Related papers: A proof of the Gordon Conjecture

In the theory of the moduli-stacks of n-pointed stable curves, there are two fundamental functors, contraction and stabilization. These functors are constructed in [4], where they are used to show that the various \bar{M_{g,n}}'s are…

The stable reduction theorem says that a family of curves of genus $g\geq 2$ over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new proof of this…

In this article, we prove that a tunnel number two knot induces a critical Heegaard splitting in its exterior if there are two weak reducing pairs such that each weak reducing pair contains the cocore disk of each tunnel. Moreover, we prove…

In [19] and [26], the authors proved the stability of multi-solitons for derivative nonlinear Schr{\"o}dinger equations. Roughly speaking, sum of finite stable solitons is stable. We predict that if there is one unstable solition then…

Let $G$ be a finite group acting vertex-transitively on a graph. We show that bounding the order of a vertex stabilizer is equivalent to bounding the second singular value of a particular bipartite graph. This yields an alternative…

We give another proof, using tools from Geometric Invariant Theory, of a result due to S. Sam and A. Snowden in 2014, concerning the stability of Kro-necker coefficients. This result states that some sequences of Kronecker coefficients…

In this note, we present a probabilistic proof of the well-known finite geometric series. The proof follows by taking the moments of the sum and the difference of two independent exponentially distributed random variables.

We give a complete proof of the generalized Khavinson conjecture which states that, for bounded harmonic functions on the unit ball of $\mathbb{R}^n$, the sharp constants in the estimates for their radial derivatives and for their gradients…

In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a…

We prove that a theory $T$ has stable forking if and only if $T^\mathrm{eq}$ has stable forking.

We give a parity condition of a Heegaard diagram to show that it is unstabilized. This improves the result of [5]. As an application, we construct unstabilized Heegaard splittings by Dehn twists on any given Heegaard splitting.

We show that positive $\alpha$-stable densities are hyperbolically completely monotone if and only if $\alpha \le 1/2$. This gives a positive answer to a question raised by L. Bondesson in 1977.

We consider the Goursat problem for linear partial differential equations with constant coefficients in two complex variables. We find the conditions for summable solutions of the Goursat problem in the case when the Newton polygon has…

We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3-manifold by an isotopy is bounded below by the smaller of twice its genus or half its Hempel distance. This is a…

We prove a conjecture of Stembridge concerning stability of Kronecker coefficients that vastly generalizes Murnaghan's theorem. The main idea is to identify the sequences of Kronecker coefficients in question with Hilbert functions of…

Stabilization of manifolds by a product of spheres or a projective space is important in geometry. There has been considerable recent work that studies the homotopy theory of stabilization for connected manifolds. This paper generalizes…

A famous example of Casson and Gordon shows that a Haken 3-manifold can have an infinite family of irreducible Heegaard splittings with different genera. In this paper, we prove that a closed non-Haken 3-manifold has only finitely many…

We give a direct combinatorial proof that the product of two descent classes in a symmetric group is a sum of descent classes. The proof is based on the fact that the group product gives a covering map when descent classes are endowed with…

We define a notion of Hempel distance for one-sided Heegaard splittings and show that the existence of alternate surfaces restricts distance for one-sided splittings in a manner similar to Hartshorn's and Scharlemann-Tomova's results for…

We define integral measures of complexity for Heegaard splittings based on the graph dual to the curve complex and on the pants complex defined by Hatcher and Thurston. As the Heegaard splitting is stabilized, the sequence of complexities…