Related papers: Proofs On Arnold Conjectures
In the 1960s Arnold conjectured that a Hamiltonian diffeomorphism of a closed connected symplectic manifold $(M,\omega)$ should have at least as many contractible fixed points as a smooth function on $M$ has critical points. Such a…
In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.
After giving an explicit description of all the non vanishing Dolbeault cohomology groups of ample line bundles on grassmannians, I give two series of vanishing theorems for ample vector bundles on a smooth projective variety. They imply a…
We prove conjectures of Rene Thom and Vladimir Arnold for C^2 solutions to the degenerate elliptic equation that is the level set equation for motion by mean curvature. We believe these results are the first instances of a general…
We formulate a tropical analogue of Grothendieck's section conjecture: that for every stable graph G of genus g>2, and every field k, the generic curve with reduction type G over k satisfies the section conjecture. We prove many cases of…
I settle a conjecture of Andrews related to the Alladi-Schur polynomials. In addition, I give further relations and implications to two families of polynomials related to the Alladi-Schur polynomials.
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
In a recent work, Andrews gave analytic proofs of two conjectures concerning some variations of two combinatorial identities between partitions of a positive integer into odd parts and partitions into distinct parts discovered by Beck.…
We prove the Shafarevich conjecture for varieties with globally generated cotangent bundle, subject to mild numerical conditions.
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
We study the following rigidity problem in symplectic geometry:can one displace a Lagrangian submanifold from a hypersurface? We relate this to the Arnold Chord Conjecture, and introduce a refined question about the existence of relative…
A proof of Petri's general conjecture on the unobstructedness of linear systems on a general curve is proposed, using only the local properties of the deformation space of the pair (curve, line bundle).
We prove some new equivalences of the paving conjecture and obtain some estimates on the paving constants. In addition we give a new family of counterexamples to one of the Akemann-Anderson conjectures.
We construct a family of points on the Lagrangian cone of a partial flag bundle associated to a (possibly non-split) vector bundle from any Weyl-invariant $I$-function of a prequotient. This result can be seen as the nonabelian analogue of…
The main model studied in this paper is a lattice of nearest neighbors coupled pendula. For certain localized coupling we prove existence of energy transfer and estimate its speed.
We prove the $p$-curvature conjecture for rank two vector bundles with connection on generic curves, by combining deformation techniques for families of varieties and topological arguments.
The Hartshorne conjecture predicts that two submanifolds X and Y in a projective manifold Z with ample normal bundles meets as soon as dim X + dim Y is at least dim Z. We mostly assume slightly stronger that one of the normal bundles is…
We prove the $l^2$ Decoupling Conjecture for compact hypersurfaces with positive definite second fundamental form and also for the cone. This has a wide range of important consequences. One of them is the validity of the Discrete…
In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…
We prove that shifted cotangent stacks carry a canonical shifted symplectic structure. We also prove that shifted conormal stacks carry a canonical Lagrangian structure. These results were believed to be true but no written proof was…