Counterexamples to Okounkov's Log-Concavity Conjecture

Logarithmic concavity of Schur and related polynomials

We show that normalized Schur polynomials are strongly log-concave. As a consequence, we obtain Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients in the special case of Kostka numbers.

A_n 型簇代数的对数凹性

Log-concavity of cluster algebras of type $A_n$

本文研究 A_n 型簇代数的对数凹性，证明其簇变量指数系数及 A_2 型 theta 基结构常数均对数凹，并提出一般簇代数 theta 基结构常数对数凹的猜想。

关于减少的克罗内克系数的猜想

Conjectures on the reduced Kronecker coefficients

本文提出关于对称群表示稳定张量积的猜想，扩展了Okounkov和Lam等人的相关结论，并在特定情况下验证了这些猜想。

The log-concavity conjecture for the Duistermaat-Heckman measure revisited

Karshon constructed the first counterexample to the log-concavity conjecture for the Duistermaat-Heckman measure: a Hamiltonian six manifold whose fixed points set is the disjoint union of two copies of $T^4$. In this article, for any closed symplectic four manifold $N$ with $b+$ greater than 1, we show that there is a Hamiltonian six manifold $M$ such that its fixed points set is the disjoint union of two copies of $N$ and such that its Duistermaat-Heckman function is not log-concave. On the other hand, we prove that if there is a torus action of complexity two such that all the symplectic re…