Xin Tong

activity

20232025

collaborators

9 papers

quant-ph2025

Interplay between Standard Quantum Detailed Balance and Thermodynamically Consistent Entropy Production

Xin-Hai Tong, Kohei Yoshimura, Tan Van Vu +1

We demonstrate that, for a quantum Markovian semigroup on a finite-dimensional Hilbert space, if it satisfies the standard quantum detailed balance condition, its generator admits…

math.AG2024

$(\infty, \infty)$ -Categorical Universal Motives

Xin Tong

Ever since the introduction of motivic homotopy theory, as a well-proposed approximation of Grothendieck's dream, algebraic geometers then have the chance to study schemes via a ho…

math.AG2024

Generalized Motives through Witt Vectors

Xin Tong

We generalize condensed motives, through Witt vectors and the associated moduli stacks of generalized line bundles.

math.NT2024

$\infty$ -Categorical Generalized Langlands Correspondence III: $\infty$ -Stackification

Xin Tong

We discuss further around the generalized Langlands Program, by using $\infty$ -categoricalization and $\infty$ -analytic stackification.

math.AG2024

Topologization and Functional Analytification III

Xin Tong

In this paper, we continue our study on the topologization and functional analytification in $\infty$ -categorical and homotopical analytic geometry. As in our previous articles on…

math.RT2024

$\infty$ -Categorical Generalized Langlands Correspondence II: Langlands Program Formalism

Xin Tong

We extend the Langlands program in various subprograms with certain different generalizations: (1) Mixed-parity functorial perturbation of the usual Langlands program after Fargues…

math.AG2024

Arithmetic Hodge-Iwasawa Moduli Stacks

Xin Tong

In this article, we are going to construct arithmetic moduli stacks of $G$ -bundles after our previous construction on Hodge-Iwasawa theory. These stacks parametrize certain Hodge-I…

math.AG2023

$\infty$ -Categorical Approaches to Hodge-Iwasawa Theory II: $\infty$ -Categorical and Derived Hodge-Iwasawa Modules

Xin Tong

This paper is a discussion on $\infty$ -categorical approaches to Hodge-Iwasawa Theory, which was initiated in our project on the $\infty$ -categorical approaches to Hodge-Iwasawa Th…

math.NT2023

$\infty$ -Categorical Generalized Langlands Program I: Mixed-Parity Modules and Sheaves

Xin Tong

Mixed-parity module emerges for instance when a de Rham Galois representation is being tensored with a square root of cyclotomic character, which produces half odd integers as the…

Interplay between Standard Quantum Detailed Balance and Thermodynamically Consistent Entropy Production

(∞,∞)-Categorical Universal Motives

Generalized Motives through Witt Vectors

∞-Categorical Generalized Langlands Correspondence III: ∞-Stackification

Topologization and Functional Analytification III

∞-Categorical Generalized Langlands Correspondence II: Langlands Program Formalism

Arithmetic Hodge-Iwasawa Moduli Stacks

∞-Categorical Approaches to Hodge-Iwasawa Theory II: ∞-Categorical and Derived Hodge-Iwasawa Modules

∞-Categorical Generalized Langlands Program I: Mixed-Parity Modules and Sheaves

$(\infty, \infty)$ -Categorical Universal Motives

$\infty$ -Categorical Generalized Langlands Correspondence III: $\infty$ -Stackification

$\infty$ -Categorical Generalized Langlands Correspondence II: Langlands Program Formalism

$\infty$ -Categorical Approaches to Hodge-Iwasawa Theory II: $\infty$ -Categorical and Derived Hodge-Iwasawa Modules

$\infty$ -Categorical Generalized Langlands Program I: Mixed-Parity Modules and Sheaves