Xinan Dai

collaborators

9 papers

math.DS2026

The Borel complexity of conjugacy for Cantor minimal systems

Xinan Dai, Wenhao Deng, Yingdong Shi +2

We prove that conjugacy of minimal homeomorphisms of the Cantor space is Borel bireducible with isomorphism of countable graphs, answering the Cantor minimal case of a question of…

math.GR2026

Centralizer Excess as an Obstruction to Carlson's Depth Conjecture

Xinan Dai, Kuok Fai Chao

Let $G = SmallGroup (128, 859)$ and $k = k$ . The cohomology ring $H^{*} (G; k)$ has depth two, and we prove that the minimum quotient dimension of an associated pri…

math.FA2026

The Minimum Cardinality of a Dependent Finite Gabor System Is Four

Xinan Dai, Wenhao Deng, Yingdong Shi +2

Recent work produced a linearly dependent system of twelve time--frequency shifts of a Schwartz function, disproving the HRT conjecture. We show that four shifts already suffice, a…

math.FA2026

Bounded Representatives in Critical Sobolev-Hodge Spaces

Xinan Dai, Wenhao Deng, Yidong Shi +2

Let $n \geq 2$ , $1 \leq ℓ \leq n - 1$ , and $1 < p < \infty$ . We prove that every $v \in W ˙^{n / p, p} (R^{n}; Λ^{ℓ})$ has a representative $u \in W ˙^{n / p, p} \cap L^{\infty}$ with $…

math.GR2026

A Finite E-Group of Nilpotency Class Three

Xinan Dai, Wenhao Deng, Yidong Shi +2

A group is an E-group if every element commutes with each of its endomorphic images. Caranti asked whether a finite E-group can have nilpotency class three. We prove that the $3$ -g…

math.KT2026

L-packet multiplicity and integral structure in the K-theory of real inner forms

Xinan Dai, Kuok Fai Chao

Let $G$ be a connected linear real semisimple group with finite centre and discrete series, and let $G_{c}$ be a fixed compact inner form. We isolate an integral structure behind the…