Incidence systems on Cartesian powers of algebraic curves

有理变换下的不变有理函数

Invariant rational functions under rational transformations

本文引入稳定代数维数量化有理自映射与平凡动力系统的交互，证明其等于代数群作用型等变有理像的最大维数，并推出不变有理函数在第二笛卡尔幂即出现。

Independence in generic incidence structures

We study the theory $T_{m,n}$ of existentially closed incidence structures omitting the complete incidence structure $K_{m,n}$, which can also be viewed as existentially closed $K_{m,n}$-free bipartite graphs. In the case $m = n = 2$, this is the theory of existentially closed projective planes. We give an $\forall\exists$-axiomatization of $T_{m,n}$, show that $T_{m,n}$ does not have a countable saturated model when $m,n\geq 2$, and show that the existence of a prime model for $T_{2,2}$ is equivalent to a longstanding open question about finite projective planes. Finally, we analyze model the…

论多范畴元定理与受限代数演绎系统的完备性

On the Multicategorical Meta-Theorem and the Completeness of Restricted Algebraic Deduction Systems

该研究在代数理论框架下建立8个范畴可靠性与完备性定理，构造上下文结构与结构范畴的双射对应及相关等式演绎系统，证明其在对应多范畴模型下的语义性质可转移。

A cubical model of homotopy type theory

We construct an algebraic weak factorization system $(L, R)$ on the cartesian cubical sets, in which the canonical path object factorization $A \to A^I \to A\times A$ induced by the 1-cube $I$ is an $L$-$R$ factorization for any $R$-object $A$.