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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Positivity and model complete fields
正性 模型完备域 有理数域
2023/11/13
In recent work with Will Johnson, we have shown that given a curve C over the rational number field Q with genus at least 2 and C(Q) is empty, the class of fields K of characteristic 0 such that C(K) ...
Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus
homogeneous spaces generalized Schubert calculus
2015/7/14
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We
give various ext...
Proof of a Positivity Conjecture on Schur Functions
symmetric function Schur function multiplier sequence totally positive sequence
2014/6/3
In the study of Zeilberger's conjecture on an integer sequence related to the Catalan numbers, Lassalle proposed the following conjecture. Let (t)n denote the rising factorial, and let ΛR denote the a...
On the (strict) positivity of solutions of the stochastic heat equation
the stochastic heat equation Probability
2012/6/30
We give a new proof of the fact that the solutions of the stochastic heat equation, started with non-negative initial conditions, are strictly positive at positive times. The proof uses concentration ...
Positivity of integrated random walks
Integrated random walk persistence one-sided exit probability unilateral small deviations area of random walk
2011/9/20
Abstract: Take a centered random walk S_n and consider the sequence of its partial sums A_n = S_1 + ... + S_n. Suppose S_1 is in the domain of normal attraction of an alpha-stable law with 1 < \alpha ...
Maximal supports and Schur-positivity among connected skew shapes
Symmetric function Schur-positive support skew shape ribbon
2011/9/19
Abstract: The Schur-positivity order on skew shapes is defined by B \leq A if the difference s_A - s_B is Schur-positive. It is an open problem to determine those connected skew shapes that are maxima...
On dual equivalence and Schur positivity
Schur positivity dual equivalence graphs quasi-symmetric functions
2011/8/22
Abstract: We define dual equivalence for any collection of combinatorial objects endowed with a descent set, and we show that giving a dual equivalence establishes the symmetry and Schur positivity of...
KP solitons and total positivity for the Grassmannian
KP solitons total positivity Grassmannian
2011/7/6
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional dispersive wave equation now known as the KP equation. It is well-known th...
KP solitons and total positivity for the Grassmannian
KP solitons total positivity Grassmannian
2011/7/6
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional dispersive wave equation now known as the KP equation. It is well-known th...
Positivity on subvarieties and vanishing of higher cohomology
Positivity on subvarieties vanishing of higher cohomology
2011/1/18
Inspired by the recent paper [14] of Totaro, we investigate the relationship between ampleness
of restrictions of line bundles to general complete intersections and the vanishing properties of higher...
Characterizations of Projective Spaces and Hyperquadrics via Positivity Properties of the Tangent Bundle
Characterizations of Projective Spaces Hyperquadrics Positivity Properties Tangent Bundle
2011/1/20
Let X be a smooth complex projective variety. A re-cent conjecture of S. Kov´acs states that if the pth-exterior power of the tangent bundle TX contains the pth-exterior power of an am-
ple vec...
Pointwise estimates for the ground states of some classes of positivity preserving operators
Hardy’s inequality ground state ultracontractivity Dirichlet form energy measure
2010/11/29
We establish pointwise estimates for the ground states of some classes of posi-tivity preserving operators. The considered operators are negatively perturbed (by measures) strongly local Dirichlet ope...
Discrete integrable systems, positivity, and continued fraction rearrangements
cluster algebras Laurent phenomenon positivity integrable systems
2010/12/3
In this review article, we present a unified approach to solving discrete,integrable, possibly non-commutative, dynamical systems, including the Qand T-systems based on Ar.
Positivity and vanishing theorems of ample vector bundles
Positivity vanishing theorems ample vector bundles
2018/4/19
In this paper, we study the Nakano-positivity and dual-Nakano-positivity of certain adjoint vector bundles associated to ample vector bundles. As applications, we get new vanishing theorems about ampl...
Schur Positivity and the q-Log-convexity of the Narayana Polynomials
q-log-concavity q-log-convexity q-Narayana number Narayana polynomial lattice permutation Schur positivity Littlewood-Richardson rule
2014/6/3
Using Schur positivity and the principal specialization of Schur functions, we provide a proof of a recent conjecture of Liu and Wang on the q-log-convexity of the Narayana polynomials, and a proof of...