Related papers: A Proof of Simon's Conjecture
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
In this paper we prove genus bounds for closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments. A stronger estimate was announced by Pitts and Rubistein but to our knowledge its proof has never…
We prove that given two compact oriented $3$-manifolds $N$ and $M,$ with $M$ satisfying only a mild hypothesis, there is a hyperbolic $3$-manifold $N'$ arbitrarily ``closely related'' to $N,$ and such that $N'$ does not embed in $M.$ For…
We prove a result, similar to the ones known as Ishihara's First and Second Trick, for sequences of functions.
We prove a law of large numbers for the volumes of families of random hyperbolic mapping tori and Heegaard splittings providing a sharp answer to a conjecture of Dunfield and Thurston.
Extending methods first used by Casson, we show how to verify a hyperbolic structure on a finite triangulation of a closed 3-manifold using interval arithmetic methods. A key ingredient is a new theoretical result (akin to a theorem by…
In this paper, we show that Gromov-Thurston's principle works for hyperbolic 3-manifolds of infinite volume and with finitely generated fundamental group. As an application, we have a new proof of Ending Lamination Theorem. Our proof…
We show that there are algorithms to determine if a 3-manifold contains an essential lamination or a Reebless foliation.
We prove a reformulation of the multiplicity upper bound conjecture and use that reformulation to prove it for three-dimensional simplicial complexes and homology manifolds with many vertices. We provide necessary conditions for a…
In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.
In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.
We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three dimensional contact subriemannian manifolds with symmetry.
We prove Manin's conjecture over imaginary quadratic number fields for a cubic surface with a singularity of type E_6.
In this paper, we establish a version of the adjunction inequality for closed symplectic 4-manifolds. As in a previous paper on the Thom conjecture, we use contact geometry and trisections of 4-manifolds to reduce this inequality to the…
In this paper, we will give another proof of Zhi-Wei Sun's three conjectures on Ap\'{e}ry-like sums involving harmonic numbers by proving some identities among special values of multiple polylogarithms.
In this paper we prove the Hodge conjecture for products of the form $S_1 \times ... S_n$, where $S_i$ are smooth projective surfaces such that $p_g(S_i)=1, q(S_i)=2$. We also prove the Hodge conjecture for arbitrary self-products of a K3…
We produce a rational homology 3-sphere that does not smoothly bound either a positive or negative definite 4-manifold. Such a 3-manifold necessarily cannot be rational homology cobordant to a Seifert fibered space or any 3-manifold…
In this paper we describe a general strategy for approaching the Weinstein conjecture in dimension three. We apply this approach to prove the Weinstein conjecture for a new class of contact manifolds (planar contact manifolds). We also…
The Generalized Smale Conjecture asserts that if M is a closed 3-manifold with constant positive curvature, then the inclusion of the group of isometries into the group of diffeomorphisms is a homotopy equivalence. For the 3-sphere, this…
We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.