of degree $d>2$. We also show that the conjecture is true up to degree $2d-1$ provided that the number of variables is…

In this note we prove that a fourth order conformal invariant on the product of a circle with an (n-1)-dimensional sphere can be arbitrarily close to that of the n-dimensional sphere, generalizing a result of Schoen about the classical…

Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.

In this note we sketch a proof of a fundamental conjecture, the codimension-three conjecture, for microdifferential holonomic systems with regular singularities. It states that any regular holonomic E-module extends beyond a…

It is conjectured that the dual variety of every smooth nonlinear subvariety of dimension $> \frac{2N}{3}$ in projective $N$-space is a hypersurface, an expectation known as the duality defect conjecture. This would follow from the truth of…

We study L^p-L^r restriction estimates for algebraic varieties in d-dimensional vector spaces over finite fields. Unlike the Euclidean case, if the dimension $d$ is even, then it is conjectured that the L^{(2d+2)/(d+3)}-L^2 Stein-Tomas…

We prove that if the Morrison cone conjecture holds for a smooth Calabi-Yau threefold $Y$, it holds for any smooth Calabi-Yau threefold deformation-equivalent to $Y$. We use this result to prove a new case of the Morrison cone conjecture.

In 1989 Kalai stated the three conjectures A, B, C of increasing strength concerning face numbers of centrally symmetric convex polytopes. The weakest conjecture, A, became known as the ``$3^d$-conjecture''. It is well-known that the three…

We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the…

The standard picture of viable higher-dimensional theories is that extra dimensions manifest themselves at short distances only, their effects being negligible at scales larger than some critical value. We show that this is not necessarily…

In the framework of the PDE's algebraic topology, previously introduced by A. Pr\'astaro, are considered {\em exotic differential equations}, i.e., differential equations admitting Cauchy manifolds $N$ identifiable with exotic spheres, or…

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

In this paper, we continue the study of Serrano's conjecture in low dimensions. We focus on two special cases of the log version of Serrano's conjecture: the ampleness conjecture and the log version of Campana--Peternell's conjecture. In…

These lectures are intended as a broad introduction to Chern Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant action -in the sense of fiber bundles- in more than three…

Whitehead aspherical conjecture says that every connected subcomplex of every aspherical 2-complex is aspherical. By an argument on ribbon sphere-links, it is confirmed that the conjecture is true for every contractible finite 2-complex. In…

This work completes the classification of the cubic vertices for arbitrary spin massless bosons in three dimensions started in a previous companion paper by constructing parity-odd vertices. Similarly to the parity-even case, there is a…

We extend the original Cachazo-Douglas-Seiberg-Witten conjecture for symmetric spaces.

We show that if the Atiyah Jones conjecture holds for a surface $X,$ then it also holds for the blow-up of $X$ at a point. Since the conjecture is known to hold for ${\mathbb P}^2$ and for ruled surfaces, it follows that the conjecture is…