Su Gao

Nankai University

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Steve Jackson

University of North Texas

Zoé Chatzidakis

Université Paris Cité

Ulrich Kohlenbach

Technical University of Darmstadt

Marat Arslanov

Kazan Federal University

Stefan Geschke

Universität Hamburg

Mirna Džamonja

Centre National de la Recherche Scientifique

Johann A. Makowsky

Technion – Israel Institute of Technology

Jean A. Larson

University of Florida

Los Aschenbrenner

Amsterdam University of Applied Sciences

Benedikt Löwe

Universität Hamburg

Cooperative Institutions

University of Amsterdam

Universitat Ramon Llull

Amsterdam University of Applied Sciences

Délégation Paris 6

University of Illinois Urbana-Champaign

University of North Texas

Yangzhou University

Berkeley College

Centre National de la Recherche Scientifique

Vassar College

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Open questions in descriptive set theory and dynamical systems

arXiv (Cornell University) (2023)

Jérôme Buzzi Nishant Chandgotia Matthew Foreman Su Gao Felipe García‐Ramos

This file is composed of questions that emerged or were of interest during the workshop "Interactions between Descriptive Set Theory and Smooth Dynamics" that took place in Banff, Canada on 2022.

Descriptive research

Dynamics

10.48550/arxiv.2305.00248

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Citations (0)

Countable abelian group actions and hyperfinite equivalence relations

Inventiones mathematicae (2015)

Su Gao Steve Jackson

Borel equivalence relation

Equivalence relation

Borel hierarchy

Borel set

Polish space

Quotient space (topology)

Borel subgroup

Second-countable space

10.1007/s00222-015-0603-y

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Citations (41)

The homeomorphism problem for countable topological spaces

Topology and its Applications (2003)

Su Gao

Homeomorphism (graph theory)

10.1016/j.topol.2003.09.005

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Citations (1)

Graev ultrametrics and surjectively universal non-Archimedean Polish groups

Topology and its Applications (2013)

Su Gao

10.1016/j.topol.2013.02.009

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Citations (10)

On the complexity of the uniform homeomorphism relation between separable Banach spaces

Transactions of the American Mathematical Society (2011)

Su Gao Steve Jackson Bünyamin Sarı

We investigate the uniform homeomorphism relation between separable Banach spaces and the related relation of local equivalence. We completely characterize the descriptive complexity of local equivalence in the Borel reducibility hierarchy. This also provides a lower bound for the complexity of the uniform homeomorphism.

Homeomorphism (graph theory)

Equivalence relation

Borel equivalence relation

10.1090/s0002-9947-2011-05075-0

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Citations (5)

The Complexity of the Classification Problems of Finite-Dimensional Continua

arXiv (Cornell University) (2019)

Cheng Chang Su Gao

We consider the homeomorphic classification of finite-dimensional continua as well as several related equivalence relations. We show that, when $n \geq 2$, the classification problem of $n$-dimensional continua is strictly more complex than the isomorphism problem of countable graphs. We also obtain results that compare the relative complexity of various equivalence relations.

Equivalence relation

Isomorphism (crystallography)

Graph isomorphism

10.48550/arxiv.1904.09634

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Citations (0)

Subshifts of finite symbolic rank

Ergodic Theory and Dynamical Systems (2024)

Su Gao RUIWEN LI

Abstract The definition of subshifts of finite symbolic rank is motivated by the finite rank measure-preserving transformations which have been extensively studied in ergodic theory. In this paper, we study subshifts of finite symbolic rank as essentially minimal Cantor systems. We show that minimal subshifts of finite symbolic rank have finite topological rank, and conversely, every minimal Cantor system of finite topological rank is either an odometer or conjugate to a minimal subshift of finite symbolic rank. We characterize the class of all minimal Cantor systems conjugate to a rank- $1$ subshift and show that it is dense but not generic in the Polish space of all minimal Cantor systems. Within some different Polish coding spaces of subshifts, we also show that the rank-1 subshifts are dense but not generic. Finally, we study topological factors of minimal subshifts of finite symbolic rank. We show that every infinite odometer and every irrational rotation is the maximal equicontinuous factor of a minimal subshift of symbolic rank $2$ , and that a subshift factor of a minimal subshift of finite symbolic rank has finite symbolic rank.

Symbolic dynamics

Rank (graph theory)

10.1017/etds.2024.45

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Steinhaus sets and Jackson sets

Contemporary mathematics - American Mathematical Society (2007)

Su Gao Arnold W. Miller William Weiss

We prove that there does not exist a subset of the plane S that meets every isometric copy of the vertices of the unit square in exactly one point.We give a complete characterization of all three point subsets F of the reals such that there does not exists a set of reals S which meets every isometric copy of F in exactly one point.

10.1090/conm/425/08122

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Citations (2)

Mn-enhanced performance of the Ni-CaO/γ-Al2O3 dual function material for CO2 capture and in situ methanation

Separation and Purification Technology (2024)

Shu-Xiang Xiang Jinpeng Wang Su Gao Zhan-Kuo Guo Huilin Jiang

Methanation

Dual function

10.1016/j.seppur.2024.130152

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Citations (0)

The action of $SL(2,\mathbb {Z})$ on the subsets of $\mathbb {Z}^2$

Proceedings of the American Mathematical Society (2000)

Su Gao

We prove that the orbit equivalence relation of the canonical action of $SL(2,\mathbb {Z})$ on the subsets of $\mathbb {Z}^2$ is a universal countable Borel equivalence relation.

Equivalence relation

Borel equivalence relation

Orbit (dynamics)

Congruence relation

10.1090/s0002-9939-00-05721-x

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Citations (5)