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Let T (S) be the Teichm¨uller space of a hyperbolic Riemann surface S and let Belt(S) be the Banach space of bounded measurable Beltrami differentials μ = μdz/dz on S with L∞-norms. Suppose M(...
This paper concerns Waring decompositions of a certain kind of plane quartics of high rank. The main result is the following. Let x, l_1, ...., l_7 be linear forms and q a quadratic form on a K-vector...
In this note, we explain that Ross-Thomas’ result [4, Theorem 1.7] on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result. This result plays an important role in...
In this note, we answer a question of Mirzakhani on asymptotic behavior of the one-point volume polynomial of moduli spaces of curves. We also present some applications of Mirzakhani’s asymptotic form...
Abstract: In this note, we explain that Ross-Thomas' result on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result. This result plays an important role in the co...
Abstract: The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter I_1(K,Z_q^o(K))=\int_K ||< :, x> ||_{L_q(K)}dx. We show that an upper bound of the...
We observe that Clay-Rolfsen’s obstruction of bi-orderability, which uses the classical Alexander polynomial, is not strengthened by using the twisted Alexander polynomials for finite representations ...
In this brief note we consider some bases in the Hecke algebra and exhibit certain dualities between them. Our results and arguments are completely combinatorial.However, to explain the motivation and...
In this note, we shall consider the following problem F(x, u,∇u,∇2u)−ZRN [u(x+z)−u(x)−1|z|<1h∇u(x).
We show that any open set in Rn is a union of an ascending sequence of bounded open sets with analytic boundary.This is just a technical result, which is probably known. We be-lieve, however, that it ...
Recently Simmons and Cardy predicted a formula for the prob-ability that the chordal SLE8/3 path passes to the left of two points in the upper half-plane. The purpose of this note is to bring it to at...
We show that the use of Brylinski's Radon transform elucidates some points of the Green-Griffiths approach to the Hodge conjecture.
Let X denote a smooth, projective, connected algebraic variety over C, of dimension n.
We give the solution of certain parabolic evolution problems (time-depending perturbations of the heat equation for the harmonic oscillator ) as explicit integrals on a space of continuous functions, ...
We study the asymptotic behavior of the emptiness formation probability for large spin strings in a translation invariant quasifree nonequilibrium steady state of the isotropic XY chain. Besides the...

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