10 papers
Lower bounds on the strength of the determinant
Qiyuan Chen, Yuhao Zhao
We establish new lower bounds for the strength and partition rank of the determinant. For every prime , we prove the exact identity \[ \operatorname{str}(\mathrm{det}_p)=p. \] A…
Spectral Intertwining Operators
Qiyuan Chen
We study spectral intertwining operators between spectral Eisenstein series , for two parabolic subgroups of a …
Geometry of multilinear varieties over infinite fields and its applications
Qiyuan Chen, Ke Ye
Multilinear varieties, defined as the sets of rational points of varieties cut out by multilinear functions, were first introduced and studied by Gowers and Milićević[Proc. Edinb.…
A base change framework for tensor functions
Qiyuan Chen
The main contribution of this note is to establish a framework to extend results of tensor functions over specific field to general field. As a consequence of this framework, we ex…
Turán problems for multilinear maps
Qiyuan Chen, Zixiang Xu, Ke Ye
We study Turán-type extremal problems for alternating and unrestricted multilinear maps. For alternating order- multilinear maps , we determi…
Isotropy and completeness indices of multilinear maps
Qiyuan Chen, Ke Ye
Structures of multilinear maps are characterized by invariants. In this paper we introduce two invariants, named the isotropy index and the completeness index. These invariants cap…
Random algebraic constructions for extremal and Ramsey problems
Qiyuan Chen, Hong Liu, Ke Ye +1
Building on Bukh's random algebraic method, we develop a framework for extremal and Ramsey problems involving apex hypergraphs. If is a -partite -unifor…
Bounds for Geometric rank in Terms of Subrank
Qiyuan Chen, Ke Ye
For tensors of fixed order, we establish three types of upper bounds for the geometric rank in terms of the subrank. Firstly, we prove that, under a mild condition on the character…
Stability of ranks under field extensions
Qiyuan Chen, Ke Ye
This paper studies the stability of tensor ranks under field extensions. Our main contributions are fourfold: (1) We prove that the analytic rank is stable under field extensions.…
A quasi-optimal lower bound for skew polynomial multiplication
Qiyuan Chen, Ke Ye
We establish a lower bound for the complexity of multiplying two skew polynomials. The lower bound coincides with the upper bound conjectured by Caruso and Borgne in 2017, up to a…